RESEARCH CENTRE

Inria Centre
at the University of Lille

2023
ACTIVITY REPORT

IN PARTNERSHIP WITH:

Ecole Centrale de Lille, Université Libre de
Bruxelles

Project-Team

INOCS

INtegrated Optimization with Complex
Structure

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Optimization, machine learning and
statistical methods

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Contents

Project-Team INOCS

1 Team members, visitors, external collaborators

2 Overall objectives

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Schedule of tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Research program

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Modeling problems with complex structures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Solving problems with complex structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Transportation and logistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Social and environmental responsibility

6 Highlights of the year

6.1 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 New software, platforms, open data

7.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 GroupTesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 INOCSBox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 New results

8.1 Large scale complex structure optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Loads scheduling for demand response in energy communities . . . . . . . . . . . .
8.1.2 How to achieve fair and efficient cooperative vehicle routing? . . . . . . . . . . . . . .
8.1.3 Improving neighborhood exploration into MOEA/D framework to solve a bi-objective
routing problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.4 Models and methods for two-level uncapacitated facility location problems . . . . .
8.1.5 Synchronized deliveries with a bike and a self-driving robot . . . . . . . . . . . . . . .
8.1.6 A column generation approach to solve the joint order batching and picker routing
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problem including picker congestion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
8.1.7 The intractability of the picker routing problem . . . . . . . . . . . . . . . . . . . . . .
8.1.8 Commodity constrained split delivery vehicle routing problems . . . . . . . . . . . .
9
8.1.9 Lower and upper bounds for the joint batching, routing and sequencing problem . 10
8.1.10 Machine learning applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.2 Bilevel programming and game theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.2.1 Moving from linear to conic markets for electricity . . . . . . . . . . . . . . . . . . . . 11
8.2.2 Grid impact aware TSO-DSO market models for flexibility procurement: coordina-

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tion, pricing efficiency, and information sharing . . . . . . . . . . . . . . . . . . . . . 11
8.2.3 Strategic resource pricing and allocation in a 5G network slicing Stackelberg game . 12
8.2.4 Modeling and analysis of a nonlinear security game . . . . . . . . . . . . . . . . . . . 12
8.2.5 Bilevel integer linear models for ranking . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.2.6 Min–max optimization of node-targeted attacks in service networks . . . . . . . . . . 12
8.2.7 Bilevel pricing model for cloud computing . . . . . . . . . . . . . . . . . . . . . . . . . 13
8.2.8 Bilevel pricing model for electric car charging problems . . . . . . . . . . . . . . . . . 13
8.2.9 Integrating new shared mobility systems within public transportation . . . . . . . . 13
8.3 Robust/Stochastic programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8.3.1 Mutli-agent reinforcement learning for strategic bidding in two stage electricity

markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8.3.2 Learning market equilibria using performative prediction: balancing efficiency and

privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.3.3 Towards forecast markets for enhanced peer-to-peer electricity trading . . . . . . . . 14
8.3.4 Exact and heuristic solution Ttchniques for mixed-integer quantile minimization

problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.3.5 The case for stochastic online segment routing under demand uncertainty . . . . . . 15

9 Bilateral contracts and grants with industry

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9.1 Bilateral grants with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

10 Partnerships and cooperations

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10.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework

10.2 International research visitors

of an Inria International Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
10.1.2 STIC/MATH/CLIMAT AmSud projects
. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
10.1.3 Participation in other International Programs . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
10.2.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.2.2 Visits to international teams
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.3.1 Horizon Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.3.2 H2020 projects
10.4 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.4.1 ANR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.5 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

10.3 European initiatives

11 Dissemination

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11.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1.2 Scientific events: selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1.3 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1.4 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.1.5 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 21
11.1.6 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.1.7 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
11.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

12 Scientific production

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12.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
12.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
12.3 Cited publications

Project INOCS

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Project-Team INOCS

Creation of the Project-Team: 2019 May 01

Keywords

Computer sciences and digital sciences

A6. – Modeling, simulation and control

A6.1. – Methods in mathematical modeling

A6.2. – Scientific computing, Numerical Analysis & Optimization

A6.2.6. – Optimization

A9. – Artificial intelligence

A9.6. – Decision support

Other research topics and application domains

B2. – Health

B4. – Energy

B6. – IT and telecom

B6.7. – Computer Industry (harware, equipments...)

B7. – Transport and logistics

B7.1. – Traffic management

B7.1.2. – Road traffic

B7.2. – Smart travel

B8.1. – Smart building/home

B8.1.1. – Energy for smart buildings

B8.2. – Connected city

B8.4. – Security and personal assistance

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Luce Brotcorne [Team leader, INRIA, Senior Researcher, HDR]

• Hélène Le Cadre [INRIA, Researcher]

Faculty Members

• Diego Cattaruzza [Centrale Lille, Associate Professor]

• Bernard Fortz [Université Libre de Bruxelles, Professor, on leave at HEC Liège since Sep 2023]

• Martine Labbé [Université Libre de Bruxelles, Professor]

• Maxime Ogier [Centrale Lille, Associate Professor]

• Frédéric Semet [Centrale Lille, Professor, HDR]

PhD Students

• Cristian Aguayo [Université Libre de Bruxelles]

• Haider Ali [Centrale Lille]

• Tifaout Almeftah [INRIA]

• Hugo Callebaut [Université Libre de Bruxelles]

• Aitor Lopez Sanchez [INRIA and University of Madrid, from Oct 2023]

• Francesco Morri [Université de Lille]

• Matteo Petris [INRIA, from Apr 2023 until Jul 2023]

• Matteo Petris [Université de Lille, until Mar 2023]

• Simon Renard [Université Libre de Bruxelles, from Oct 2023]

• Luis Antonio Rojo Gonzalez [INRIA, from Jul 2023]

• Juan Pablo Sepulveda Adriazola [INRIA, from December 2021]

• Wenjiao Sun [Centrale Lille, from September 2021]

• Pablo Torrealba Gonzalez [Centrale Lille, from February 2021]

• Nathalia Isabel Wolf Garcia [INRIA, from Apr 2023]

Technical Staff

• Sylvain Clay [INRIA, until March 2023, Engineer]

• Youness El Houssaini [INRIA, Engineer, until Jul 2023]

• Gael Guillot [INRIA, from January 2023, Engineer]

• Nathalia Isabel Wolf Garcia [INRIA, Engineer, until Mar 2023]

Interns and Apprentices

• Ahmed Jed Boufaied [INRIA, Intern, from Oct 2023]

• Mariam Sangare [LIRMM, until Feb 2023]

Project INOCS

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Administrative Assistants

• Nathalie Bonte [INRIA]

• Karine Lewandowski [INRIA]

Visiting Scientists

• Pamela Bustamante Faundez [PUC, until Jan 2023]

• Sophia Calderon Pimienta [Universidad de O’Higgins, from Feb 2023 until Apr 2023]

• Clara Chini Nielsen [Danish Technology University, from Mar 2023 until May 2023]

• Alejandro Jofre [CMM, until Feb 2023]

• Walter Rei [Quebec University at Montréal, from Aug 2023 until Sep 2023]

External Collaborator

• Pierre Gruet [EDF, from September 2023]

2 Overall objectives

2.1 Introduction

INOCS is a cross-border “France-Belgium” project team in the Applied Mathematics Computation and
Simulation Inria domain. The main goal of this team is the study of optimization problems involving
complex structures. The scientific objectives of INOCS are related to modeling and methodological
concerns. The INOCS team focuses on:

(i) integrated models for problems with Complex Structure (CS) taking into account the whole struc-

ture of the problem;

(ii) the development of solution methods taking explicitly into account the nature and the structure of

the decisions as well as the properties of the problem.

Even if CS problems are in general NP-hard due to their complex nature, exact solution methods or
matheuristics (heuristics based on exact optimization methods) are developed by INOCS. The scientific
contribution of INOCS will result in a toolbox of models and methods to solve challenging real-life
problems.

2.2 Schedule of tasks

The research program development of INOCS is to move alternatively:

• from problems towards new approaches in optimization: models and solution algorithms will be
developed to fit the structure and properties of the problem. From them, new generic approaches
will be used to optimize problems with similar properties.

• from innovative approaches towards problems: The relevance of the proposed approaches will
be assessed by designing new models and/or solution methods for various classes of problems.
These models and methods will be based on the extension and integration of specific, well-studied
models and methods.

Even if these two axes are developed sequentially in a first phase, their interactions will lead us to

explore them jointly in the mid-term.

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Inria Annual Report 2023

3 Research program

3.1 Introduction

An optimization problem consists in finding a best solution from a set of feasible solutions. Such a
problem can be typically modeled as a mathematical program in which decision variables must (i) satisfy
a set of constraints that translate the feasibility of the solution and (ii) optimize some (or several) objective
function(s). Optimization problems are usually classified into strategic, tactical and operational problems,
according to the types of decisions to be taken.

We consider that an optimization problem presents a complex structure (CS) when it involves decisions
of different types/nature (i.e. strategic, tactical or operational) and/or presents some hierarchical leader-
follower structure. The set of constraints may usually be partitioned into global constraints, linking
variables associated with the different types/nature of decision, and constraints involving each type
of variables separately. Optimization problems with complex structure lead to extremely challenging
problems since a global optimum with respect to the whole sets of decision variables and of constraints
must be determined.

Significant progress has been made in optimization to solve academic problems. Nowadays large-
scale instances of some N P -hard problems are routinely solved to optimality. Our vision within INOCS
is to make the same advances while addressing CS optimization problems. To achieve this goal we aim
to develop global solution approaches at the opposite of the current trend. INOCS team members
have already proposed some successful methods following this research lines to model and solve CS
problems (e.g. ANR project RESPET, Brotcorne et al. [61, 62], Gendron et al. [63, 64, 65], and Strack
et al. [66]). However, these are preliminary attempts and a number of challenges regarding modeling and
methodological issues have still to be met.

3.2 Modeling problems with complex structures

A classical optimization problem can be formulated as follows:

min f (x)
s. t .

x ∈ X .

(1)

In this problem, X is the set of feasible solutions. Typically, in mathematical programming, X is

defined by a set of constraints. x may be also limited to non-negative integer values.

The INOCS team plans to address optimization problem where two types of decision are addressed
jointly and are interrelated. More precisely, let us assume that variables x and y are associated with these
decisions. A generic model for CS problems is the following:

min g (x, y)
x ∈ X ,
s. t .
(x, y) ∈ X Y ,
y ∈ Y (x).

(2)

In this model, X is the set of feasible values for x. X Y is the set of feasible values for x and y jointly.
This set is typically modeled through linking constraints. Last, Y (x) is the set of feasible values for y for a
given x. In INOCS, we do not assume that Y (x) has any properties.

The INOCS team plans to model optimization CS problems according to three types of optimization
paradigms: large scale complex structures optimization, bilevel optimization and robust/stochastic
optimization. These paradigms instantiate specific variants of the generic model.

Large scale complex structures optimization problems can be formulated through the simplest variant
of the generic model given above. In this case, it is assumed that Y (x) does not depend on x. In such
models, X and Y are associated with constraints on x and on y, X Y are the linking constraints. x and y
can take continuous or integer values. Note that all the problem data are deterministically known.

Bilevel programs allow the modeling of situations in which a decision-maker, hereafter the leader,
optimizes his objective by taking explicitly into account the response of another decision maker or set
of decision makers (the follower) to their decisions. Bilevel programs are closely related to Stackelberg
(leader-follower) games as well as to the principal-agent paradigm in economics. In other words, bilevel

Project INOCS

5

programs can be considered as demand-offer equilibrium models where the demand is the result of
another mathematical problem. Bilevel problems can be formulated through the generic CS model
when Y (x) corresponds to the optimal solutions of a mathematical program defined for a given x, i.e.
Y (x) = arg min (cid:169)h(x, y)|y ∈ Y2, (x, y) ∈ X Y2
(cid:170) where Y2 is defined by a set of constraints on y, and X Y2 is
associated with the linking constraints.

In robust/stochastic optimization, it is assumed that the data related to a problem are subject to
uncertainty. In stochastic optimization, probability distributions governing the data are known, and the
objective function involves mathematical expectation(s). In robust optimization, uncertain data take
value within specified sets, and the function to optimize is formulated in terms of a min-max objective
typically (the solution must be optimal for the worst-case scenario). A standard modeling of uncertainty
on data is obtained by defining a set of possible scenarios that can be described explicitly or implicitly. In
stochastic optimization, in addition, a probability of occurrence is associated with each scenario and the
expected objective value is optimized.

3.3 Solving problems with complex structures

Standard solution methods developed for CS problems solve independent subproblems associated with
each type of variables without explicitly integrating their interactions or integrating them iteratively in
a heuristic way. However these subproblems are intrinsically linked and should be addressed jointly.
In mathematical optimization a classical approach is to approximate the convex hull of the integer
solutions of the model by its linear relaxation. The main solution methods are (1) polyhedral solution
methods which strengthen this linear relaxation by adding valid inequalities, (2) decomposition solution
methods (Dantzig Wolfe, Lagrangian Relaxation, Benders decomposition) which aim to obtain a better
approximation and solve it by generating extreme points/rays. Main challenges are (1) the analysis of
the strength of the cuts and their separations for polyhedral solution methods, (2) the decomposition
schemes and (3) the extreme points/rays generations for the decomposition solution methods.

The main difficulty in solving bilevel problems is due to their nonconvexity and nondifferentiability.
Even linear bilevel programs, where all functions involved are affine, are computationally challenging
despite their apparent simplicity. Up to now, much research has been devoted to bilevel problems
with linear or convex follower problems. In this case, the problem can be reformulated as a single-
level program involving complementarity constraints, exemplifying the dual nature, continuous and
combinatorial, of bilevel programs.

4 Application domains

4.1 Energy

In energy, the team mainly focuses on pricing models for demand side management, on bids definition
in the energy market and on the design and pricing of electric car charging stations.

Demand side management methods are traditionally used to control electricity demand which
became quite irregular recently and resulted in inefficiency in supply. We have explored the relationship
between energy suppliers and customers who are connected to a smart grid. The smart grid technology
allows customers to keep track of hourly prices and shift their demand accordingly, and allows the
provider to observe the actual demand response to its pricing strategy. We tackle pricing problems
in energy according to the bilevel optimization approaches. Some research works in this domain are
supported by bilateral grants with EDF.

The increasing number of agents, with different characteristics interacting on the energy market leads
to the definition of new types of bidding process. We have modeled this problem as a bilevel one where
the lower level is the instance allocating the bids (the ISO).

The proliferation of electric cars in cities has lead to the challenging problem of designing and pricing
charging stations in order to smooth the demand over time. We are modeling this problem as a bilevel
one where the lower level represents the choice of users in a preference list.

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Inria Annual Report 2023

4.2 Transportation and logistics

In transportation and logistics, the team addresses mainly integrated problems, which require taking
into account simultaneously different types of decision. Examples are location and routing, inventory
management and routing or staff scheduling and warehouse operations management. Such problems
occur from the supply chain design level to the logistic facility level.

4.3 Telecommunications

In telecommunications, the team mainly focuses on network design problems and on routing problems.
Such problems are optimization problems with complex structure, since the optimization of capacity
installation and traffic flow routing have to be addressed simultaneously.

5 Social and environmental responsibility

The research works developed in the INOCS team have environmental and societal impacts through the
application areas they target. At the environmental level, the works on the optimization of transportation
systems aim at reducing the impact of transportation on society. The applied works in energy aim at a
better use of the smart grid and the optimization of electricity production from renewable sources. At
the societal level, the works developed in the framework of the ANR AGIRE project takes into account
musculoskeletal disorders in the activity of employees within a warehouse. Finally, in health, the works
conducted on group testing allow the development of effective campaigns of testing of the population in
preventive medicine for example.

6 Highlights of the year

6.1 Awards

• Hugo Callebaut: ORBEL Award 2023 (Best master thesis in operations research in Belgium).

7 New software, platforms, open data

7.1 New software

7.1.1 GroupTesting

Keywords: Linear optimization, Group Testing, Graph algorithmics

Functional Description: Group testing is a screening strategy that involves dividing a population into
several disjoint groups of subjects. In its simplest implementation, each group is tested with a
single test in the first phase, while in the second phase only subjects in positive groups, if any, need
to be tested again individually.

To contribute to the effort to tackle the COVID-19 sanitary crisis, we developed this software which
allows to create groups of individuals to test via the group testing technique while minimizing a
linear combination of the expected number of false negative and false positive classifications.

The test design problem is modeled as a constrained shortest path problem on a specific graph and
we design and implement an ad hoc algorithm to solve this problem. We validate the algorithm on
instances based on Santé Publique France data on COVID-19 screening tests.

Contact: Frederic Semet

Project INOCS

7.1.2 INOCSBox

7

Keywords: Linear optimization, Operational research, Toolbox

Functional Description: This software is a toolbox that contains algorithms that are frequently used to

solve optimization problems tackled by (but not only) the team.

The objective of the toolbox is to contain a set of code skeletons that allow researchers to integrate
adequate data structures and basic algorithms for different structures complexity that appears
in the optimization problems we study. The current version of the toolbox contains classical
heuristic tools (generic local search) to solve, among others, the vehicle rouring problem and its
variants. It also contain a code to exactly and heuristically solve the Shortest Path Problem with
Ressource Constraints that is usually encountered in the resolution of problem with Branch-and-
Price algorithms.

The future objective is to include automatic reformulation tools for bi-level optimization problems
and state-of-the-art codes for the development of decomposition methods.

Contact: Tifaout Almeftah

8 New results

During the year 2023, we addressed different problems/challenges related to the three lines of research:
large scale complex structure optimization, bilevel programming and game theory, robust/stochastic
programming. The main contributions are summarized in the next sections. In addition, besides these
contributions, additional results [12, 15, 17, 18, 26] were obtained which are not discussed hereafter in
order to keep the presentation focused on the main achievements.

8.1 Large scale complex structure optimization

Participants:

Luce Brotcorne, Diego Cattaruzza, Bernard Fortz, Martine Labbé,
Maxime Ogier, Frédéric Semet.

8.1.1 Loads scheduling for demand response in energy communities

Energy communities are promising measures aimed at promoting local energy generation and consump-
tion, which are needed to meet the energy transition targets. In [28], the focus is on the optimization of the
collective self-consumption rate in energy communities by scheduling members’ loads. The community
remains connected to the public grid and comprises prosumers, traditional consumers, and distributed
storage units. Prosumers can exchange their energy with the public grid or other members. The pro-
posed strategy aims at implementing a Demand Side Management (DSM) program taking advantage
of controllable loads’ characteristics. A mixed integer linear programming (MILP) formulation of the
problem allows, on the one hand, to give the optimal planning for electrical devices’ operations. On the
other hand, it provides optimal solutions for managing the storage units, peer-to-peer exchanges, and
interactions with the public grid to minimize the energy flows from the public grid over time. However,
this MILP only allows for solving small problem instances. Thus, we develop a column generation-based
heuristic for large problem instances. Our numerical experiments based on real data collected in the
south of France show that joining an energy community saves money on energy bills and reduces the
total energy drawn from the primary grid by at least 15%.

8.1.2 How to achieve fair and efficient cooperative vehicle routing?

In addition of allowing self-consumption reduction, communties often allows the socialisation of the total
cost among its members. In this setting, a recurrent question is related to the design of fair cost allocation
mechanisms. In [24], a cooperative is modeled as a business entity whose primary purpose is to provide
benefits, services, and goods to its members, who both own and democratically control it. In the context

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Inria Annual Report 2023

of a cooperative, a fleet typically consists of vehicles owned by self-concerned, individually rational
owners who prioritize their own efficiency and the fairness of the system. This fairness refers to how their
individual gain aligns with the gain of others. In this paper, we focus on the routing of such cooperative
fleets. If we consider only the efficiency of the fleet in terms of minimizing its total cost, the problem
studied corresponds to the Multiple Traveling Salesman Problem (MTSP). However, our interest lies in
finding both efficient and fair solutions, so we propose two new variants of this problem that integrate
and maximize the egalitarian and elitist social welfare. Additionally, to enhance the balance between
fleet efficiency and fairness, we propose the systematic elitist and systematic egalitarian social welfare
optimization algorithm. Through simulation results, we observe a wide diversity of routes depending on
the approach considered. Therefore, a cooperative may choose a model that best balances criteria of
efficiency maximization and fairness for its fleet based on its specific requirements.

8.1.3 Improving neighborhood exploration into MOEA/D framework to solve a bi-objective routing

problem

Vehicle Routing Problems (VRPs) are classical optimization problems in transportation and logistics. In
INOCS, we address complex routing problems generalizing the VRP, combining the VRP with another
optimization problem, or hybridizing VRP with machine learning approaches. In [23], a MOEA/D
framework including a Local Search (LS) based mutation and knowledge discovery mechanisms is the
core algorithm used to solve a bi-objective VRP with Time Windows (bVRPTW) where the total traveling
cost and the total waiting time of drivers have to be minimized. We enhance the classical LS exploration
strategy of the neighborhood from the literature of scheduling and propose new metrics based on
customers distances and waiting times to reduce the neighborhood size. We conduct a deep analysis of
the parameters to give a fine-tuning of the MOEA/D framework adapted to the LS variants and to the
bVRPTW. Experiments show that the proposed neighborhood strategies lead to better performance on
both Solomon’s and Gehring and Homberger’s benchmarks.

8.1.4 Models and methods for two-level uncapacitated facility location problems

Neighborhood search methods are also considered in [47] which tackles Two-level Uncapacitated Facility
Location Problems with Single-assignment constraints (TUFLP-S), a problem that arises in industrial
applications in freight transportation and telecommunications. First, we recall the real-life application
that motivates this research work. Then, we present an integer programming formulation for this variant
with modular costs of the TUFLP-S, and we describe an adaptation of variable neighborhood search
to the classical TUFLP-S and the variant with modular costs. Focusing on the TUFLP-S, we introduce
mathematical programming models based on reformulation techniques and on the relaxation of the
integrality of some of the variables associated with location decisions. We then present a Lagrangian
relaxation approach for the TUFLP-S, based on solving a single-level uncapacitated facility location
problem (UFLP) as the Lagrangian subproblem. We also describe a matheuristic based on a mixed-integer
programming-based large neighborhood search. Synthetic computational results on instances derived
from the industrial application as well as on large, hard, artificial instances are reported throughout the
paper.

8.1.5 Synchronized deliveries with a bike and a self-driving robot

An innovative application of the VRP is considered in [29]. Inspired by the current practices at JD.com (the
largest online retailer by revenue in China), we investigate a delivery problem that we call the traveling
salesman problem with bike and robot (TSPBR), where a cargo bike is aided by a self-driving robot to
deliver parcels to customers in urban areas. We present two mixed-integer linear programming models
and describe a set of valid inequalities to strengthen their linear relaxation. We show that these models
can yield optimal solutions of TSPBR instances with up to 60 nodes. To efficiently find heuristic solutions,
we also present a genetic algorithm based on a dynamic programming recursion that efficiently explores
large neighborhoods. We computationally assess this genetic algorithm on instances provided by JD.com
and show that high-quality solutions can be found in a few minutes of computing time. Finally, we
provide some managerial insights to assess the impact of deploying the bike-and-robot tandem to deliver
parcels in the TSPBR setting.

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8.1.6 A column generation approach to solve the joint order batching and picker routing problem

including picker congestion

Order picking is a crucial process in warehouse operations. In a human-operated warehouse, pickers
prepare different customer orders. From a managerial perspective, two major decisions need to be
made: (i) grouping orders to be collected together by a picker, and (ii) for each picker, determining
the route to retrieve the needed items. The Joint Order Batching and Picker Routing Problem (JOBPRP
integrates both decisions into a single problem, usually minimizing either total distance or time. In the
literature, the JOBPRP usually assumes a situation without any congestion caused by the pickers, however
unrealistic when there are many pickers in a warehouse. In practice, congestion causes inefficiency,
increases costs, reduces performance, and leads to accidents. To estimate congestion levels, we divide the
planning horizon of the picking activity into different time intervals and timing variables are introduced.
If two or more pickers are in the same sub-aisle during the same time interval, a delay in travel time
is imposed. Because picking activities are performed by humans, practical considerations must be
taken into account when defining a feasible picking route, e.g. a picker cannot unnecessarily wait and
cannot follow complicated or long paths between two consecutive picking positions. To solve the JOBPRP
including the effect of picker congestion, an extended mathematical formulation is presented, with the
main objective of minimizing the total time, including delay. A heuristic solving approach is proposed
based on solving of the linear relaxation of the formulation by an exact column generation procedure. In
each iteration, a negative reduced column is produced using a dedicated labelling algorithm, exploring
routes associated to congestion level for each sub-aisle and time interval. To evaluate the modelling and
the performance of the solutions provided by the proposed approach, a discrete event simulation tool is
developed. Several experiments are performed to compare the results with optimal JOBPRP solutions not
considering congestion [45].

8.1.7 The intractability of the picker routing problem

The Picker Routing Problem (PRP), which consists in finding a minimum-length tour between a set of
storage locations in a warehouse, is one of the most important problems in the warehousing logistics
literature. Despite its popularity, the tractability of the PRP in conventional multi-block warehouses
remains an open question. The technical note in [58] aims to fill this research gap by establishing that the
PRP is strongly NP-hard.

8.1.8 Commodity constrained split delivery vehicle routing problems

We propose a survey [20] on vehicle routing problems with multiple commodities. In most routing
problems, only one commodity is explicitly considered. This may be due to the fact that, indeed, a single
commodity is involved, or multiple commodities are transported, but they are aggregated and modeled
as a single commodity, as no specific requirement imposes their explicit consideration. However, there
exist cases in which this aggregation is not possible due to the characteristics of the commodities or to
the fact that it would lead to sub-optimal routing plans. The survey focuses on the analysis of the settings
of the problems and the features of the commodities that require explicit consideration of disaggregated
commodities in routing problems. We show that problem settings are inherently different with respect to
the single commodity problems, and this has a consequence on both models and solution approaches,
which cannot be straightforwardly adapted from the single commodity cases. We propose a classification
of the routing problems with multiple commodities and discuss the motivations that force considering
the presence of multiple commodities explicitly. Specifically, we focus on the modeling perspective by
proposing a general formulation for routing problems with multiple commodities and showing how this
formulation can be adapted to the different features that characterize the problem classes discussed in
the survey. Also, for each major class of problems, promising future research directions are discussed by
analyzing what has been studied in the current literature and focusing on challenging topics not covered
yet.

We address two specific routing problems with multiple commodities. The commodity constrained
Split Delivery Vehicle Routing Problem (C-SDVRP) is a routing problem where customer demands are
composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a
way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers

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are allowed to be visited multiple times. However, the demand for a single commodity must be delivered
by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the
C-SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially-many
variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation
of the formulation by means of a column generation approach which embeds a new pricing heuristic
aimed to reduce the computational time. We test the heuristic algorithm on benchmark instances from
the literature. The comparison with the state-of-the-art heuristics for solving the C-SDVRP shows that
our approach significantly improves the solution time, while keeping a comparable solution quality and
improving some best-known solutions. In addition, our approach is able to solve large instances with 100
customers and six commodities, and also provides very good quality lower bounds [57].

A extended variant of the C-SDVRP is the Multi-Commodity two-echelon Distribution Problem
(MC2DP). In the MC2DP, multiple commodities are distributed in a two-echelon distribution system
involving suppliers, distribution centres and customers. Each supplier may provide different commodities
and each customer may request several commodities as well. In the first echelon, capacitated vehicles
perform direct trips to transport the commodities from the suppliers to the distribution centres for
consolidation purposes. In the second echelon, each distribution centre owns a fleet of capacitated
vehicles to deliver the commodities to the customers through multi-stop routes. Commodities are
compatible, i.e., they can be mixed in the vehicles. Finally, customer requests can be split by commodities,
that is, a customer can be visited by several vehicles, but the total amount of each commodity has to
be delivered by a single vehicle. The aim of the MC2DP is to minimise the total transportation cost to
satisfy customer demands. We propose a set covering formulation for the MC2DP where the exponential
number of variables relates to the routes in the delivery echelon. We develop a Branch-Price-and-Cut
algorithm (BPC) to solve the problem. The pricing problem results in solving an Elementary Shortest
Path Problem with Resource Constraints (ESPPRC) per distribution center. We tackle the ESPPRC with a
label setting dynamic programming algorithm which incorporates ng-path relaxation and a bidirectional
labelling search. Pricing heuristics are invoked to speed up the procedure. In addition, the formulation is
strengthened by integrating capacity cuts and two families of valid inequalities specific for the multiple
commodities aspect of the problem. Our approach solves to optimality 439 over the 736 benchmark
instances from the literature [60]. The optimality gap of the unsolved instances is 2.1%, on average.

8.1.9 Lower and upper bounds for the joint batching, routing and sequencing problem

Warehouses are the scene of complex logistic problems integrating different decision layers. This work
addresses the Joint Order Batching, Picker Routing and Sequencing Problem with Deadlines (JOBPRSP-D)
in rectangular warehouses. To tackle the problem an exponential linear programming formulation is
proposed. It is solved with a column generation heuristic able to provide valid lower and upper bounds on
the optimal value. We start by showing that the JOBPRSP-D is related to the bin packing problem rather
than the scheduling problem. We take advantage of this aspect to derive a number of valid inequalities
that enhance the resolution of the master problem. The proposed algorithm is evaluated on publicly
available data-sets. It is able to optimally solve instances with up to 18 orders in few minutes. It is also
able to prove optimality or to provide high-quality lower bounds on larger instances with 100 orders [39,
49]. To the best of our knowledge this is the first work that provides optimality guarantee on large size
instances for the JOBPRSP-D, the results can therefore be used to assert the quality of heuristics proposed
for the same problem.

8.1.10 Machine learning applications

Feature selection is a fundamental process to avoid overfitting and to reduce the size of databases
without significant loss of information that applies to hierarchical clustering. Dendrograms are graphical
representations of hierarchical clustering algorithms that for single linkage clustering can be interpreted
as minimum spanning trees in the complete network defined by the database. In [21], we introduce
the problem that determines jointly a set of features and a dendrogram, according to the single linkage
method. We propose different formulations that include the minimum spanning tree problem constraints
as well as the feature selection constraints.

In [11], we study a discrete version of the classical classification problem in Euclidean space, to be

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called the geodesic classification problem. It is defined on a graph, where some vertices are initially
assigned a class and the remaining ones must be classified. This vertex partition into classes is grounded
on the concept of geodesic convexity on graphs, as a replacement for Euclidean convexity in the multi-
dimensional space. We propose two new integer programming models along with branch-and-bound
algorithms.

8.2 Bilevel programming and game theory

Participants:

Luce Brotcorne, Diego Cattaruzza, Bernard Fortz, Martine Labbé,
Hélène Le Cadre, Frédéric Semet.

8.2.1 Moving from linear to conic markets for electricity

The massive integration of renewable energy and the growing involvement of prosumers have changed
the energy landscape, calling for an urgent restructuring of the electricity market. Game theory is a
powerful tool to analyse the outcome of situation of conflicts involving a large number of heterogeneous
agents with selfish interest. In this setting, we propose a new forward electricity market framework that
admits heterogeneous market participants with second-order cone strategy sets, who accurately express
the nonlinearities in their costs and constraints through conic bids, and a network operator facing conic
operational constraints. In contrast to the prevalent linear-programming-based electricity markets, we
highlight how the inclusion of second-order cone constraints improves uncertainty-, asset-, and network-
awareness of the market, which is key to the successful transition towards an electricity system based on
weather-dependent renewable energy sources. We analyze our general market-clearing proposal in [27]
using conic duality theory to derive efficient spatially-differentiated prices for the multiple commodities,
comprised of energy and flexibility services. Under the assumption of perfect competition, we prove the
equivalence of the centrally-solved market-clearing optimization problem to a competitive spatial price
equilibrium involving a set of rational and self-interested participants and a price setter. Finally, under
common assumptions, we prove that moving towards conic markets does not incur the loss of desirable
economic properties of markets, namely market efficiency, cost recovery, and revenue adequacy. Our
numerical studies focus on the specific use case of uncertainty-aware market design and demonstrate that
the proposed conic market brings advantages over existing alternatives within the linear programming
market framework.

8.2.2 Grid impact aware TSO-DSO market models for flexibility procurement: coordination, pricing

efficiency, and information sharing

Information sharing and coordination mechanisms impact the properties of the resulting market equiliria.
Five market models for the procurement of flexibility by Transmission (TSO) and Distribution System
Operators (DSOs), based on several TSO-DSO coordination schemes, including a disjoint distribution,
disjoint transmission, common, fragmented, and multi-level market are proposed in [25]. The properties
of these models are then analyzed. In particular, the common market is first proven to be more efficient
than the other market models. Then, different methods are proposed to adequately price TSO/DSO
interface flows, when procuring cross-grid flexibility. It is then shown that, when interface flows are op-
timally priced, the fragmented and multi-level market solutions converge to those of the common market,
reaching optimal efficiency. To prevent the need for any network information sharing among system
operators in the different coordination schemes, decomposition methods based on bi-level programming
and the Alternating Direction Method of Multipliers (ADMM) are proposed. A developed case study,
considering an interconnected transmission-distribution system, corroborates the mathematical findings
by highlighting the greater efficiency of the common market, the effect of adequate interface pricing on
reducing procurement costs, and the capability of the decomposition methods to reach optimal market
solutions with limited information exchange.

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8.2.3 Strategic resource pricing and allocation in a 5G network slicing Stackelberg game

The duality results from standard optimization setup that we applied to noncooperative games in [25] can
be extended to strategic pricing and resource allocation problems for communication networks. In [16],
we consider a marketplace in the context of 5G network slicing, where Application Service Providers (ASP),
i.e., slice tenants, providing heterogeneous services, are in competition for the access to the virtualized
network resource owned by a Network Slice Provider (NSP), who relies on network slicing. We model the
interactions between the end users (followers) and the ASPs (leaders) as a Stackelberg game. We prove that
the competition between the ASPs results in a multi-resource Tullock rent-seeking game. To determine
resource pricing and allocation, we devise two innovative market mechanisms. First, we assume that the
ASPs are pre-assigned with fixed shares (budgets) of infrastructure, and rely on a trading post mechanism
to allocate the resource. Under this mechanism, the ASPs can redistribute their budgets in bids and
customise their allocations to maximize their profits. In case a single resource is considered, we prove
that the ASPs’ coupled decision problems give rise to a unique Nash equilibrium. Second, when ASPs
have no bound on their budget, we formulate the problem as a pricing game with coupling constraints
capturing the shared resource finite capacities, and derive the market prices as the duals of the coupling
constraints. In addition, we prove that the pricing game admits a unique variational equilibrium. We
implement two online learning algorithms to compute solutions of the market mechanisms. A third fully
distributed algorithm based on a proximal method is proposed to compute the Variational equilibrium
solution of the pricing game. Finally, we run numerical simulations to analyse the market mechanism’s
economic properties and the convergence rates of the algorithms.

8.2.4 Modeling and analysis of a nonlinear security game

We formulate a security game in a context of mixed armament acquisition, involving a finite set of
Nations in strategic relationship, with utility functions which are nonlinear and non-differentiable on the
boundary of their sets of definition. Since we want to study the long-term effect of the Nations’ investment
in nuclear weapons, we focus on the steady-state analysis of the game. This requires us to extend the
classical results from Rosen on compact-convex games, to unbounded convex games, relying on the
coercivity property of the Nations’ utility functions. In addition, we prove the existence and uniqueness,
under mild assumptions, of an interior point Nash Equilibrium solution of the game. Simulations are
performed in case of a duopoly, highlighting the efficiency loss reduction and stabilizing effect of nuclear
armaments by comparison with the conventional-only setting [32, 55].

8.2.5 Bilevel integer linear models for ranking

Item and set orderings help with data management. Depending on the context, it is just as important
to order a list of items (customers from different provinces, companies from different sectors, players
from different teams) as it is to order a list of sets of these items (provinces, sectors, teams). It is evident
that the order that is chosen for the items is not independent of the order that is chosen for the sets. It
is possible that several set orders are sensible for the same item order and vice versa, that several item
orders are sensible for the same set order. In [22], we propose a bilevel model to calculate an adequate
order of items when an order of sets is available and another bilevel model to calculate an adequate order
of sets when an order of items is available. In addition, it is shown how to reduce both bilevel models to
single level models.

8.2.6 Min–max optimization of node-targeted attacks in service networks

In [19], we consider resilience of service networks that are composed of service and control nodes to
node-targeted attacks. Two complementary problems of selecting attacked nodes and placing control
nodes reflect the interaction between the network operator and the network attacker. This interaction can
be analyzed within the framework of game theory. Considering the limited performance of the previously
introduced iterative solution algorithms based on non-compact problem models, new compact integer
programming formulations of the node attack optimization problem are proposed, which are based on
the notion of pseudo-components and on a bilevel model. The efficiency of the new formulations is

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illustrated by the numerical study that uses two reference networks (medium-size and large-size), and a
wide range of the sizes of attacks and controllers placements.

8.2.7 Bilevel pricing model for cloud computing

Cloud computing has transformed numerous sectors of businesses, governments, and individuals’ lives
with its benefits of processing power, resource simplicity, scalability, and accessibility. Predictions an-
ticipate a significant upsurge in global data traffic by 2025, driven by an increase in demand for cloud
computing. Although cloud computing is energy-efficient compared to private computers, it is still waste-
ful. Data centers often underutilize servers, which continue to consume considerable amounts of energy
even when idle. The inefficiency originates in the overstocking of computers due to consumer behavior
and service-level buffering.1 To face this problem, we propose a cloud sharing system to enhance resource
efficiency. The system’s framework is formulated as a mixed integer bilevel problem, which features
two distinct follower types representing the different types of customers in the public cloud, namely,
long-term consumers with monthly subscriptions and short-term consumers who seek on-demand
access. The cloud service manager’s (CSM) goal, operating as the leader, is to incentivize long-term
consumers to share their resources through rewards to allocate shortterm consumers without requiring
new resources. Resources energy consumptions measures are included in the objective functions of the
leader. We have defined new cuts and have developped a branch and cut algorithm to solve the problem.

8.2.8 Bilevel pricing model for electric car charging problems

We consider a provider of electric vehicle charging that operates a network of charging stations and
wishes to use dynamic pricing to maximize profit and reduce the impact on the electric grid. We propose
a bilevel model with a single leader and multiple disjoint followers. The customers are followers, and
each makes decisions independently from the others. The provider is the leader, sets the prices for
each station at each time slot, and ensures there is enough energy to charge. The behavior of each
customer is represented by the combination of a preference list of (station, time) pairs and a reserve
price. In this way, the proposed model accounts for the heterogeneity of customers with respect to price
sensitivity and charging preferences. We solve the bilevel optimization problem using a reformulation
based on optimality conditions and compare our results to other approaches in the literature. The
proposed reformulation is able to solve large-scale instances, and the computational results show that the
maximum consumption peak can be significantly reduced with only a slight degradation of the provider’s
profit.

In the same spirit another work is related to the charging of autonomous electrical cars. A special
attention is devited to the interactions between the transportation and electrical grid networks. A new
model based on an extension of the pick-up and delivery problem is proposed.

8.2.9 Integrating new shared mobility systems within public transportation

The overall objective of the EuropanSUM project is to facilitate the transformation of mobility in 15
European cities by 2026 and in 30 European cities by 2030. This transformation involves the integration
of new shared mobility modes with public transport, focusing on innovation, interconnectivity, envir-
onmental sustainability, safety, resilience and replicability. The aim is to ensure the affordability and
reliability of these modes for end users, while maintaining financial sustainability that strengthens the
competitiveness of European businesses.

In this setting we develop new bilevel joint pricing models to incetivize the users to combine new

shared mobility modes with public transportation. Several path offers will be provided to the users.

8.3 Robust/Stochastic programming

Participants:

Luce Brotcorne, Diego Cattaruzza, Bernard Fortz, Martine Labbé,
Hélène Le Cadre.

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8.3.1 Mutli-agent reinforcement learning for strategic bidding in two stage electricity markets

INOCS has recently started a research track on the study of Multi-Agent Reinforcement Learning (MARL)
in stochastic networks of agents. Within this area, our goal is to study the dynamics of electricity markets
involving multiple competitive generators through MARL approaches. We start by formulating the
electricity market as a two-stage stochastic game, involving a finite set of conventional and renewable
energy producers, which bid on the day-ahead market, and an Independent System Operator (ISO), which
is responsible for the clearing of the market. We assume that a predetermined part of the producers are
non-strategic, bidding at their marginal costs, while the others might bid strategically trying to learn the
outcome of the clearing. In the first stage, the strategic producers optimize simultaneously their bids by
minimizing their expected costs (opposite of the expected profits), which is the difference between their
production cost and the payment they receive from the ISO. The renewable energy producers’ objective
functions include a penalty assigning a cost to the imbalances caused by their forecast errors. In the
second stage, the ISO receives the bids of all the producers. It clears the market by determining the
activated volumes for each producer and a price minimizing the total cost under capacity constraints,
including a conditional value at risk (CVaR) constraint for the renewable producers, capturing the
risk aversion level that the requested volume violates their uncertain capacity. We derive closed form
expressions for the producers’ best-responses considering pay-as-clear and pay-as-bid as pricing schemes,
and simulate the market dynamics, using MARL. To that purpose, we rely on modified versions of two
actor-critic algorithms: Deep Deterministic Policy Gradient (DDPG) and Soft Actor-Critic (SAC). The
simulations show how the producers adapt dynamically their strategies to learn the best bidding strategy,
under limited information exchange. Finally, we identify conditions for the convergence of MARL
algorithms to local equilibria of the stochastic game. First results in this area have been presented in [35,
41].

8.3.2 Learning market equilibria using performative prediction: balancing efficiency and privacy

MARL is a widely researched technique for decentralized control in complex large-scale systems with
interacting agents. When predictions support decisions they may influence the outcome they aim to
predict. We call such prediction performative, i.e., the prediction influence the target. A conceptual
novelty is an equilibrium notion called performative stability in the literature. We apply this new concept
to a peer-to-peer electricity market modeled as a network game, where End Users (EUs) minimize their
cost by computing their demand and generation while satisfying a set of local and coupling constraints.
Their nominal demand constitutes sensitive information, that they might want to keep private. We
prove that the network game admits a unique Variational Equilibrium (VE), which depends on the
private information of all the EUs. A data aggregator is introduced, which aims to learn the EUs’ private
information. The EUs might have incentives to report biased and noisy readings to preserve their
privacy, which creates shifts in their strategies. Relying on performative prediction, we define a decision-
dependent game Gstoch to couple the network game with a data market in [38, 54]. Two variants of
the Repeated Stochastic Gradient Method (RSGM) are proposed to compute the Performatively Stable
Equilibrium (PSE) solution of Gstoch, that outperform RSGM with respect to efficiency gap minimization,
privacy preservation, and convergence rates in numerical simulations.

8.3.3 Towards forecast markets for enhanced peer-to-peer electricity trading

In [37], we examine the impact of the coupling between an introduced data market, in which agents
can purchase a forecast of their renewable energy sources’ generation levels to improve their estimation
quality, and a peer-to-peer electricity market, enabling prosumers to trade energy in a decentralized
manner with their peers, amidst the growing trend of decentralization and uncertainty of Renewable
Energy Sources (RES) in electricity markets. The study formulates the P2P trading as a generalized Nash
equilibrium problem and identifies conditions for achieving a maximized efficiency of the peer-to-peer
electricity market, one of which is prosumers’ participation in the forecast market. Along these lines,
the analysis demonstrates that prosumers have incentives to participate in the forecast market and
outlines the conditions, considering the case in which the forecasts are given in the form of a Gaussian
distribution. Numerical examples using Pecan Street data demonstrate the theoretical findings and

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provide illustrations for the general case, as well as highlight the mutual benefits of market coupling for
forecast sellers and electricity market agents.

8.3.4 Exact and heuristic solution Ttchniques for mixed-integer quantile minimization problems

We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are
very hard to solve for real-world instances. We motivate the study of this problem class by two important
realworld problems: a maintenance planning problem for electricity networks and a quantile-based
variant of the classic portfolio optimization problem. For these problems, we develop valid inequalities
and present an overlapping alternating direction method. Moreover, we discuss an adaptive scenario
clustering method for which we prove that it terminates after a finite number of iterations with a global
optimal solution. We study the computational impact of all presented techniques and finally show that
their combination leads to an overall method that can solve the maintenance planning problem on
large-scale real-world instances provided by the EURO/ROADEF challenge 2020 and that they also lead to
significant improvements when solving a quantile-version of the classic portfolio optimization problem
[14].

8.3.5 The case for stochastic online segment routing under demand uncertainty

In [31], we present a novel algorithmic approach to optimize traffic engineering in segment routing
networks, accounting for demand uncertainty. In particular, we propose a stochastic approach to online
segment routing which uses a conditional value at risk when accounting for the traffic matrix uncertainty.
This approach can perform significantly better than the worst-case approach often considered in the
literature. We also show that depending on the demand volatility, our stochastic approach can be further
optimized in that it is sufficient to account for only a part of the demand without sacrificing traffic
engineering quality.

9 Bilateral contracts and grants with industry

Participants:

Luce Brotcorne, Hélène Le Cadre.

9.1 Bilateral grants with industry

Program PGMO funded by the Fondation Mathématiques Jacques Hadamard and EDF R&D. Stackelberg
Games for Flexibility (Dis)Aggregation (2022 – 2024).

10 Partnerships and cooperations

10.1 International initiatives

10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an

Inria International Program

BIO-SEL
Title: Bilevel Optimization in Security, Energy and Logistics

Participants: Martine Labbé, Frédéric Semet.

Duration: 2020–2023
PIs: Martine Labbé (Université Libre de Bruxelles), Vladimir Marianov (PUC Chile)

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Partners: Pontificia Universidad Catolica de Chile Santiago (Chile)
Summary: This projet is devoted to bilevel optimization problems with application in the security,
energy, and logistics domains. Stackelberg games, including one defender and several followers, bidding
problems in energy supply markets and product selection problems will be considered. Mixed integer
optimization models and efficient algorithms to solve them will be developed.

GALANGAL
Title: Game Theoretic Learning and Optimization for Networked Electricity Markets

Participants:

Luce Brotcorne, Bernard Fortz, Hélène Le Cadre.

Duration: 2023–2025
PIs: Hélène Le Cadre (Inria), Michel Gendreau (Polytechnique Montréal, Canada)
Partners: Polytechnique Montréal (Canada), Edinburgh University (Scotland)
Summary: Game Theory is the study of interacting decision makers. A large part of the work in this
area has focused on equilibrium computation, but another relevant question is how agents might reach
an equilibrium, especially given that no single agent has full information on the state of the system or
full authority over the strategies of the other agents. GALANGAL research directions are split into three
axes: (i) learning market equilibria preserving statistical privacy using performative prediction, (ii) deep
reinforcement learning to control interconnected buildings, (iii) equilibrium tracking, towards robust
markets.

10.1.2 STIC/MATH/CLIMAT AmSud projects

SOGGA
Title: Stochastic Optimization, Generalized Games and Applications

Participants:

Luce Brotcorne, Hélène Le Cadre.

Duration: 2024–2025
Coordinator: Dider Aussel (Université de Perpignan, France)
Partners: University of Perpignan, Universidad de Chile and Universidad de O’Higgins (Chile), Univer-
sidad del Pacifico (Peru), Inria Lille
Summary: SOGGA proposes to focus in four theoretical research lines: (i) continuity-like properties
in equilibrium problems, (ii) regularity in generalized equilibrium problems, (iii) bilevel games with
decision-dependent uncertainty (Luce Brotcorne), (iv) algorithms and mechanism design in learning
games (Hélène Le Cadre).

10.1.3 Participation in other International Programs

Title: CityFreight – Freight Logistics in Sustainable Cities

Participant:

Frédéric Semet.

Partner Institution(s):

• University of Bergen, Center for Climate and Energy Transformation

• The Norwegian Public Roads Administration

• Sparebanken Vest

• City of Bergen

Project INOCS

17

• Vestland Country, Bergen Chamber of Commerce and Industry, Nordic Edge AS (Norway)

• Centrale Lille

• The Polytechnic University of Turin (Italy)

• Sichuan University, Chengdu (China)

Duration: 2020–2024

Additionnal info/keywords: The primary objective of this project is to provide public authorities, partic-
ularly in smaller, topologically complicated, cities and initially the City of Bergen, with a toolbox for
realistically evaluating major decisions that would make a city more energy efficient and sustainable
in terms of freight transportation

10.2 International research visitors

10.2.1 Visits of international scientists

Pamela Bustamante

• Status: Ph.D. Student

• Institution of origin: Pontifica Universidad Catolica de Chile

• Country: Chile

• Dates: Until January 2023

• Context of the visit: Stackelberg games

• Mobility program/type of mobility: research stay – Ph.D. co-supervision

Sophia Calderon Pimienta

• Status: Master Student

• Institution of origin: O’Higgins Universidad

• Country: Chile

• Dates:From February to April 2023

• Context of the visit: Predict and Optimize - Bilevel optimization

• Mobility program/type of mobility: research stay

Clara Chini Nielsen

• Status: Ph.D. Student

• Institution of origin: Technical University of Denmark

• Country: Denmark

• Dates:From march to June 2023

• Context of the visit: Field service routing problem

• Mobility program/type of mobility: research stay

Alejandro Jofre

• Status: Professor

• Institution of origin: CMM

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Inria Annual Report 2023

• Country: Chile

• Dates: February 2023

• Context of the visit: Learning games

• Mobility program/type of mobility: research stay – Masters internship co-supervision

Walter Rei

• Status: Professor

• Institution of origin: Quebec University at Montréal

• Country: Canada

• Dates: August 2023–September 2023

• Context of the visit: Stochastic optimization

• Mobility program/type of mobility: research stay

10.2.2 Visits to international teams

Research stays abroad

• Francesco Morri, Polytechnique Montréal (Canada), one month visit, funding GALANGAL Associate

Team.

• Gaël Guillot, University of Edinburgh (Scotland), two weeks visit, funding GALANGAL Associate

Team.

10.3 European initiatives

10.3.1 Horizon Europe

SUM

Title: Seamless Shared Urban Mobility
Duration: 2023–2026
Partners: Inria INOCS (project coordinator), Delft University (The Netherlands), NTUA, Ertico, Polis,
Vedecom, Technical University of Munich, City of Munich, Municipality of Pentali, sixt, Freenow, Krakow
Municipality, Jagiellonian University, Ret, Fredrikstad Municipality, Nextbike Cyprus, Chalmers University
of Technology, MOBYx, Cunisa, Coimbra Municipality, ZF, TU Coimbra, Jerusalem Municipality, Tel Aviv
University, Sigma6, Larnaca Public Transport, Siemens Mobility B.V., HYKE, University of Twente, TPG.
Summary: The overall objective of the SUM project is to facilitate the transformation of mobility
in 15 European cities by 2026 and in 30 European cities by 2030. This transformation involves the
integration of new shared mobility modes with public transport, focusing on innovation, interconnectivity,
environmental sustainability, safety, resilience and replicability. The aim is to ensure the affordability and
reliability of these modes for end users, while maintaining financial sustainability that strengthens the
competitiveness of European businesses.

10.3.2 H2020 projects

CHIST–ERA SEC–OREA

Title: Supporting Energy Communities – Operational Research and Energy Analytics
Duration: 2022–2025
Partners: Inria INOCS, Université Libre de Bruxelles (Belgium), University College of Dublin (Ireland),

Riga Technical University (Lithuania)

Summary: SEC–OREA aims to enable local energy communities (LECs) to participate in the decar-
bonisation of the energy sector by developing advanced efficient algorithms and analytics technologies.
The SEC–OREA projects has enabled the hiring of two Ph.D. students within INOCS: Juan Sepulvea and
Cristian Aguayo.

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10.4 National initiatives

10.4.1 ANR

ANR project AGIRE (2020-2024): "Decision system for smart management of resources in warehouses" in
collaboration with Ecole des Mines de Saint-Etienne (Gardanne), Université Gustave Eiffel (Champs-sur-
Marne), HappyChic (Tourcoing). This project addresses human resources management in warehouses
which supply either sale points (B2B) or final consumers (B2C). Nowadays, such warehouses are under
pressure. This is mainly due to the no inventory policy at the sale points and to the constant growth of
e-commerce sales in France and Europe. In terms of logistics, this translates into an increasing number of
parcels to prepare and to ship to satisfy an order, which is known typically a few hours before. Moreover,
the total number of products to be packed varies very significantly from day-to-day by a factor of at least
3. The novelty of the project is twofold: (1) The human factor is explicitly be taken into account. It is
integrated in the mathematical models and algorithms that are developed for the project. The aim is
to improve the quality of employees’ work ensuring the efficiency of the logistic system; (2) Problems
at different decision levels are integrated and tackled jointly. At the tactical level, the main issues are
workload smoothing and the management of the storage zone. At operational level, the major issues
concern the rearrangement of the picking zone, the picking tours, and the dynamic reorganization of
activities to manage uncertainties.

ANR project ADELE (2022-2025): “Resource Allocation in City Logistics with Demand Uncertainty” in
collaboration with LCOMS (Univ. of Lorraine), Toulouse Business School, Colisweb. A central issue in city
logistics (CL) is to design logistics systems that move goods to, from, and within urban areas while meeting
sustainability goals. A central role is played by the orchestrator. The orchestrator is the stakeholder that
operates and organizes a CL system when multiple stakeholders are implied. In ADELE, we tackle the
planning problem faced by the orchestrator in coordinating and managing the resources offered by
carriers or logistics service providers. The problem aims to determine what logistics facilities should be
used and when and where the vehicles of the carriers should be assigned to cover the demand in the most
efficient way. A key feature is that demand is uncertain. We consider two main variants depending on
whether the CL system is one or two tiers. ADELE aims to develop new efficient mathematical models
and decision support methods. we aim to design and implement ad-hoc optimization algorithms based
on mathematical modeling. This project is a continuation of the INRIA Innovation Lab Colinocs.

10.5 Regional initiatives

STaRS project SITAR (2022-2025): The SITAR project is funded by the Région Hauts-de-France. The
research within SITAR is split into two axes: (1) modeling and analysis of an optimal taxation problem,
involving sanctions, formulated as a Stackelberg game involving a partial equilibrium problem at the lower
level. The set of equilibria will be characterized analytically. Different settings with multi-commodity
competition and different out-neighbors communication patterns will be considered. Applications will be
made to the gas market. (2) development and performance analysis of learning algorithms for equilibrium
tracking. A fundamental open problem is game theory is the computation of a specific equilibrium among
all the possible ones, e.g., the optimal one with respect to (the possible combination of) different criteria,
e.g., efficiency loss minimization, accuracy of the equilibrium approximation maximization, convergence
rate minimization. The existing algorithms have convergence guarantees toward an arbitrary, possibly
inefficient (with respect to those criteria), equilibrium. We aim to contribute to this second axis by
deriving distributed algorithms for the computation of an optimal equilibrium in noncooperative games,
and extend the results to the time-varying setting to track the sequence of optimal equilibria. The SITAR
project has enabled the hiring of a 18 months postdoc researcher, Fedy Pokou, who will join the INOCS
Team in February 2024.

Participants:

Luce Brotcorne, Diego Cattaruzza, Bernard Fortz, Martine Labbé, Mar-
tine Le Cadre, Maxime Ogier, Frédéric Semet.

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Inria Annual Report 2023

11 Dissemination

11.1 Promoting scientific activities

11.1.1 Scientific events: organisation

General chair, scientific chair

• General chair of SynchroTrans 2023, Lille, 21-22 september 2023: Diego Cattaruzza, Maxime Ogier,

Frédéric Semet.

• General chair of GO 2023, Spa, Belgium, 2-5 July 2023: Bernard Fortz.

Member of the organizing committees

• 10t h International Congress on Industrial and Applied Mathematics (ICIAM 2023): Martine Labbé.

• LIV Brazilian Symposium on Operational Research (LIV SBPO): Martine Labbé.

• Bilevel Optimization Conference 2023: Martine Labbé.

11.1.2 Scientific events: selection

Member of the conference program committees

• The 23r d Conference of the International Federation of Operational Research Societies (IFORS2023):

Bernard Fortz.

• CoDIT 2023 : Frédéric Semet

• ROADEF 2023 : Luce Brotcorne, Diego Cattaruzza, Maxime Ogier, Frédéric Semet

Reviewer

• The Genetic and Evolutionary Computation Conference (GECCO) 2023: Diego Cattaruzza.

• European Control Conference (ECC) 2023: Hélène Le Cadre.

• Control and Decision Conference (CDC) 2023: Hélène Le Cadre.

11.1.3 Journal

Member of the editorial boards

• Computers & Operations Research Optimization: Luce Brotcorne – Member of the Editorial Advis-

ory Board.

• International Transactions in Operations Research: Luce Brotcorne – Associate editor.

• Journal of Optimization Theory and Applications (JOTA): Diego Cattaruzza, associate editor; Bern-

ard Fortz, associate editor; Martine Labbé, area editor.

• Open Journal of Mathematical Optimization: Martine Labbé, member of the steering committee.

• Transportation Science: Martine Labbé, member of the advisory board.

• International Transactions in Operations Research: Bernard Fortz, associate editor; Martine Labbé,

associate editor.

• European Journal of Computational Optimization: Bernard Fortz, associate editor; Martine Labbé,

associate editor.

• Networks: Bernard Fortz, associate editor.

• INFORMS Journal on Computing: Bernard Fortz, associate editor.

Project INOCS

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Reviewer - reviewing activities Annals of Operations Research, Applied Computing and Informatics,
Central European Journal of Operations Research, Computers & Operations Research, Computational
Optimization and Applications, Discrete Applied Mathematics, EURO Journal on Transportation and
Logistics, European Journal of Operational Research, IISE Transactions, INFORMS Journal on Computing,
International Journal of Management Science and Engineering Management, International Transactions
in Operational Research, Journal of Optimization Theory and Applications, Mathematical Programming
Computation, Networks, Omega, Operations Research, Optimization and Engineering, RAIRO - Opera-
tions Research, Transportation Science, IEEE Transactions on Automatic Control: Luce Brotcorne, Diego
Cattaruzza, Bernard Fortz,Martine Labbé, Hélène Le Cadre, Maxime Ogier, Frédéric Semet.

11.1.4 Invited talks

Multi-Agent Reinforcement Learning for Strategic Bidding in Two Stage Electricity Markets. IMACS23 –
21st IMACS World congress, Rome, Italy, Sep 11, 2023: Francesco Morri.

11.1.5 Leadership within the scientific community

• PGMO: Luce Brotcorne, member of the scientific committee.

• INFORMS, Energy Natural Resources and the Environmentatl Section: Luce Brotcorne,secretary &

treasurer.

• EURO Working Group "Pricing and revenue management": Luce Brotcorne, coordinator.

• EURO Working Group "Vehicle Routing and Logistics Optimization (VEROLOG)": Frédéric Semet,

member of the board.

• ORBEL (Belgian Operations Research Society): Bernard Fortz, member of the administration board.

• GdR Recherche Opérationnelle et Décision: Frédéric Semet, member of the board.

11.1.6 Scientific expertise

• ANID, Chile Evaluation Group: Luce Brotcorne.

• Scientific committee of France-Netherlands Exchange Program: Luce Brotcorne - Member.

• Evaluation committee for INRIA/MITACS Exchange Program: Luce Brotcorne - Member.

• Evaluation committee COST GTRI: Luce Brotcorne - Member.

• NSERC Evaluation Group 1509: Bernard Fortz.

• Hiring Committee for the Professor Position on Modeling and Optimization of Electricity Systems

and Markets, CORE, LIDAM, UCLouvain, Louvain-la-Neuve, Belgium: Hélène Le Cadre.

• Hiring Committee for the Associate Professor Position in Computer Science, University of Lille,

France: Diego Cattaruzza.

• IVADO International Advisory Committee, Canada : Matine Labbé - Member.

• Scientific orientation committee of the Interuniversity Centre on Entreprise Networks, Transporta-

tion and Logistics (CIRRELT), Canada: Bernard Fortz, Frédéric Semet - Members.

• Research Council of Norway, Norway: Frédéric Semet - Panel member.

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Inria Annual Report 2023

11.1.7 Research administration

• Vice–president of the Inria Evaluation Committee: Luce Brotcorne.

• Elected Member of the Inria Evaluation Committee: Hélène Le Cadre.

• Member of the "Commission Emploi Recherche" (CER) at Inria Lille: Hélène Le Cadre.

• Corresponding Member for Inria Lille of the "Mission Jeunes Chercheurs": Hélène Le Cadre.

• Deputy-director of CRIStAL: Frédéric Semet.

• Member of the OPTIMA Scientific Council: Diego Cattaruzza.

• Member of Scientific Council of Centrale Lille: Diego Cattaruzza.

11.2 Teaching - Supervision - Juries

11.2.1 Teaching

• Master: Bernard Fortz, Recherche Opérationnelle et Applications, 30hrs, M1, University of Mons

(Charleroi campus), Belgium.

• Master: Bernard Fortz, Continuous Optimization, 24hrs, M1 & M2, Université libre de Bruxelles,

Belgium.

• Master: Frédéric Semet, Supply Chain Management, 30hrs, M2, Centrale Lille.

• Master: Frédéric Semet, Operations Research, 28hrs, M2, Centrale Lille.

• Master: Luce Brotcorne, Optimisation, 14hrs, M1, Polytech Lille.

• Master: Luce Brotcorne, Recherche opérationnelle, 16hrs, M1 apprentissage, Polytech Lille.

• Master: Diego Cattaruzza, Frédéric Semet, Prescriptive analytics and optimization, 64hrs, M1,

Centrale Lille.

• Master: Diego Cattaruzza, Object-Oriented Programming, 48hrs, M1, Centrale Lille.

• Master: Diego Cattaruzza, Operations Research, 16hrs, M1, Centrale Lille.

• Licence: Diego Cattaruzza, Maxime Ogier, Object-Oriented Programming, 40hrs, L3, Centrale Lille.

• Licence: Frédéric Semet, Advanced programming and Complexity, 24hrs, L3, Centrale Lille.

• Licence: Diego Cattaruzza, Maxime Ogier, Object-Oriented Programming, 44hrs, L2, Centrale Lille.

• Licence: Bernard Fortz, Algorithmique 1, 12hrs, L1, Université libre de Bruxelles, Belgium.

• Licence: Bernard Fortz, Algorithmique et Recherche Opérationnelle, 24hrs, L3, Université libre de

Bruxelles, Belgium.

11.2.2 Supervision

• PhD completed: Matteo Petris, Column generation approaches for integrated operationnal prob-

lems, September 2023, Diego Cattaruzza, Maxime Ogier, Frédéric Semet.

• PhD completed: Ilia Shilov, Game-Theoretic Approaches for Peer-to-Peer Energy Trading, Septem-
ber 2023, Hélène Le Cadre, Ana Busic (Inria Paris/ENS Paris), Bartek Blaszczyszyn (Inria Paris/ENS
Paris).

• PhD in progress: Cristian Aguayo, Models and Algorithms for Energy Disptaching in Local Energy

Communities, from July 2021, Bernard Fortz.

Project INOCS

23

• PhD in progress: Tifaout Almeftah, Models and algorithms for group testing, from December 2021,

Diego Cattaruzza, Martine Labbé, Frédéric Semet.

• PhD in progress: Haider Ali,Optimal techniques for charging autonomous electric vehicles with
renewable energy sources, from October 2021, Luce Brotcorne, Bruno François (Centrale Lille).

• PhD in progress: Hugo Callebaut, Segment routing optimization, from September 2022, Bernard

Fortz.

• Phd in progress: Clement Legrand, Intégration de Machine Learning pour la résolution de MO-
VRPTWs. Diego Cattaruzza, Marie-Eleonore Kessaci (Polytech Lile), Laetitia Jourdan (University of
Lille).

• PhD in progress: Aitor Lopez Sanchez, Distributed, Scalable, and Efficient Fleet Coordination for

Agriculture Mobile Robots, from September 2022, Frédéric Semet, Marin Lujak.

• PhD in progress: Francesco Morri, Game-Theoretic Learning in Intelligent Marketplaces, from

October 2022, Hélène Le Cadre, Luce Brotcorne.

• PhD in progress: Thibault Prunet, Models and algorithm for tactical problems in warehouses with
human factor considerations, from February 2020, Nabil Absi (Ecole desMines de Saint Etienne),
Valeria Borodin (Ecole des Mines de Saint Etienne), Diego Cattaruzza.

• PhD in progress: Simon Renard, Integration of machine learning and branch and bound algorithms,

from October 2023, Bernard Fortz.

• PhD in progress: Luis Pablo Rojo, Incentive mechanisms for electric vehicle charging, from Oc-
tober 2021, Luce Brotcorne, Michel Gendreau (Polytehcnique Montréal, Canada), Miguel Anjos
(University of Edinburgh, UK).

• PhD in progress: Juan Sepulveda, New optimization models and algorithms to represent energy
exchanges in local energy communities, from December 2021, Hélène Le Cadre, Luce Brotcorne.

• PhD in progress: Pablo Torrealba Gonzalez, Batching and picker routing problems in warehouses
taking into account human factors, from February 2021, Dominique Feillet (Ecole des Mines de
Saint Etienne), Maxime Ogier, Frédéric Semet.

• PhD in progress: Wenjiao Sun, Exact methods for integrated routing and scheduling problems,

from October 2021, Maxime Ogier, Frédéric Semet.

• PhD in progress: Natalia Isabel Wolf Garcia, Towards energy-based pricing strategies for the cloud,

from April 2023, Luce Brotcorne, Bernard Fortz.

11.2.3 Juries

• Hector Gatt, IMT Atlantique, Construction d’une méthodologie et d’un outil associé pour la con-

ception et la planification d’un réseau de bus: Luce Brotcorne – Reviewer.

• Quentin Jacquet, Institut Polytechnique de Paris, Stackelberg games, optimal pricing and applica-

tion to electricity markets: Luce Brotcorne – Reviewer.

• Harol Mauricio Gamez, PhD, Univerity of Antwerp, Scattered storage assignment optimization:
towards more efficient order fulfillment in e-commerce warehouses: Diego Cattaruzza – Reviewer.

• Ruben D’Haen, PhD, Univerity of Hasselt, Heuristic algorithms for the online integrated optimisa-

tion of order picking and vehicle routing decisions: Diego Cattaruzza – Reviewer.

• Zacharie Ales, ENSTA Paris, Contributions to solving hard combinatorial optimization problems

(HDR): Bernard Fortz – Reviewer.

• Chen Dang, Université PSL, Heuristics Learning for Solving Network Optimization Problems:

Bernard Fortz – Member.

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Inria Annual Report 2023

• Ilia Shilov, ENS Paris, Game-Theoretic Approaches for Peer-to-Peer Energy Trading: Hélène Le

Cadre – Member (co-advisor).

• Fred Michael Gonsalves, IMT Atlantique, Leveraging Machine Learning and Operations Research

to Enhance Cruise Ship Energy Efficiency: Hélène Le Cadre – Member.

• Manuel Trotta, Université Clermont Auvergne, Pickup and delivery problems with autonomous

and electric vehicles : Frédéric Semet – Chairman of the committee.

• Daniil Khachai, Université de Bordeaux, Algorithmes efficaces pour les problèmes de routage avec

des contraintes spécifiques: Frédéric Semet – Reviewer.

12 Scientific production

12.1 Major publications

[1] N. Absi, D. Cattaruzza, D. Feillet, M. Ogier and F. Semet. ‘A heuristic branch-cut-and-price algorithm
for the ROADEF/EURO challenge on Inventory Routing’. In: Transportation Science (2019). URL:
https://hal-emse.ccsd.cnrs.fr/emse-02163171.

[2] L. Brotcorne, D. Aussel, S. Lepaul and L. Von Niederhäusen. ‘A Trilevel Model for Best Response
in Energy Demand-Side Management’. In: European Journal of Operational Research (2020). URL:
https://hal.inria.fr/hal-02414600.

[3] L. Brotcorne, F. Cirinei, P. Marcotte and G. Savard. ‘An exact algorithm for the network pricing
problem’. In: Discrete Optimization 8.2 (2011), pp. 246–258. URL: https://dx.doi.org/10.1016
/j.disopt.2010.09.003.

[4] H. Calik and B. Fortz. ‘A Benders decomposition method for locating stations in a one-way electric
car sharing system under demand uncertainty’. In: Transportation Research Part B: Methodological
125 (July 2019), pp. 121–150. DOI: 10.1016/j.trb.2019.05.004. URL: https://hal.inria.fr
/hal-02409510.

[5] C. Casorrán, B. Fortz, M. Labbé and F. Ordóñez. ‘A study of general and security Stackelberg
game formulations’. In: European Journal of Operational Research 278.3 (2019), pp. 855–868. DOI:
10.1016/j.ejor.2019.05.012. URL: https://hal.inria.fr/hal-01917798.

[6] D. Cattaruzza, M. Labbé, M. Petris, M. Roland and M. Schmidt. ‘Exact and Heuristic Solution Tech-
niques for Mixed-Integer Quantile Minimization Problems’. In: INFORMS Journal on Computing
(2024). URL: https://hal.science/hal-03665771.

[7] B. Fortz, E. Gorgone and D. Papadimitriou. ‘A Lagrangian heuristic algorithm for the time-dependent
combined network design and routing problem’. In: Networks 69.1 (2017), pp. 110–123. DOI: 10.10
02/net.21721. URL: http://dx.doi.org/10.1002/net.21721.

[8] M. Restrepo, F. Semet and T. Pocreau. ‘Integrated Shift Scheduling and Load Assignment Optim-
ization for Attended Home Delivery’. In: Transportation Science 53 (2019), pp. 917–1212. URL:
https://hal.inria.fr/hal-01963916.

[9] R. Taisant, M. Datar, H. Le Cadre and E. Altman. ‘Learning Market Equilibria Using Performative
Prediction: Balancing Efficiency and Privacy’. In: ECC 2023 - European Control Conference. 2023
European Control Conference (ECC). Bucharest, Romania, June 2023. DOI: 10.23919/ECC57647
.2023.10178247. URL: https://inria.hal.science/hal-03816949.

[10] Y. Zhao, D. Cattaruzza, N. Kang and R. Roberti. ‘Synchronized Deliveries with a Bike and a Self-
Driving Robot’. In: Transportation Science (8th Dec. 2023). DOI: 10.1287/trsc.2023.0169. URL:
https://hal.science/hal-04362883.

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12.2 Publications of the year

International journals

[11] P. H. M. Araújo, M. Campêlo, R. C. Corrêa and M. Labbé. ‘Integer Programming Models and
Polyhedral Study for the Geodesic Classification Problem on Graphs’. In: European Journal of
Operational Research 314.3 (Aug. 2023), pp. 894–911. DOI: 10.1016/j.ejor.2023.08.029. URL:
https://cnrs.hal.science/hal-03727579.

[12] L. Brotcorne, J. Ezpeleta and C. Galé. ‘A biobjective model for resource provisioning in multi-cloud
environments with capacity constraints’. In: Operational Research 23.2 (3rd May 2023), p. 31. DOI:
10.1007/s12351-023-00773-x. URL: https://inria.hal.science/hal-04398447.

[13] H. Callebaut, J. de Boeck and B. Fortz. ‘Preprocessing for segment routing optimization’. In: Net-
works 82.4 (25th July 2023), pp. 459–478. DOI: 10.1002/net.22165. URL: https://inria.hal.s
cience/hal-04399116.

[14] D. Cattaruzza, M. Labbé, M. Petris, M. Roland and M. Schmidt. ‘Exact and Heuristic Solution Tech-
niques for Mixed-Integer Quantile Minimization Problems’. In: INFORMS Journal on Computing
(2024). URL: https://hal.science/hal-03665771.

[15] C. Clavijo López, Y. Crama, T. Pironet and F. Semet. ‘Multi-period distribution networks with
purchase commitment contracts’. In: European Journal of Operational Research 312.2 (2024),
pp. 556–572. DOI: 10.1016/j.ejor.2023.07.007. URL: https://inria.hal.science/hal-0
3715328.

[16] M. Datar, E. Altman and H. Le Cadre. ‘Strategic Resource Pricing and Allocation in a 5G Network
Slicing Stackelberg Game’. In: IEEE Transactions on Network and Service Management 20.1 (2023),
pp. 1932–4537. DOI: 10.1109/TNSM.2022.3216588. URL: https://inria.hal.science/hal-0
3824540.

[17] P. Escalona, A. Angulo, L. Brotcorne, B. Fortz and P. Tapia. ‘Fill-rate service level constrained
distribution network design’. In: International Transactions in Operational Research 31.1 (8th June
2023), pp. 5–28. DOI: 10.1111/itor.13331. URL: https://inria.hal.science/hal-0439837
0.

[18] P. Escalona, L. Brotcorne, B. Fortz and M. Ramirez. ‘Fare inspection patrolling under in-station
selective inspection policy’. In: Annals of Operations Research (13th Nov. 2023). DOI: 10.1007/s10
479-023-05670-2. URL: https://inria.hal.science/hal-04398408.

[19] B. Fortz, M. Mycek, M. Pióro and A. Tomaszewski. ‘Min–max optimization of node-targeted attacks
in service networks’. In: Networks (10th Oct. 2023). DOI: 10.1002/net.22191. URL: https://inr
ia.hal.science/hal-04399113.

[20] W. Gu, C. Archetti, D. Cattaruzza, M. Ogier, F. Semet and M. G. Speranza. ‘Vehicle routing problems
with multiple commodities: A survey’. In: European Journal of Operational Research (2024). DOI:
10.1016/j.ejor.2023.11.032. URL: https://hal.science/hal-04387456.

[21] M. Labbé, M. Landete and M. Leal. ‘Dendrograms, Minimum Spanning Trees and Feature Selection’.
In: European Journal of Operational Research 308.2 (July 2023), pp. 555–567. DOI: 10.1016/j.ejor
.2022.11.031. URL: https://cnrs.hal.science/hal-03727566.

[22] M. Labbé, M. Landete and J. F. Monge. ‘Bilevel integer linear models for ranking items and sets’. In:
Operations Research Perspectives 10 (2023), p. 100271. DOI: 10.1016/j.orp.2023.100271. URL:
https://hal.science/hal-04400123.

[23] C. Legrand, D. Cattaruzza, L. Jourdan and M.-E. Kessaci. ‘Improving neighborhood exploration
into MOEA/D framework to solve a bi-objective routing problem’. In: International Transactions in
Operational Research. Developments in Metaheuristics 30.2 (24th Sept. 2023), pp. 1179–1180. DOI:
10.1111/itor.13223. URL: https://hal.science/hal-04299349.

[24] A. López Sánchez, M. Lujak, F. Semet and H. Billhardt. ‘How to achieve fair and efficient cooperative
vehicle routing?’ In: AI Communications (28th July 2023), pp. 1–23. DOI: 10.3233/AIC-220315.
URL: https://inria.hal.science/hal-04347319.

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[25] L. Marques, A. Sanjab, Y. Mou, H. Le Cadre and K. Kessels. ‘Grid Impact Aware TSO-DSO Market
Models for Flexibility Procurement: Coordination, Pricing Efficiency, and Information Sharing’. In:
IEEE Transactions on Power Systems 38.2 (Mar. 2023), pp. 1918–1931. DOI: 10.1109/tpwrs.2022
.3185460. URL: https://inria.hal.science/hal-04007926.

[26] F. Petropoulos, G. Laporte, E. Aktas, S. A. Alumur, C. Archetti, H. Ayhan, M. Battarra, J. A. Bennell,
J.-M. Bourjolly, J. E. Boylan et al. ‘Operational Research: methods and applications’. In: Journal of
the Operational Research Society (27th Dec. 2023), pp. 1–195. DOI: 10.1080/01605682.2023.225
3852. URL: https://inria.hal.science/hal-04399101.

[27] A. Ratha, P. Pinson, H. Le Cadre, A. Virag and J. Kazempour. ‘Moving from Linear to Conic Markets
for Electricity’. In: European Journal of Operational Research 309.2 (2023), pp. 762–783. URL: https:
//inria.hal.science/hal-03799767.

[28] M. Sangaré, E. Bourreau, B. Fortz, A. Pachurka and M. Poss. ‘Loads scheduling for demand response
in energy communities’. In: Computers and Operations Research 160 (Dec. 2023), p. 106358. DOI:
10.2139/ssrn.4255726. URL: https://hal.science/hal-03880548.

[29] Y. Zhao, D. Cattaruzza, N. Kang and R. Roberti. ‘Synchronized Deliveries with a Bike and a Self-
Driving Robot’. In: Transportation Science (8th Dec. 2023). DOI: 10.1287/trsc.2023.0169. URL:
https://hal.science/hal-04362883.

Invited conferences

[30] P. Torrealba-González, D. Feillet, M. Ogier and F. Semet. ‘Modelling and solving the Joint Order
Batching and Picker Routing Problem including picker congestion’. In: SynchroTrans 2023: Third
International Workshop on Synchronization in Transport. Lille, France, 21st Sept. 2023. URL: https
://hal.science/hal-04391103.

International peer-reviewed conferences

[31]

[32]

J. de Boeck, B. Fortz and S. Schmid. ‘The Case for Stochastic Online Segment Routing under
Demand Uncertainty’. In: 2023 IFIP Networking Conference (IFIP Networking). Barcelone, Spain:
IEEE, 2023, pp. 1–8. DOI: 10.23919/IFIPNetworking57963.2023.10186361. URL: https://in
ria.hal.science/hal-04399123.

J. Le Hénaff and H. Le Cadre. ‘Modeling and Analysis of a Nonlinear Security Game with Mixed
Armament’. In: Conference on Decision and Game Theory for Security (GameSec). Avignon, France,
18th Oct. 2023. URL: https://inria.hal.science/hal-04260233.

[33] C. Legrand, D. Cattaruzza, L. Jourdan and M.-E. Kessaci. ‘Improving MOEA/D with Knowledge
Discovery. Application to a Bi-objective Routing Problem’. In: Lecture Notes in Computer Science
book series. EMO 2023 - Evolutionary Multi-Criterion Optimization. Vol. 13970. Lecture Notes in
Computer Science. Leiden, Netherlands: Springer Nature Switzerland, 9th Mar. 2023, pp. 462–475.
DOI: 10.1007/978-3-031-27250-9_33. URL: https://hal.science/hal-04040436.

[34] A. López Sánchez, M. Lujak, F. Semet and H. Billhardt. ‘Vehicle Routing Problem with Fair Profits
and Time Windows’. In: IEEE Conference on Systems, Man, and Cybernetics. Honolulu, United
States, 1st Oct. 2023. URL: https://inria.hal.science/hal-04395379.

[35] F. Morri, H. Le Cadre, P. Gruet and L. Brotcorne. ‘Multi-Agent Reinforcement Learning for Strategic
Bidding in Two Stage Electricity Markets’. In: IMACS23 - 21st IMACS World congress. Rome, Italy,
11th Sept. 2023. URL: https://hal.science/hal-04199940.

[36] L. Salazar-Zendeja, D. Cattaruzza, M. Labbé and F. Semet. ‘Models for the Interdiction Problem for
the Minimum Spanning’. In: 10th International Congress on Industrial and Applied Mathematics.
Tokyo (JP), Japan, Aug. 2023. URL: https://inria.hal.science/hal-04398295.

[37]

I. Shilov, H. Le Cadre, A. Buši´c, A. Sanjab and P. Pinson. ‘Towards Forecast Markets For Enhanced
Peer-to-Peer Electricity Trading’. In: IEEE SmartGridComm. Glasgow, United Kingdom, 31st Oct.
2023. DOI: 10.1109/smartgridcomm57358.2023.10333930. URL: https://inria.hal.scien
ce/hal-04344943.

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[38] R. Taisant, M. Datar, H. Le Cadre and E. Altman. ‘Learning Market Equilibria Using Performative
Prediction: Balancing Efficiency and Privacy’. In: ECC 2023 - European Control Conference. 2023
European Control Conference (ECC). Bucharest, Romania, June 2023. DOI: 10.23919/ECC57647
.2023.10178247. URL: https://inria.hal.science/hal-03816949.

Conferences without proceedings

[39] O. Briant, H. Cambazard, N. Catusse, D. Cattaruzza, M. Ogier and A.-L. Ladier. ‘Lower bounds for
the joint batching, routing and sequencing problem’. In: 37th annual conference of the Belgian
Operational Research Society (ORBEL37). Liège, Belgium, 25th May 2023. URL: https://hal.sci
ence/hal-04391089.

[40]

S. Calderón Pimienta, G. Munoz, V. Bucarey and F. Semet. ‘Non-convex optimization methods for
finding regret-minimization predictions’. In: 23rd Conference of the International Federation of
Operational Research Societies. Santiago, Chile, 10th July 2023. URL: https://inria.hal.scien
ce/hal-04396099.

[41] F. Morri, H. Le Cadre, P. Gruet and L. Brotcorne. ‘Multi-Agent Reinforcement Learning for Strategic
Bidding in Two Stage Electricity Markets’. In: LION17 (17ème Conférence sur l’apprentissage et
l’optimisation intelligente). Nice, France, 4th June 2023. URL: https://hal.science/hal-04199
919.

[42] L. Salazar-Zendeja, D. Cattaruzza, M. Labbé and F. Semet. ‘The Interdiction Problem for the Min-
imum Spanning Tree’. In: Optimization Workshop in Logistics. Lecce (ITALY), Italy, June 2023. URL:
https://inria.hal.science/hal-04398019.

[43] W. Sun, M. Ogier and F. Semet. ‘A generic model for integrated vehicle routing and driver scheduling
problem’. In: ROADEF 2023 : 24ème congrès de la Société Française de Recherche Opérationnelle et
d’Aide à la Décision. Rennes, France, 20th Feb. 2023. URL: https://hal.science/hal-04391172.

[44] P. Torrealba-González, D. Feillet, M. Ogier and F. Semet. ‘A column generation approach to solve
the Joint Order Batching and Picker Routing Problem including congestion’. In: ROADEF 2023 :
24ème congrès de la Société Française de Recherche Opérationnelle et d’Aide à la Décision. Rennes,
France, 20th Feb. 2023. URL: https://hal.science/hal-04391679.

[45] P. Torrealba-González, M. Ogier, F. Semet and D. Feillet. ‘A column generation approach to solve
the Joint Order Batching and Picker Routing Problem including picker congestion’. In: 37th annual
conference of the Belgian Operational Research Society (ORBEL 37). Liège, Belgium, 25th May 2023.
URL: https://hal.science/hal-04391684.

Scientific book chapters

[46] T. G. Crainic, J. Gonzalez-Feliu, N. Ricciardi, F. Semet and T. van Woensel. ‘Operations Research for
Planning and Managing City Logistics Systems’. In: Handbook on City Logistics and Urban Freight.
2023. DOI: 10.4337/9781800370173.00019. URL: https://inria.hal.science/hal-034640
29.

[47] B. Gendron, P.-V. Khuong and F. Semet. ‘Models and Methods for Two-Level Uncapacitated Facility
Location problems’. In: Contributions to Combinatorial Optimization and Applications. June 2023.
URL: https://inria.hal.science/hal-04384267.

Edition (books, proceedings, special issue of a journal)

[48] A. E. Smith, J. Vera and B. Fortz, eds. Proceedings of the 23rd International Conference of the
International Federation of Operational Research Societies. The 23rd Conference of the International
Federation of Operational Research Societies. International Federation of Operational Research
Societies, 2023. DOI: 10.1287/ifors.2023. URL: https://inria.hal.science/hal-0439913
7.

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Inria Annual Report 2023

Reports & preprints

[49] O. Briant, H. Cambazard, D. Cattaruzza, N. Catusse, A.-L. Ladier and M. Ogier. Lower and upper
bounds for the joint batching, routing and sequencing problem. 30th Mar. 2023. URL: https://hal
.science/hal-04052967.

[50] V. Bucarey, N. González-Blanco, M. Labbé and J. Mesa. On λ-Cent-Dians and Generalized-Center
for Network Design. 2024. DOI: 10.2139/ssrn.4645382. URL: https://hal.science/hal-044
00064.

[51] V. Bucarey, S. Calderón, G. Muñoz and F. SEMET. Decision-focused predictions via pessimistic
bilevel optimization: a computational study. 2023. DOI: 10.48550/arXiv.2312.17640. URL:
https://inria.hal.science/hal-04397536.

[52] P. Bustamante, V. Bucarey, M. Labbé, V. Marianov and F. Ordoñez. Playing Stackelberg Security
Games in Perfect Formulations. 2023. DOI: 10.2139/ssrn.4588054. URL: https://hal.science
/hal-04400100.

[53] S. Dávila-Gálvez, M. Labbé, V. Marianov, F. Ordoñez and F. Semet. A Mixed-Integer Optimization
Formulation for Buyers Formation. 2023. DOI: 10.2139/ssrn.4345341. URL: https://inria.ha
l.science/hal-04347339.

[54] H. Le Cadre, M. Datar, M. Guckert and E. Altman. Learning Market Equilibria Preserving Statistical
Privacy Using Performative Prediction. 23rd June 2023. URL: https://inria.hal.science/hal-
04343535.

[55]

[56]

J. Le Hénaff, J. Boufaied and H. Le Cadre. On Stability of Nonlinear Armsbuilding Security Games.
23rd Jan. 2024. URL: https://inria.hal.science/hal-04411599.

J. Le Hénaff and H. Le Cadre. Modeling and Analysis of a Nonlinear Security Game with Mixed
Armament. 15th June 2023. URL: https://inria.hal.science/hal-04129364.

[57] M. Petris, C. Archetti, D. Cattaruzza, M. Ogier and F. Semet. A heuristic with a performance guarantee
for the Commodity constrained Split Delivery Vehicle Routing Problem. 5th Jan. 2023. URL: https:
//inria.hal.science/hal-03924873.

[58] T. Prunet, N. Absi and D. Cattaruzza. The Intractability of the Picker Routing Problem. 2023. DOI:

10.48550/arXiv.2312.01857. URL: https://hal.science/hal-04394208.

[59]

I. Shilov, H. Le Cadre, A. Buši´c and G. de Almeida Terça. A Stackelberg Game Analysis of Risk-Hedging
Strategies in Decentralized Electricity Markets. 16th Jan. 2023. URL: https://hal.science/hal-0
3674562.

Other scientific publications

[60] M. Petris, C. Archetti, D. Cattaruzza, M. Ogier and F. Semet. Instances and detailed results for
the whole testbed of "A Branch-Price-and-Cut algorithm for the Multi-Commodity two-echelon
Distribution Problem". 19th Jan. 2023. URL: https://inria.hal.science/hal-03946477.

12.3 Cited publications

[61] L. Brotcorne, F. Cirinei, P. Marcotte and G. Savard. ‘A Tabu search algorithm for the network pricing
problem’. In: Comput. Oper. Res. 39.11 (2012), pp. 2603–2611. DOI: 10.1016/j.cor.2012.01.005.
URL: https://doi.org/10.1016/j.cor.2012.01.005.

[62] L. Brotcorne, F. Cirinei, P. Marcotte and G. Savard. ‘An exact algorithm for the network pricing
problem’. In: Discret. Optim. 8.2 (2011), pp. 246–258. DOI: 10.1016/j.disopt.2010.09.003. URL:
https://doi.org/10.1016/j.disopt.2010.09.003.

[63] A. M. Costa, J. Cordeau and B. Gendron. ‘Benders, metric and cutset inequalities for multicom-
modity capacitated network design’. In: Comput. Optim. Appl. 42.3 (2009), pp. 371–392. DOI:
10.1007/s10589-007-9122-0. URL: https://doi.org/10.1007/s10589-007-9122-0.

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[64] A. Frangioni and B. Gendron. ‘0-1 reformulations of the multicommodity capacitated network
design problem’. In: Discret. Appl. Math. 157.6 (2009), pp. 1229–1241. DOI: 10.1016/j.dam.2008
.04.022. URL: https://doi.org/10.1016/j.dam.2008.04.022.

[65] B. Gendron and F. Semet. ‘Formulations and relaxations for a multi-echelon capacitated location-
distribution problem’. In: Comput. Oper. Res. 36.5 (2009), pp. 1335–1355. DOI: 10.1016/j.cor.20
08.02.009. URL: https://doi.org/10.1016/j.cor.2008.02.009.

[66] G. Strack, B. Fortz and F. Riane. ‘Heuristic Approaches for Integrated Production and Distribution
Planning’. In: International Conference on Industrial Engineering and Systems Management. URL:
https://hal.archives-ouvertes.fr/hal-01255550.
<scratchpad>
- Main topic: Research Centre INOCS at the University of Lille
- Key points:
  - Focus on optimization problems with complex structures
  - Research program development
  - Partnerships with institutions like Ecole Centrale de Lille and Université Libre de Bruxelles
  - Application domains: energy, transportation, and telecommunications
  - Use of bilevel programming and game theory
  - Importance of robust/stochastic optimization
- Structure: The document is divided into several sections, including activity report, project-team information, research program, application domains, and dissemination.
- Potential artifacts to ignore: web-related elements, unnecessary links, and formatting tags
</scratchpad>

<final_summary>
The INOCS research centre at the University of Lille focuses on optimization problems with complex structures, developing a research program that involves partnerships with institutions like Ecole Centrale de Lille and Université Libre de Bruxelles. The centre explores application domains in energy, transportation, and telecommunications, employing bilevel programming and game theory to address these challenges. Robust/stochastic optimization is also a key aspect of the research, ensuring that the centre's solutions can handle uncertainty and complexity. Through its work, INOCS aims to develop efficient and effective optimization methods for real-world problems, with implications for industries and societies.
The INOCS research centre at the University of Lille focuses on optimization problems with complex structures, developing a research program that involves partnerships with institutions like Ecole Centrale de Lille and Université Libre de Bruxelles. The centre explores application domains in energy, transportation, and telecommunications, employing bilevel programming and game theory to address these challenges. Robust/stochastic optimization is also a key aspect of the research, ensuring that the centre's solutions can handle uncertainty and complexity. Through its work, INOCS aims to develop efficient and effective optimization methods for real-world problems, with implications for industries and societies.