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:

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.

The research program development of INOCS is to move alternatively:

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.

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 types of decision 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 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. 59, 60, Gendron et al. 61, 62, 63, and Strack et al. 64). However, these are preliminary attempts and a number of challenges regarding modeling and methodological issues have still to be met.

A classical optimization problem can be formulated as follows:

In this problem,

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

In this model,

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

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 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

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.

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 mathematicaloptimization
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
non convexity and non differentiability. 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.

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 cars 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 has a bilevel one where the lower lever 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 lever represents the choice of users in a preference list.

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.

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.

The research works developed in the INOCS team have environmental and societal impacts through the application areas it targets. 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 smartgrid 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.

The following awards have been obtained in 2022:

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.

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.

During the year 2022, we addressed different problems/challenges related to the three lines of research: large scale complex structure optimization, bilevel programming, robust/stochastic programming. The main contributions are summarized in the next sections. In addition, besides these contributions, additional results(20,22, 23) were obtained which are not discussed hereafter in order to keep the presentation focused on the main achievements.

Several classes of models have been proposed in the literature for the Steiner tree problem with hop constraints. One class is characterized by having hop‐indexed arc variables. Although such models have proved to have a very strong linear programming bound, they are not easy to use because of the huge number of variables. This has motivated some studies with models involving fewer variables that use, instead of the hop‐indexed arc variables, hop‐indexed node variables. We contextualized the linear programming relaxation of these node‐based models in terms of the linear programming relaxation of known arc‐based models. We showed that the linear programming relaxation of a general node‐based model is implied by the linear programming relaxation of a straightforward arc‐based model 17.

Picking is the process of retrieving products from inventory. It is considered the most expensive of warehouse management operations. In INOCS, we addressed the Joint Order Batching and Picker Routing Problem (JOBPRP) that is a challenging optimization problem with two integrated decisions: customer orders are grouped into batches (order batching problem) that are collected by pickers who travel the shortest possible distance (picker routing problem). Human pickers often perform picking, so we proposed to explicitly consider human factors in the JOBPRP, by first studying the consideration of congestion effects when several pickers share the same space at the same time 42, 31. These congestion situations are really stressful for the pickers, and considering them in mathematical models is really challenging since a temporal aspect must be included.

We also started to address an extension of the JOBPRP that includes the sequencing question, i.e. the additional assignment and sequencing of batches for each picker to meet the required deadlines of orders. We show that a bin-packing formulation permits solving the problem with a column generation approach efficiently 32.

Another relevant problem we study in INOCS is the Operational Storage Location Assignment Problem, which asks to optimize the location of products in warehouses to minimize the distance walked by the picker 27.

Planning transportation operations within a supply chain is a difficult task often outsourced to logistics providers. At the tactical level, the problem of distributing products through a multi-echelon network is defined in the literature as the Logistics Service Network Design Problem (LSNDP). To solve the LSNDP, we propose a solution approach based on Benders decomposition. In a previous paper 58, we proposed an enhanced Benders decomposition algorithm for solving the LSNDP, which consists in strengthening the master problem with variables and constraints that model the need to route a super-product derived from the aggregation of all the products to be transported. We developed a more elaborated algorithmic strategy that exploits this partial Benders decomposition by intelligently varying the amount of subproblem information used to formulate the master problem. We refer to this strategy as Meta Partial Benders Decomposition (Meta-PBD). Meta-PBD operates in two steps, with the first aiming to explore different areas within the feasible region of the original problem and to quickly determine high-quality solutions. To do so, the number of super-products used to formulate the master problem changes dynamically while respecting a threshold value to ensure computational tractability. Next, a second phase aims to close the optimality gap. This second phase increases the amount of subproblem information used to formulate the master problem, such that the latter becomes provably equivalent to the original problem. While this master problem is computationally challenging, high-quality solutions generated through the first phase enable many nodes of the resulting branch-and-bound search tree to be pruned, accelerating convergence 12.

Vehicle Routing Problems (VRPs) are classical optimization problems in transportation and logistics. In INOCS, we address complex routing problems generalizing the VRP or combining the VRP with another optimization problem. We studied an extension of the VRP in a context where customers require several commodities that can be transported in the same vehicle, and each customer is allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. The problem is coined as the Commodity constrained Split Delivery VRP (C-SDVRP). We developed a heuristic column generation with performance guarantee to solve the C-SDVRP 37. We also studied an extension of the C-SDVRP in a two-echelon context and multiple intermediate depots. The first echelon considers collecting several commodities with direct trips while the second is a multi-depot version of the C-SDVRP. To solve this complex problem, we first proposed a generic sequential approach with a comparison of different strategies 18. Then, we also developed an exact branch-price-and-cut algorithm to solve the problem 39.

Another extension of the VRP that we addressed is an integrated production scheduling problem and multi-trip VRPTW, where the products have a limited lifespan so they have to be delivered shortly after their production. Hence, the scheduling and the routing problems are really interrelated, and finding feasible solutions with a sequential approach is not trivial. This problem finds an application in home chemotherapy with a limited lifespan of the drugs. To solve this problem, we developed a dedicated large neighborhood search approach where production and routing sequences are iteratively modified while a linear program is used to determine optimal start times of the production and routing tasks 44.

Last, we explore the operational planning and the real-time management of a fleet of highly automated agriculture vehicles that perform tasks throughout multiple fields potentially owned by different farmers and/or enterprises. In this context, the concepts of fairness and equity must be considered to balance the execution of tasks between vehicles and also between farmers. We studied new variants of the operational planning problem that maximize utilitarian, egalitarian, and elitist social welfare and balance workload and efficiency of the fleet 26.

Infrastructure network design constitutes a major step in the planning of a transportation network whose purpose is to improve the mobility of the inhabitants of a city or metropolitan area. In the area of passengers transportation, the aim is to get the infrastructure close to potential customers. In this case, one might select a sub(network) from an underlying network to capture or cover as much traffic for a reasonable construction cost. The paper 14 is devoted to this problem, and considers the Maximum Covering Network Design Problem (MC) as well as the closely related Partial Covering Network Design Problem (PC), in which one minimizes the network design cost for building the network under the constraint that a minimum percentage of the total traffic demand is covered. Models for problems (MC) and (PC), as well as exact methods based on Benders decomposition are provided and compared through computational experiments.

Feature selection is an important issue to avoid overfitting when applying a support vector machine (SVM) approach. The classical SVM model minimizes a compromise between the structural risk and the empirical risk. In 11, we consider the Support Vector Machine with feature selection and we design and implement a bi-objective evolutionary algorithm for approximating the Pareto optimal frontier of the two objectives.

With the emerging deregulated electricity markets, a part of the electricity trading takes place in day-ahead markets where producers and retailers place bids in order to maximize their profit. We present a price-maker model for strategic bidding from the perspective of a producer in Price Coupled Regions (PCR) considering a capacitated transmission network between local day-ahead markets. The aim for the bidder is to establish a production plan and set its bids taking into consideration the reaction of the market. We consider the problem as deterministic, that is, the bids of the competitors are known in advance. We are facing a bilevel optimization problem where the first level is a Unit Commitment problem, modeled as a Mixed Integer Linear Program (MILP), and the second level models a market equilibrium problem through a Linear Program. The problem is first reformulated as a single level problem. Properties of the optimal spot prices are studied to obtain an extended formulation that is linearized and tightened using new valid inequalities. Several properties of the spot prices allow to reduce significantly the number of binary variables. Two novel heuristics are proposed 13.

In 52, we investigate equilibrium problems arising in various decentralized designs of the electricity market involving risk-averse prosumers. The prosumers have the possibility to hedge their risks through financial contracts that they can trade with peers or purchase from an insurance company. We build several market designs of increasing complexity, from a one-stage market design with inter-agent financial contract trading to a Stackelberg game where an insurance company acts as a leader and prosumers are followers. We derive risk-hedging pricing scheme for each model and show that the Stackelberg game pessimistic formulation might have no solution. We propose an equivalent reformulation as a
parametrized generalized Nash equilibrium problem, and characterize the set of equilibria. We prove that the insurance
company can design price incentives that guarantee the existence of a solution of the pessimistic formulation, which is

We consider the problem faced by a retail chain that must select what mutual-substitute items to display in each one of its stores to maximize revenues. The number of items cannot exceed the limit space capacity of each store. Customers purchase the one product that maximizes their utility, which depends on the product price, travel cost to the store, and reservation price, known to the retailer. The retailer solves a mixed-integer bilevel optimization problem, which can be formulated as a single-level optimization problem. In 16, we propose Branch and Cut and Cut and Branch methods and include a family of valid inequalities to solve the problem.

In 15, 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.

During the last decades, the European gas market has undergone ongoing liberalization, resulting in the so-called entry-exit market system. The main goal of this market reorganization is the decoupling of trading and actual gas transport. To achieve this goal within the European entry-exit market, gas traders interact with transport system operators (TSOs) via bookings and nominations. A booking is a capacity-right contract in which a trader reserves a maximum injection or withdrawal capacity at an entry or exit node of the TSO’s network. On a day-ahead basis, these traders are then allowed to nominate an actual load flow up to the booked capacity. To this end, the traders specify the actual amount of gas to be injected to or withdrawn from the network such that the total injection and withdrawal quantities are balanced. On the other hand, the TSO is responsible for the transport of the nominated amounts of gas. By having signed the booking contract, the TSO guarantees that the nominated amounts can actually be transported through the network. More precisely, the TSO needs to be able to transport every set of nominations that complies with the signed booking contracts. Thus, an infinite number of possible nominations must be anticipated and checked for feasibility when the TSO accepts bookings. As a consequence, the entry-exit market decouples trading and transport. However, it also introduces many new challenges, e.g. the checking of feasibility of bookings or the computation of bookable capacities on the network.

In 21, we consider networks with linearly modeled active elements such as compressors and control valves that do not lie on cycles of the network. Since these active elements allow the TSO to control the gas flow, the single-level approaches from the literature are no longer applicable. We thus present a bilevel approach to decide the feasibility of bookings in networks with active elements. Besides the classical Karush–Kuhn–Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations, which also lead to novel characterizations of feasible bookings in active networks. We compare the performance of our methods by a case study based on data from the GasLib.

In this work 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 real-world 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 46.

In blockchains, transaction fees are fixed by the users. The probability for a transaction to be processed quickly increases with the fee level. We studied the transaction fee optimization problem in the Ethereum blockchain. This problem consists of determining the minimum price a user should pay so that its transaction is processed with a given probability in a given amount of time. To reach this goal, we define a new solution method based on a Monte Carlo approach to predict the probability that a transaction will be mined within a given time limit. Numerical results on real data highlight the quality of the results 19.

We consider 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, 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

Urban hub (2019-2023) Development of an integrated tool for warehouse management and delivery to the end customer: www.urbanhub.fr.

INRIA Défi with OVH Cloud (2021-2025). Until now, cloud computing operators, such as OVHcloud, have applied pricing strategies driven by the reservation of
virtualized resources. More precisely, OVHcloud offers two types of services to its customers: VPS (virtual private server)
and Public Cloud. VPS is a cost-effective solution for pre-production and production environments that do not require constant performance. The PublicCloud of OVHcloud
offers a multi-server infrastructure with high machine availability.
Unfortunately, the resources reserved in the Public Cloud are underutilized, which can lead to energy inefficiency in the
infrastructure, while the VPS favors an over-allocation of hardware resources, not allowing
resources, which does not provide any guarantee of performance for customers. The research activity in this project aims at identifying a viable balance between these 2 options to allow customers to benefit from guaranteed performance while minimizing
the energy footprint of the OVHcloud infrastructure.
In particular, we want to determine discounts to offer to customers to encourage them to free up resources when they do not need them,
to offer these available resources to other customers-or services-while smoothing the
demand.

Through this new offer, and its dynamic pricing, we wish to maintain a high performance criterion while eliminating the waste of underutilized resources.

This problem is a hierarchical decision making process between a leader (OVH) and followers (the two type of customers). Bilevel optimizations models are defined and solved to answer these questions. The collaboration with the INRIA Spirals team aims to measure cloud services energy consumptions.

In the medium term, the integration of renewable energy production in the demand smoothing process could be another research issue for this work. This will lead to the resolution of stochastic bilevel optimization problems. www.inria.fr/fr/inria-ovhcloud

CHIST-ERA SEC-OREA project: “Supporting Energy Communities-Operational Research and
Energy Analytics”. (2020 – 2023)
SEC-OREA aims to enable local energy communities (LECs) to participate in the decarbonisation of the energy sector by developing advanced efficient algorithms and analytics technologies.

Partners: INRIA- INOCS (France), Université Libre de Bruxelles (Belgique), Uuniversity college Dublin (Ireland), Riga technical University (Lithuania)

ANR project AGIRE (2020-2024) – Decision system for smart management of resources in warehouses.

In collaboration with Ecole des Mines de Saint-Etienne (Gardanne), IFSTTAR (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.

STaRS grant from the région Hauts-de-France SITAR (2022-2025): “Impact of Information Structures on Services Pricing”. The objective of SITAR is to refine the approach by menus with levels of priority. The problem will be formalized as a decision-dependent game, involving on the one side end users
which minimize their cost while satisfying a set of local and coupling constraints.
Their nominal demand constitutes sensitive information, that
they might want to keep private, and on the other side a data aggregator, which aims to learn the end users’ private information.
The end users might have incentives to report biased and noisy
readings to preserve their privacy, which creates shifts in their
strategies. The contributions will be on (1) the methodological side, to advance the understanding of theoretical properties of decision-dependent games, (2) the alogrithmic side to develop distributed algorithms enabling to approximate equilibria, (3) on the service pricing side, to understand how local objectives like individual privacy might impact the optimal design of menus.

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, Mathematical Programming Computation, Networks, Omega, Operations Research, Optimization and Engineering, RAIRO - Operations Research, Transportation Science, IEEE Transactions on Automatic Control: Luce Brotcorne, Diego Cattaruzza, Bernard Fortz, Martine Labbé, Hélène Le Cadre, Maxime Ogier, Frédéric Semet.