Search

In the context of the maximum stable set problem, rank inequalities impose that the cardinality of any set of vertices contained in a stable set be, at most, as large as the stability number of the subgraph induced by such a set. Rank inequalities are very general, as they subsume many classical inequalities such as clique, hole, antihole, web, and antiweb inequalities. In spite of their generality, the exact separation of rank inequalities has never been addressed without the introduction of topological restrictions on the induced subgraph and the tightness of their closure has never been investigated systematically. In this work, we propose a methodology for optimizing over the closure of all rank inequalities with a right-hand side no larger than a small constant without imposing any restrictions on the topology of the induced subgraph. Our method relies on the exact separation of a relaxation of rank inequalities, which we call relaxed k-rank inequalities, whose closure is as tight. We investigate the corresponding separation problem, a bilevel programming problem asking for a subgraph of maximum weight with a bound on its stability number, whose study could be of independent interest. We first prove that the problem is [Formula: see text]-hard and provide some insights on its polyhedral structure. We then propose two exact methods for its solution: a branch-and-cut algorithm (which relies on a family of faced-defining inequalities which we introduce in this paper) and a purely combinatorial branch-and-bound algorithm. Our computational results show that the closure of rank inequalities with a right-hand side no larger than a small constant can yield a bound that is stronger, in some cases, than Lovász’s Theta function, and substantially stronger than bounds obtained with standard inequalities that are valid for the stable set problem, including odd-cycle inequalities and wheel inequalities. Summary of Contribution: This paper proposes two original methods for solving a challenging cut-separation problem (of bilevel type) for a large class of inequalities valid for one of the key operations research problems, namely, the max stable set problem. An extensive set of experimental results validates the proposed methods. All the source code and data sets are available online on GitHub.

The paper formulates the problem of a government maximizing tax revenue in presence of profit maximizing perfectly competitive firm as a bilevel programming problem, where the output of the firm is described by theCobb–Douglas production function and the per-unit tax is modeled as an amount per unit product. The government collects tax on output quantity of the firm. Government is the leader and decides about tax amount with the objective of maximizing its tax revenue. Perfectly competitive firm is the follower who, given the leader’s tax decision, decides about input levels and thus output quantity with the objective of maximizing the profit. The first part of the paper considers the case of the Cobb–Douglas production function of two inputs, labor and capital, and derives the optimal decision of the leader and the follower, as well as the exact form of the tax revenue function. Also, it studies the properties of the tax revenue function. This case is illustrated by two numerical examples. The model is then generalized for the case of the Cobb– Douglas production function of any number of inputs.

Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush−Kuhn−Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.

In this paper, we present the problem in which a municipal company operating in the waste management sector willing to encourage users to use differentiated waste collection facilities, designs a utility user function to attain such a goal. The problem is modeled in terms of bilevel optimization where the leader is the municipal firm which aims at maximizing the concurrent fraction of user waste demand thrown in recycling facilities, and the follower are users aiming at maximizing the utility function proposed by the leader. The resulting bilevel model is analysed in terms of stability showing that its optimistic solution value equals the pessimistic solution value. A solution approach is presented. Finally, a computational study shows the effectiveness of our proposal.

The interdependence between electricity and natural gas systems has lately increased due to the wide deployment of gas-fired power plants (GFPPs). Moreover, weather-driven renewables introduce uncertainty in the operation of the integrated energy system, increasing the need for operational flexibility. Recently proposed stochastic dispatch models optimally use the available flexibility and minimize the total expected system cost. However, these models are incompatible with the current sequential market design. We propose a novel method to optimally define the available natural gas volume for power production scheduling, anticipating the real-time flexibility needs. This volume-based model is formulated as a stochastic bilevel program that aims to enhance the inter-temporal coordination of scheduling and balancing operations, while remaining compatible with the sequential clearing of day-ahead and real-time markets. The proposed model accounts for the inherent flexibility of the natural gas system via the proper modeling of linepack capabilities and reduces the total expected system cost by the optimal definition of natural gas volume availability for GFPPs at the forward phase. The volume-based coordination model is compared with a price-based coordination alternative, which was recently proposed. In the latter one, the natural gas price perceived by GFPPs is similarly adjusted to enhance the temporal coordination of scheduling and balancing stages. This comparison enables us to highlight the main properties and differences between the two coordination mechanisms.

We consider the bilevel knapsack problem with interdiction constraints, an extension of the classic 0–1 knapsack problem formulated as a Stackelberg game with two agents, a leader and a follower, that choose items from a common set and hold their own private knapsacks. First, the leader selects some items to be interdicted for the follower while satisfying a capacity constraint. Then the follower packs a set of the remaining items according to his knapsack constraint in order to maximize the profits. The goal of the leader is to minimize the follower’s total profit. We derive effective lower bounds for the bilevel knapsack problem and present an exact method that exploits the structure of the induced follower’s problem. The approach strongly outperforms the current state-of-the-art algorithms designed for the problem. We extend the same algorithmic framework to the interval min–max regret knapsack problem after providing a novel bilevel programming reformulation. Also for this problem, the proposed approach outperforms the exact algorithms available in the literature.

Critical network defense and attack problems, usually modeled as network interdiction, is of great significance. It is of great interest from the interdictor's view to study saturation property of resource allocations. This paper presents a bi-objective shortest path network interdiction model with node interdiction, in which the interdictor seeks to interdict a set of nodes in the network that is Pareto-optimal with respect to two objectives, i.e., maximization of shortest path length and minimization of resources cost. A novel subgraph sequence algorithm is developed to identify the efficient frontier through a sequence of single-objective problems. Novel subgraph decomposition algorithms are proposed to solve single-objective problems. Features and time complexity of those problems and algorithms are analyzed. Moreover, to make a trade-off between the resource investment and the interdiction performance, the definition and the computing method of saturation point are introduced in this paper. Both simulated grid network and real-world transportation network data are used to evaluate the performance of algorithms in numerical experiments. The results show that the subgraph sequence algorithm can achieve the optimal Pareto-frontier of this bi-objective problem effectively.

Compressed natural gas (CNG) main stations are critical components of the urban energy infrastructure for CNG distribution. Due to its high electrification and significant power consumption, researching the economic operation of the CNG main station in demand response (DR)-based electricity pricing environments is crucial. In this paper, the dehydration process is considered in the CNG main station energy consumption model to enhance its participation in DR. A bilevel economic dispatch model for the CNG main station is proposed, considering critical peak pricing. The upper-level and lower-level models represent the energy cost minimization problems of the pre-system and rear-system, respectively, with safety operation constraints. The bilevel programming model is solved using a genetic algorithm combined with a bilevel programming method, which has better efficiency and convergence. The proposed optimization scheme has better control performance and stability, reduces the daily electricity cost by approximately 21.04%, and decreases the compressor switching frequency by 50.00% without changing the CNG filling demand, thus significantly extending the compressor’s service life. Moreover, the average comprehensive power cost of processing one unit of CNG reduces 20.62%.

Reversible lanes constitute an important solutions for sustainable transportation, with the aim to solve the practical problem of reversible lane optimization of urban road networks constrained by adjustment time. Considering the relationship between the number of lanes and the capacity of sections, a mixed-integer bilevel programming model of reversible lane optimization constrained by adjustment time is constructed in order to minimize the total travel time of the system. The results show that the model can effectively obtain the optimal strategy for any number of reversible sections subject to adjustment time constraints. With the increase of the number of reversible sections that can be optimized within the adjustment time, the cumulative reduced system time increases monotonically and the road network optimization effect improves, but as a whole, the optimization effect of the newly added reversible sections in each stage shows a decreasing trend. When the number of reversible sections that can be optimized within the adjustment time reaches a certain number, increasing the number of reversible sections will have a limited further effect on the overall system. For the reversible lane optimization problem of urban road networks, only efficient reversible sections need to be optimized to achieve a good optimization effect.

Spatially separated locations may differ greatly with respect to their electricity demand, available space, and local weather conditions. Thus, the regions that are best suited to operating wind turbines are often not those where electricity is demanded the most. Optimally, renewable generation facilities are constructed where the maximum generation can be expected. With transmission lines limited in capacity though, it might be economically rational to install renewable power sources in geographically less favourable locations. In this paper, a stochastic bilevel optimisation is developed as a mixed-integer linear programme to find the socially optimal investment decisions for generation expansion in a multi-node system with transmission constraints under an emissions reduction policy. The geographic heterogeneity is captured by using differently skewed distributions as a basis for scenario generation for wind speeds as well as different opportunities to install generation facilities at each node. The results reinforce that binding transmission constraints can greatly decrease total economic and emissions efficiency, implying additional incentives to enhance transmission capacity between the optimal supplier locations and large demand centres.

Multilevel optimization problems often arise in various applications (in economics, ecology, power engineering and other areas) when modeling complex systems with a hierarchical structure associated with independent actions of subsystems. The difficulty of analyzing such complex systems requires first of all the study of bilevel models, the management of which would be an integral part of the analysis of more complex systems. In solving bilevel programming problems, an important role is played by the property of partial calmness, the presence of which allows us to reduce the bilevel problem to the classical nonlinear programming problem with a nonsmooth objective function. It is known that linear bilevel programming problems are partially stable. The proof of this property for more complex problems meets difficulties. In particular, our article shows the inaccuracy of some results in this area. The goal of the paper is to obtain some new results in the partial calmness of bilevel programming. In particular, new sufficient conditions for bilevel problems are proved. The results are obtained on the base of Lipschitz-like properties for multivalued mappings. In the paper we propose new sufficient conditions for partial calmness which are based on some modification of the known constraint qualification RCPLD which have been proposed by the researches Andreani, Haeser, Schuverdt and Silva.

The family of critical node detection problems asks for finding a subset of vertices, deletion of which minimizes or maximizes a predefined connectivity measure on the remaining network. We study a problem of this family called the k-vertex cut problem. The problem asks for determining the minimum weight subset of nodes whose removal disconnects a graph into at least k components. We provide two new integer linear programming formulations, along with families of strengthening valid inequalities. Both models involve an exponential number of constraints for which we provide poly-time separation procedures and design the respective branch-and-cut algorithms. In the first formulation one representative vertex is chosen for each of the k mutually disconnected vertex subsets of the remaining graph. In the second formulation, the model is derived from the perspective of a two-phase Stackelberg game in which a leader deletes the vertices in the first phase, and in the second phase a follower builds connected components in the remaining graph. Our computational study demonstrates that a hybrid model in which valid inequalities of both formulations are combined significantly outperforms the state-of-the-art exact methods from the literature.

We provide decision-making models for a manufacturer which plans to produce multiple short life cycle products with the one-shot decision theory. The obtained optimal production quantities are based on the most appropriate scenarios for the manufacturer. Since the models are the bilevel programming problems with the max–min or min–max operator in the lower levels, we propose two approaches to translate them into general single-level optimization problems such that they can be solved via the commonly used optimization methods. The effectiveness of our approaches is examined from the theoretical and computational aspects.

This paper proposes strategic biddings for a consumer demand that participates in both the day-ahead and balancing markets. The strategic behavior of the consumer is represented by the bilevel optimization programming with minimization of consumer costs at the upper level (UL) subject to the co-optimization of energy and reserve in the market clearing process at the lower level problem (LL). Using the Karush-Kuhn-Tucker (KKT) optimality constraints to replace the LL problem, the bilevel model is recast into a single-level mathematical program with equilibrium constraints (MPEC). The resulted model is finally formulated as a mixed-integer linear programming (MILP) problem using the exact linearization technique and Fortuny-Amat transformation to replace bilinear terms and the complementarity constraints, respectively. The results demonstrate a reduction in the electricity consumption payment for the strategic consumer and a decline in social welfare.

Esta tesis está dedicada a un estudio en profundidad del Problema de Tarificación basado en Preferencias (del inglés, Rank Pricing Problem (RPP)) y dos generalizaciones. El RPP es un problema de optimización combinatoria que tiene como objetivo fijar el precio de los productos de una compañía para maximizar su beneficio. En él, intervienen clientes unit-demand, es decir, clientes que están interesados en varios de los productos de la empresa, pero pretenden comprar como mucho uno de ellos. Los clientes tienen un presupuesto fijo y clasifican los productos que les interesan formando un ranking del “mejor” al “peor”. Cuando la compañía fije los precios, cada cliente comprará su producto preferido de entre los que se puede permitir. En el RPP, asumimos que los productos se ofertan en cantidad ilimitada, lo cual encaja si consideramos que la compañía tiene suficientes productos para satisfacer la demanda, o cuando los productos se pueden producir rápidamente con un coste despreciable (por ejemplo, los bienes digitales). Esta tesis doctoral consta de cuatro capítulos. El primero de ellos es un capítulo de introducción al problema y a los conceptos matemáticos presentes en la tesis, mientras que los tres siguientes se centran en cada uno de los problemas estudiados: el RPP y dos generalizaciones. Así, el tercer capítulo está dedicado al estudio del Problema de Tarificación basado en Preferencias con Empates (RPPT por sus siglas en inglés, Rank Pricing Problem with Ties). En esta extensión del problema, asumimos que los clientes pueden expresar su indiferencia entre productos de su interés mediante empates en su lista de preferencia. Y el último capítulo de la tesis comprende el estudio del Problema de Tarificación Capacitado basado en Preferencias o Capacitated Rank Pricing Problem (CRPP) con envidia. En esta extensión, hemos asumido precios de reserva en los clientes que reflejan lo que están dispuestos a pagar por cada producto, en vez de un solo presupuesto por consumidor. No obstante, la principal diferencia es que en el CRPP la compañía tiene un número limitado de productos y puede no ser capaz de satisfacer la demanda de todos los clientes. El objetivo de la tesis es obtener formulaciones lineales enteras mixtas para los tres problemas estudiados, y compararlas teórica y/o computacionalmente. Para ello, la metodología empleada se basa en la propuesta de variables de decisión y restricciones apropiadas que modelicen el problema. El siguiente objetivo es la mejora de estas formulaciones mediante desigualdades válidas que reducen la región factible de la relajación del problema y permiten obtener una mejor cota de la relajación lineal. Y finalmente, un tercer objetivo es la propuesta de algoritmos de resolución para cada uno de estos modelos, y su posterior comparativa mediante la realización de estudios computacionales y resolución mediante optimizadores comerciales. En el Capítulo 2 introducimos dos formulaciones no lineales para el RPP, una que surge de una formulación binivel y otra que está formulada directamente en un solo nivel. Las comparamos teóricamente, linealizamos su función objetivo (que es la misma en ambos casos) de dos formas distintas y proponemos técnicas de preprocesamiento que reducen el tamaño de las instancias fijando variables binarias a cero o a uno. También estudiamos el problema de empaquetamiento asociado a las variables binarias del mejor modelo, con lo que probamos que esta formulación es muy fuerte porque la mayoría de las restricciones que contiene definen facetas del subproblema asociado. Los resultados computacionales son consistentes con nuestra comparación teórica, ya que muestran la superioridad del modelo uninivel. También revelan que se obtienen mejores cotas y un mejor rendimiento en general con una de las linealizaciones propuestas, que se emplea en capítulos posteriores. En el Capítulo 3, proponemos la primera formulación con variables de tres índices para el RPPT. Luego incluimos un método de resolución basado en la introducción de un modelo más débil con un conjunto de variables y restricciones de menor tamaño (el modelo de dos índices), formulación que a continuación fortalecemos añadiendo desigualdades válidas. El segundo método de resolución propuesto está basado en la descomposición de Benders, un método ampliamente utilizado para problemas enteros mixtos. Así, proponemos un Modelo de Benders válido con un conjunto de variables y restricciones pequeño, que reforzamos mediante desigualdades válidas que surgen de la resolución de los subproblemas de Benders. En los experimentos computacionales, observamos que cada uno de los algoritmos de resolución propuestos destaca en una fase de la resolución del problema. En la fase de la relajación lineal, resulta más rápida la adición de cortes en el modelo de dos índices, ya que las desigualdades se pueden separar por productos (incluso si se incluyen más cortes). En la fase entera, sin embargo, el Modelo de Benders lleva a cabo la exploración de nodos más rápido que el otro modelo, probablemente debido a su reducido número de variables y restricciones. El Capítulo 4 comienza introduciendo una formulación con variables de tres índices para resolver el CRPP. Al contrario que en los capítulos precedentes, en este se incluyen varios conjuntos de desigualdades válidas para dicha formulación que utilizan las restricciones de capacidad y nuevas variables binarias. Estos conjuntos se utilizan después cuando se proyecta el modelo de tres índices en el modelo de dos índices, por lo que las desigualdades obtenidas son más difíciles de separar porque dependen de seis conjuntos de parámetros. Además de resolver el problema de separación con Xpress, también separamos teóricamente un conjunto de desigualdades que resulta muy efectivo en la práctica, y lo relacionamos con un conjunto de cortes propuesto para el RPP. La combinación de estas desigualdades con las últimas que proponemos da como resultado un algoritmo muy eficiente que reúne las ventajas de ambas: proporciona unas de las mejores cotas de la relajación lineal y las fases de inclusión de cortes en el nodo raíz y de ramificación son muy rápidas This doctorate is entirely devoted to an in-depth study of the Rank Pricing Problem (RPP) and two generalizations. The RPP is a combinatorial optimization problem which aims at setting the prices of a series of products of a company to maximize its revenue. This problem is specified by a set of unit-demand customers, that is, customers interested in a subset of the products offered by the company which intend to buy at most one of them. To do so, they count on a fixed budget, and they rank the products of their interest from the “best” to the “worst”. Once the prices are established by the company, they will purchase their highest-ranked product among the ones they can afford. In the RPP, it is assumed an unlimited supply of products, which is consistent with a company having enough copies of a product to satisfy the demand, or with a setting where the products can be produced quickly at negligible cost (e.g., digital goods). This dissertation consists of four chapters. The first chapter introduces the RPP problem and the mathematical concepts present in the work, whereas each of the next three chapters tackles the resolution of each of the problems of study: the RPP and two generalizations. Thus, Chapter 3 is dedicated to the Rank Pricing Problem with Ties (RPPT), an extension of the RPP where we consider that customers can express indifference among products in their preference list. And the last chapter of the thesis is devoted to a generalization of the problem that we have named the Capacitated Rank Pricing Problem (CRPP) with envy. For this generalization, we have considered reservation prices of customers for the different products that reflect their willingness to pay, instead of a single budget per customer. However, the main difference is that, in the CRPP, the company has a limited supply of products and might not be able to satisfy all the customers’ requests. This is a realistic assumption that we can find in many companies. The aim of this thesis is the proposal of mixed-integer linear formulations for the three problems of study, and their theoretical and/or computational comparison. The methodology used is based on the introduction of decision variables and adequate restrictions to model the problems. Another objective consists in strengthening the formulations by means of valid inequalities that reduce the feasible region of the relaxed problem and allow us to obtain better linear relaxation bounds. Finally, a third goal is to derive resolution algorithms for each of these models and compare them computationally, using commercial solvers. In Chapter 2, we give two nonlinear formulations for the RPP, one that comes from a bilevel formulation and another one that is directly formulated as a single-level one. We compare them theoretically, linearize their objective functions (which are the same) in two different ways and propose preprocessing techniques that effectively reduce the size of the instances by fixing variables to either zero or one. By studying the Set Packing Problem associated to the binary variables of the strongest model, we prove that this formulation is very tight, since most of its constraints are facet-defining in the corresponding subproblem. The computational results are consistent with our theoretical comparison, given that they show the superiority of the single-level model. They also disclose that one of the linearizations (used in following chapters) outperforms the other. In Chapter 3, we propose the first formulation with three-index variables for the RPPT. Next, we propose a resolution method based on the introduction of a weaker model with much less variables and constraints (the two-index model) and its strengthening by means of valid inequalities. The second resolution method is based on the Benders decomposition, a widely used approach for solving mixed-integer programs. Thus, we introduce a valid Benders Model with a small number of variables and constraints. Next, we reinforce the model dynamically adding valid inequalities obtained solving the Benders subproblems. In the computational testing, each of the resolution algorithms proposed excels in a specific phase. In the linear relaxation phase, the separation procedure designed to add valid inequalities is faster for the two-index model, since these inequalities can be separated by products. In the integer phase, however, the Benders Model outperforms the two-index model in the tree search because the node exploration is faster, probably due to the small number of variables and constraints it has. Chapter 4 begins with the introduction of a model with three-index variables for the CRPP. Unlike in the previous chapters, here the capacity constraints and the inclusion of new variables associated to the capacity allow to derive several sets of valid inequalities for the three-index formulation. These sets are then included in the projection of the three-index formulation into the two-index one, so the resultant inequalities are more difficult to separate because they depend on six sets of parameters. Besides solving the separation problem with Xpress, we theoretically separate a particular set of inequalities that proves to be very effective in practice, and link it with a family proposed for the RPP. The combination of these inequalities with the last set proposed results in a very efficient resolution method that combines the best linear relaxation gap with a rather quick inclusion of cuts in the root node and an effective node search.

The paper proposes a formulation for a generalized Nash equilibrium model which incorporates the strategic biddings of some consumers capable of providing reserve and balancing services in the day-ahead and balancing markets, respectively. The strategic bidding in the electricity market is modelled using a bilevel optimization programming, where the electricity cost of consumers is minimized at the upper level (UL), and the energy and reserve costs in the market clearing process are co-optimized at the lower level (LL). By means of the strong duality theorem, the original bilevel model is transformed into an equivalent single-level mathematical problem with equilibrium constraints (MPEC). The joint problem of all MPECs, one per consumer, constitutes an equilibrium problem with equilibrium constraints (EPEC). The resulting EPEC is finally formulated as an auxiliary mixed-integer linear programming (MILP) problem. To this end, an exact linearization technique and Fortuny-Amat transformation are adopted to substitute the nonlinear terms and the complementarity conditions. In addition, a parametrization technique is used to replace the dual variable associated with the strong duality equation which appears in the EPEC problem. The diagonalization method is also adopted in this part as an ex-post analysis to verify the obtained solutions of the resulted MILP. Finally, a 3-bus illustrative example and the IEEE RTS 24-Bus System and 118-Bus System are considered to investigate the performance of the proposed approach.

Pricing under a consumer choice model has been extensively studied in economics and revenue management. In this paper, we tackle a generalization of the Rank Pricing Problem (RPP), a multi-product pricing problem with unit-demand customers and a ranking-based consumer choice model. We generalize the RPP assuming that each product has a limited amount of copies for sale, and we call this extension the Capacitated Rank Pricing Problem (CRPP). We compare the envy-free allocation of the products (a fairness criterion requiring that customers receive their highest-ranked product given the pricing) with the envy version of the problem. Next, we focus on the CRPP with envy. We introduce two integer linear formulations for the CRPP and derive valid inequalities leveraging the structure of the problem. Afterwards, we develop separation procedures for the families of valid inequalities of greater size. The performance of the formulations and the resolution algorithms developed is tested by means of extensive computational experiments.

Some consumers, particularly households, are unwilling to face volatile electricity prices, and they can perceive as unfair price differentiation in the same local area. For these reasons, nodal prices in distribution networks are rarely employed. However, the increasing availability of renewable resources and emerging price-elastic behaviours pave the way for the effective introduction of marginal nodal pricing schemes in distribution networks. The aim of the proposed framework is to show how traditional non-flexible consumers can coexist with flexible users in a local distribution area. Flexible users will pay nodal prices, whereas non-flexible consumers will be charged a fixed price derived from the underlying nodal prices. Moreover, the developed approach shows how a distribution system operator should manage the local grid by optimally determining the lines to be expanded, and the collected network tariff levied on grid users, while accounting for both congestion rent and investment costs. The proposed model is formulated as a non-linear integer bilevel program, which is then recast as an equivalent single optimization problem, by using integer algebra and complementarity relations. The power flows in the distribution area are modelled by resorting to a second-order cone relaxation, whose solution is exact for radial networks under mild assumptions. The final model results in a mixed-integer quadratically constrained program, which can be solved with off-the-shelf solvers. Numerical test cases based on both 5-bus and 33-bus networks are reported to show the effectiveness of the proposed method.

The Evasive Flow Capturing Problem is defined as the problem of locating a set of law enforcement facilities on the arcs of a road network to intercept unlawful vehicle flows traveling between origin-destination pairs, who in turn deviate from their route to avoid any encounter with such facilities. Such deviations are bounded by a given tolerance. We first propose a bilevel program that, in contrast to previous studies, does not require a priori route generation. We then transform this bilevel model into a single-stage equivalent model using duality theory to yield a compact formulation. We finally reformulate the problem by describing the extreme rays of the polyhedral cone of the compact formulation and by projecting out the auxiliary variables, which leads to facet-defining inequalities and a cut formulation with an exponential number of constraints. We develop a branch-and-cut algorithm for the resulting model, as well as two separation algorithms to solve the cut formulation. Through extensive experiments on real and randomly generated networks, we demonstrate that our best model and algorithm accelerate the solution process by at least two orders of magnitude compared with the best published algorithm. Furthermore, our best model significantly increases the size of the instances that can be solved optimally.

The increasing shares of stochastic renewables bring higher uncertainty in power system operation and underline the need for optimal utilization of flexibility. However, the European market structure that separates energy and reserve capacity trading is prone to inefficient utilization of flexible assets, such as the HVDC interconnections, since their capacity has to be ex-ante allocated between these services. Stochastic programming models that co-optimize day-ahead energy schedules with reserve procurement and dispatch, provide endogenously the optimal transmission allocation in terms of minimum expected system cost. However, this perfect temporal coordination of trading floors cannot be attained in practice under the existing market design. To this end, we propose a decision-support tool that enables an implicit temporal coupling of the different trading floors using as control parameters the inter-regional transmission capacity allocation between energy and reserves and the area reserve requirements. The proposed method is formulated as a stochastic bilevel program and cast as mixed-integer linear programming problem, which can be efficiently solved using a Benders decomposition approach that improves computational tractability. This model bears the anticipativity features of a transmission allocation model based on a pure stochastic programming formulation, while being compatible with the current market structure. Our analysis shows that the proposed mechanism reduces the expected system cost and thus can facilitate the large-scale integration of intermittent renewables.

High variability and unreliable expectations on product yields substantially hinder the industrialization of microorganism derived biochemicals as they present a risk to the profitability and safety of the underlying systems. Therefore, in this work, we propose an optimization approach to determine the lower and upper product yield expectations for the sustainable production of C-phycocyanin. Kinetic modeling is adopted in this study as it is an outstanding tool for fast prototyping, prediction and optimization of chemical and biochemical processes. On the upside, parameters in bioprocess kinetic models are used as a simplification of complex metabolic networks to enable the simulation, design and control of the process. On the downside, this conglomeration of parameters may result in significant model uncertainty. To address this shortcoming, we formulate a bilevel max-min optimization problem to obtain the worst-case scenario of our system given the uncertainty on the model parameters. By constructing parameter confidence ellipsoids, we determined the feasible region along which the parameters can minimize the system’s performance, while nutrient and light controls are used to maximize the biorenewable production. The inner minimization problem is embedded by means of the optimality conditions into the upper maximization problem and hence both are solved simultaneously. Through this approach, we determined pessimistic and optimistic scenarios for the bioproduction of C-phycocyanin and hence compute reliable expectations on the yield and profit of the process.

A bilevel programming problem (BLPP) is a hierarchical optimization problem where the constraint region of the upper level is implicitly determined by the lower level optimization problem. In this paper, a bilevel programming problem is considered in which the objective functions are linear fractional and the feasible region is a convex polyhedron. Linear fractional objectives in BLPP are useful in production planning, financial planning, corporate planning and so forth. Here, the cost coefficient of the objective functions are multi-choice parameters. The multi-choice parameters are replaced using interpolating polynomials. Then, fuzzy programming is used to find a compromise solution of the transformed BLPP. An algorithm is developed to find a compromise solution of BLPP. The method is illustrated with the help of an example.

International audience; In this paper, we present a duality approach using conjugacy for a semivectorial bilevel programming problem (S) where the upper and lower levels are vectorial and scalar respectively. This approach uses the Fenchel–Lagrange duality and is given via a regularization of problem (S) and the operation of scalarization. Then, using this approach, we provide necessary optimality conditions for a class of properly efficient solutions of (S). Finally, sufficient optimality conditions are given for (S) regardless of the duality approach. Examples are given for illustration.

We study connections between optimistic bilevel programming problems and generalized Nash equilibrium problems. We remark that, with respect to bilevel problems, we consider the general case in which the lower level program is not assumed to have a unique solution. Inspired by the optimal value approach, we propose a Nash game that, transforming the so-called implicit value function constraint into an explicitly defined constraint function, incorporates some taste of hierarchy and turns out to be related to the bilevel programming problem. We provide a complete theoretical analysis of the relationship between the vertical bilevel problem and our ``uneven'' horizontal model: in particular, we define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of our game. Furthermore, by referring to some applications in economics, we show that our ``uneven'' horizontal model, in some sense, lies between the vertical bilevel model and a ``pure'' horizontal game.

This paper presents a hierarchical decision-making strategy for the energy management of a smart city. The proposed decision process supports the city energy manager and local policy makers in taking energy retrofit decisions on different urban sectors by an integrated, structured, and transparent management. To this aim, in the proposed decision strategy, a bilevel programming model integrates several local decision-making units, each focusing on the energy retrofit optimization of a specific urban subsystem, and a central decision unit. We solve the hierarchical decision problem by a game theoretic distributed algorithm. We apply the developed decision model to the case study of the city of Bari (Italy), where a smart city program has recently been launched.

International audience; One of the main concerns in management and economic planning is to sell the right product to the right customer for the right price. Companies in retail and manufacturing employ pricing strategies to maximize their revenues. The Rank Pricing Problem considers a unit-demand model with unlimited supply and uniform budgets in which customers have a rank-buying behavior. Under these assumptions, the problem is first analyzed from the perspective of bilevel pricing models and formulated as a non linear bilevel program with multiple independent followers. We also present a direct non linear single level formulation bearing in mind the aim of the problem. Two different linearizations of the models are carried out and two families of valid inequalities are obtained which, embedded in the formulations by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. We also study the polyhedral structure of the models, taking advantage of the fact that a subset of their constraints constitutes a special case of the Set Packing Problem, and characterize all the clique facets. Besides, we develop a preprocessing procedure to reduce the size of the instances. Finally, we show the efficiency of the formulations, the branch-and-cut algorithms and the preprocessing through extensive computational experiments.

The Radio Communications Interdiction Problem (RCIP) seeks to identify the locations of transmitters on the battlefield that will lead to a robust radio communications network by anticipating the effects of intentional radio jamming attacks used by an adversary during electronic warfare. RCIP is a sequential game defined between two opponents that target each other's military units in a conventional warfare. First, a defender locates a limited number of transmitters on the defender's side of the battlefield to optimize the relay of information among its units. After observing the locations of radio transmitters, an attacker locates a limited number of radio jammers on the attacker's side to disrupt the communication network of the defender. We formulate RCIP as a binary bilevel (max-min) programming problem, present the equivalent single level formulation, and propose an exact solution method using a decomposition scheme. We enhance the performance of the algorithm by utilizing dominance relations, preprocessing, and initial starting heuristics. To reflect a more realistic jamming representation, we also introduce the probabilistic version of RCIP where a jamming probability is associated at each receiver site as a function of the prevalent jamming to signal ratios leading to an expected coverage of receivers as an objective function. We approximate the nonlinearity in the jamming probability function using a piecewise linear convex function and solve this version by adapting the decomposition algorithm constructed for RCIP. Our extensive computational results on realistic scenarios show the efficacy of the solution approaches and provide valuable tactical insights. (C) 2019 Elsevier Ltd. All rights reserved.

This paper proposes a biobjective continuous transportation network design problem concerning road congestion charging with the consideration of speed limit. The efficiency of the traffic network and the reduction of pollution in the network environment are improved by designing a reasonable road capacity enhancement and speed limit strategy. A biobjective bilevel programming model is developed to formulate the proposed network design problem. The first target of the upper problem is the optimization of road charging efficiency, and the other target is the total cost of vehicle emissions, these objectives are required to devise the optimal road capacity enhancement scheme, speed limiting schemes for different time periods, and the road pricing scheme. The lower-level problem involving travellers’ route choice behaviours uses stochastic user equilibrium (SUE) theory. Based on the nondominated sorting genetic algorithm, which is applied to solve the bilevel programming model, a numerical example is developed to illustrate the effectiveness of the proposed model and algorithm. The results show that the implementation of congestion charging measures on the congested road sections would help to alleviate road congestion in the transportation network, effectively save transportation infrastructure investment and limited urban land resources, increase fiscal revenue, and open up new sources of funds for urban infrastructure construction.

In the restructured power industry, demand responsiveness is a key factor whose importance will be boosted due to the impetus provided by the development of Smart grids. Within the context of pool-based electricity markets, this paper addresses the incorporation of price-responsive demand in multiperiod energy scheduling driven by consumer payment minimization. Although consumer payment minimization has drawn considerable attention mainly in an operational setting and also recently under a planning framework, available models and solution approaches typically neglect demand-side participation. The proposed scheduling model considers a marginal pricing scheme as well as the effects of both network constraints and intertemporal constraints associated with generation operation. Modeling demand-side participation leads to bilinear payment terms that significantly increase the mathematical complexity of the optimization process. The resulting problema is formulated as a mixed-integer nonlinear bilevel program for which no exact solution technique is currently available. This paper presents a novel methodology by which the original bilevel and bilinear problem is converted into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation is based on the application of duality theory of linear programming, integer algebra, and Karush?Kuhn?Tucker optimality conditions. The proposed approach has been successfully applied to the IEEE 118-bus system.

The U.S. military's ability to project military force is being challenged. This research develops and demonstrates the application of three respective sensor location, relocation, and network intrusion models to provide the mathematical basis for the strategic engagement of emerging technologically advanced, highly-mobile, Integrated Air Defense Systems. First, we propose a bilevel mathematical programming model for locating a heterogeneous set of sensors to maximize the minimum exposure of an intruder's penetration path through a defended region. Next, we formulate a multi-objective, bilevel optimization model to relocate surviving sensors to maximize an intruder's minimal expected exposure to traverse a defended border region, minimize the maximum sensor relocation time, and minimize the total number of sensors requiring relocation. Lastly, we present a trilevel, attacker-defender-attacker formulation for the heterogeneous sensor network intrusion problem to optimally incapacitate a subset of the defender's sensors and degrade a subset of the defender's network to ultimately determine the attacker's optimal penetration path through a defended network.

This work fits in the context of community microgrids, where members of a community can exchange energy and services among themselves, without going through the usual channels of the public electricity grid. We introduce and analyze a framework to operate a community microgrid, and to share the resulting revenues and costs among its members. A market-oriented pricing of energy exchanges within the community is obtained by implementing an internal local market based on the marginal pricing scheme. The market aims at maximizing the social welfare of the community, thanks to the more efficient allocation of resources, the reduction of the peak power to be paid, and the increased amount of reserve, achieved at an aggregate level. A community microgrid operator, acting as a benevolent planner, redistributes revenues and costs among the members, in such a way that the solution achieved by each member within the community is not worse than the solution it would achieve by acting individually. In this way, each member is incentivized to participate in the community on a voluntary basis. The overall framework is formulated in the form of a bilevel model, where the lower level problem clears the market, while the upper level problem plays the role of the community microgrid operator. Numerical results obtained on a real test case implemented in Belgium show around 54% cost savings on a yearly scale for the community, as compared to the case when its members act individually., Comment: 16 pages, 15 figures

We study the problem of computing Stackelberg equilibria in Stackelberg games whose underlying structure is a congestion game, focusing on singleton congestion games, i.e., on congestion games where each player can choose a single resource, and assuming that one of them acts as leader while the other ones act as followers. We provide a comprehensive picture of the computational complexity of finding equilibria in these games, investigating different forms of commitment (pure-strategy and mixed-strategy) and followers' tie-breaking rules (optimistic and pessimistic). We identify two features of such games, namely, identical/different action spaces and monotonic/generic cost functions, by which we provide a complete characterization of the cases in which the equilibrium-finding problem is either easy or hard. In particular, we show that, in the case where the action spaces are different, the cost the leader incurs in an optimistic or pessimistic Stackelberg equilibrium cannot be approximated in polynomial time up to any polynomial factor in the size of the game unless P = NP , independently of the cost functions being monotonic or generic. This result holds even when the commitment is restricted to pure strategies. For general mixed-strategy commitments, we show that a similar result also holds when the players have generic cost functions, even if their action spaces are identical. Furthermore, we prove that the case with identical action spaces and monotonic cost functions is easy. We also improve the efficiency of a polynomial-time algorithm available in the literature for the computation of a socially optimal Nash equilibrium in non-Stackelberg singleton congestion games with identical action spaces and generic cost functions, and we extend it to the computation of a Stackelberg equilibrium for the case where the leader is restricted to playing pure strategies. For the cases in which the problem of finding an equilibrium is hard, we show how, in the optimistic setting where the followers break ties in favor of the leader, the problem can be formulated via mixed-integer linear programming techniques. We also provide an experimental evaluation of our algorithms both on random instances and on instances generated from our inapproximability reductions.

A specialized genetic algorithm applied to the solution of the electric grid interdiction problem is presented in this paper. This problem consists in the interaction of a disruptive agent who aims at maximizing damage of the power system (measured as load shed), and the system operator, who implements corrective actions to minimize system load shed. This problem, also known as “the terrorist threat problem”, is formulated in a bilevel programming structure and solved by means of a genetic algorithm. The solution identifies the most vulnerable links of the network in terms of a terrorist attack, providing signals for future reinforcement of the network or more strict surveillance of critical elements. The proposed approach has been tested on three case studies: a didactic five-bus power system, a prototype of the Colombian power system and the IEEE Reliability Test System. Results show the robustness and applicability of the proposed approach.

In this paper, we study a capacitated facility location problem with two decision makers. One (say, the leader) decides on which subset of facilities to open and the capacity to be installed in each facility with the goal of minimizing the overall costs; the second decision maker (say, the follower), once the facilities have been designed, aims at maximizing the profit deriving from satisfying the demands of a given set of clients beyond a certain threshold imposed by the leader. The leader can foresee but cannot control the follower’s behavior. The resulting mathematical formulation is a discrete–continuous bilevel optimization problem. We propose a decomposition approach to cope with the bilevel structure of the problem and the integrality of a subset of variables under the control of the leader. Such a proposal has been tested on a set of benchmark instances available in the literature.

The electricity market clearing process can be affected to varying degrees by norms set by regulators. One possible rule is the Uniform Purchase Price, which is implemented, for example, in the Italian day-ahead market with the name of Prezzo Unico Nazionale, which literally means unique national price. This rule requires that all the consumers pay the same price in all the market zones. On the contrary, producers receive the zonal prices, which may differ from one zone to another. As a consequence, traditional market clearing techniques cannot be employed because of this difference in the paid and received price, and current state-of-the-art methods still rely on heuristic search procedures. Starting from a non-linear mixed integer bilevel formulation of the clearing process in presence of uniform purchase price, this paper shows how to obtain a mixed integer linear programming model, which is computationally tractable and able to solve exactly the uniform purchase price problem. Numerical results are reported by testing the algorithm using real data from the Italian day-ahead market.

This paper addresses strategic decision making issues for the energy management of urban street lighting. We propose a hierarchical decision procedure that supports the energy manager in determining the optimal energy retrofit plan of an existing public street lighting system throughout a wide urban area. A bi-level programming model integrates several decision making units, each focusing on the energy optimization of a specific limited zone lighting system, and a central decision unit, aiming at a fair distribution of actions among these various systems, while ensuring an efficient use of public funds. We apply the technique to the case study of the city of Bari (Italy), to demonstrate the applicability and efficiency of the proposed optimization model.

We introduce a model for analyzing the upgrade of the national transmission grid that explicitly accounts for responses given by the power producers in terms of generation unit expansion. The problem is modeled as a bilevel program with a mixed integer structure in both upper and lower level. The upper level is defined by the transmission company problem which has to decide on how to upgrade the network. The lower level models the reactions of both power producers, who take a decision on new facilities and power output, and Market Operator, which strikes a new balance between demand and supply, providing new Locational Marginal Prices. We illustrate our methodology by means of an example based on the Garver’s 6-bus Network.

The Continuous Network Design Problem (CNDP) is recognized to be one of the most difficult problems in transportation field since the bilevel formulation of the CNDP is nonconvex. On the other hand, the computation time is crucial importance for solving the CNDP because the algorithms implemented on real sized networks require solving traffic assignment model many times, which is the most time consuming part of the solution process. Although the methods developed so far are capable of solving the CNDP, an efficient algorithm, which is able to solve the CNDP with less number of User Equilibrium (UE) assignments, is still needed. Therefore, this paper deals with solving the CNDP using MOdified Differential Evolution (MODE) algorithm with a new local search and mutation operators. For this purpose, a bilevel model is proposed, in which the upper level problem deals with minimizing the sum of total travel time and investment cost of link capacity expansions, while at the lower level problem, UE link Bows are determined by Wardrop's first principle. A numerical example is presented to compare the proposed MODE algorithm with some existing methods. Results showed that the proposed algorithm may effectively be used in order to reduce the number of UE assignments in solving the CNDP. (C) 2013 The Authors. Published by Elsevier Ltd.

We present a global optimization algorithm, Branch-and-Sandwich, for optimistic bilevel programming problems that satisfy a regularity condition in the inner problem. The functions involved are assumed to be nonconvex and twice continuously differentiable. The proposed approach can be interpreted as the exploration of two solution spaces (corresponding to the inner and the outer problems) using a single branch-and-bound tree. A novel branching scheme is developed such that classical branch-and-bound is applied to both spaces without violating the hierarchy in the decisions and the requirement for (global) optimality in the inner problem. To achieve this, the well-known features of branch-and-bound algorithms are customized appropriately. For instance, two pairs of lower and upper bounds are computed: one for the outer optimal objective value and the other for the inner value function. The proposed bounding problems do not grow in size during the algorithm and are obtained from the corresponding problems at the parent node.

Este artículo presenta una nueva técnica de análisis de vulnerabilidad en sistemas de potencia bajo múltiples contingencias. El modelo bajo estudio es conocido como el "Problema del Terrorista". El principal aporte de este trabajo es la formulación y solución de la versión AC de este problema, lo que permite identificar los elementos más críticos del sistema de potencia y dar señales tempranas al operador, asociadas a la vulnerabilidad del sistema de potencia. Adicionalmente, la versión AC del modelo permite obtener resultados más realistas que la versión DC tradicional ya que considera el efecto de la potencia reactiva y los niveles de tensión en las barras del sistema. El modelo propuesto se solucionó mediante una técnica metaheurística híbrida que combina algoritmos genéticos y búsqueda local. Los resultados obtenidos utilizando el sistema de prueba IEEE RTS de 24 barras muestran la pertinencia y aplicabilidad de la metodología propuesta. This paper presents a new technique for vulnerability analysis in power systems under multiple contingencies. The model under study is known as the "Terrorist Problem". The main contribution of this work is the formulation and solution of the AC version of this problem, which allows identifying the most critical elements of the power system and gives early signals to the system operator regarding the vulnerability of the system. Furthermore, the AC version of the model allows obtaining more realistic results than the traditional DC model, due to the fact that such version considers the effect of reactive power and voltage magnitudes in the system buses. The proposed model is solved by means of a hybrid metaheuristic technique that combines genetic algorithms with local search. The results obtained using the IEEE RTS - 24 bus test system show the relevance and applicability of the proposed methodology.

This paper deals with day-ahead static security assessment with respect to a postulated set of contingencies while taking into account uncertainties about the next day system conditions. We propose a heuristic approach to compute the worst-case under operation uncertainty for a contingency with respect to overloads. We formulate this problem as a non-convex nonlinear bilevel program that we solve approximately by a heuristic approach which relies on the solution of successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. The method aims at revealing those combinations of uncertainties and contingencies for which the best combination of preventive and corrective actions would not suffice to ensure security. Extensive numerical results on a small, a medium, and a very large system prove the interest of the approach.

The paper considers some new results of creating load-carrying systems that have uprated strength, rigidity and safety, and therefore are called geometrically hardening systems. Indicated structural features are found exactly with allowance for geometrical nonlinearity. Material deforming diagrams can be non-monotonic and non-smooth, and constraints can be unilateral, with gaps. The optimization mathematic models of structures as discrete mechanical systems withstanding dead load, monotonic or cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the bilevel mathematic programming problem statement. Here is given a set of criteria for plastic yielding stability of structures, including for non-smooth and non-convex problems of optimization. In the paper an example of using the proposed methods is presented and geometrically hardening system is taken into account.

Railway dispatchers reschedule trains in real-time in order to limit the propagation of disturbances and to regulate traffic in their respective dispatching areas by minimizing the deviation from the off-line timetable. However, the decisions taken in one area may influence the quality and even the feasibility of train schedules in the other areas. Regional control centers coordinate the dispatchers’ work for multiple areas in order to regulate traffic at the global level and to avoid situations of global infeasibility. Differently from the dispatcher problem, the coordination activity of regional control centers is still underinvestigated, even if this activity is a key factor for effective traffic management. This paper studies the problem of coordinating several dispatchers with the objective of driving their behavior towards globally optimal solutions. With our model, a coordinator may impose constraints at the border of each dispatching area. Each dispatcher must then schedule trains in its area by producing a locally feasible solution compliant with the border constraints imposed by the coordinator. The problem faced by the coordinator is therefore a bilevel programming problem in which the variables controlled by the coordinator are the border constraints. We demonstrate that the coordinator problem can be solved to optimality with a branch and bound procedure. The coordination algorithm has been tested on a large real railway network in the Netherlands with busy traffic conditions. Our experimental results show that a proven optimal solution is frequently found for various network divisions within computation times compatible with real-time operations., Procedia - Social and Behavioral Sciences, 17

In this work, we reformulate the inverse optimal value problem equivalently as a corresponding nonlinear bilevel programming (BLP) problem. For the nonlinear BLP problem, the duality gap of the lower level problem is appended to the upper level objective with a penalty, and then a penalized problem is obtained. On the basis of the concept of partial calmness, we prove that the penalty function is exact. Then, an algorithm is proposed and an inverse optimal value problem is resolved to illustrate the algorithm.

This paper considers a type of biobjective bilevel programming problem, which is derived from a single objective bilevel programming problem via lifting the objective function at the lower level up to the upper level. The efficient solutions to such a model can be considered as candidates for the after optimization bargaining between the decision-makers at both levels who retain the original bilevel decision-making structure. We use a popular multiobjective evolutionary algorithm, NSGA-II, to solve this type of problem. The algorithm is tested on some small-dimensional benchmark problems from the literature. Computational results show that the NSGA-II algorithm is capable of solving the problems efficiently and effectively. Hence, it provides a promising visualization tool to help the decision-makers find the best trade-off in bargaining.

In order to consider the inverse optimal value problem under more general conditions, we transform the inverse optimal value problem into a corresponding nonlinear bilevel programming problem equivalently. Using the Kuhn–Tucker optimality condition of the lower level problem, we transform the nonlinear bilevel programming into a normal nonlinear programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Then we give via an exact penalty method an existence theorem of solutions and propose an algorithm for the inverse optimal value problem, also analysis the convergence of the proposed algorithm. The numerical result shows that the algorithm can solve a wider class of inverse optimal value problem.

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem. In this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative, the lower level one is linear and the common constraint region is a bounded polyhedron. After replacing the lower level problem by its Karush–Kuhn–Tucker conditions, the existence of an extreme point which solves the problem is proved by using a penalty function approach. Besides, an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution. Finally, we generalise the problem by including upper level constraints which involve both level variables.

Inspired by the optimal value approach, we propose a new reformulation of the optimistic Bilevel programming Problem (BP) as a suitable Generalized Nash Equilibrium Problem (GNEP). We provide a complete analysis of the relationship between the original hierarchical BP and the corresponding "more democratic" GNEP. Moreover, we investigate solvability and convexity issues of our reformulation. Finally, relying on the vast literature on solution methods for GNEPs, we devise a new effective algorithmic framework for the solution of signicant classes of BPs.

This paper deals with the market-bidding problem of a cluster of price-responsive consumers of electricity. We develop an inverse optimization scheme that, recast as a bilevel programming problem, uses price-consumption data to estimate the complex market bid that best captures the price-response of the cluster. The complex market bid is defined as a series of marginal utility functions plus some constraints on demand, such as maximum pick-up and drop-off rates. The proposed modeling approach also leverages information on exogenous factors that may influence the consumption behavior of the cluster, e.g., weather conditions and calendar effects. We test the proposed methodology for a particular application: forecasting the power consumption of a small aggregation of households that took part in the Olympic Peninsula project. Results show that the price-sensitive consumption of the cluster of flexible loads can be largely captured in the form of a complex market bid, so that this could be ultimately used for the cluster to participate in the wholesale electricity market.

In this paper, we introduce the group decision problems in a bilevel programming structure, and its corresponding optimization with equilibrium constraints (MPEC for short) problems. For these models, we establish new existence results, which extend some known results to infinite-dimensional space setting. We also establish the links between group decision problems in a bilevel programming structure and its corresponding MPEC problems in Banach spaces. An interesting example about the mean-variance portfolio optimization is given and the existence and uniqueness results for its corresponding MPEC problems are obtained.