Matheuristics for robust optimization: application to real-world problems

In the field of optimization, the perspective that the problem data are subject to uncertainty is gaining more and more interest. The uncertainty in an optimization problem represents the measurement errors during the phase of collecting data, or unforeseen changes in the environment while implementing the optimal solution in practice. When the uncertainty is ignored, an optimal solution according to the mathematical model can turn out to be far from optimal, or even infeasible in reality. Robust optimization is an umbrella term for mathematical modelling methodologies focused on finding solutions that are reliable against the data perturbations caused by the uncertainty. Among the relatively more recent robust optimization methodologies, an important concept studied is the degree of conservativeness, which can be explained as the amount of targeted reliability against the uncertainty while looking for a solution. Because the reliability and solution cost usually end up being conflicting objectives, it is important for the decision maker to be able to configure the conservativeness degree, so that the desired balance between the cost and reliability can be obtained, and the most practical solution can be found for the problem at hand. The robust optimization methodologies are typically proposed within the framework of mathematical programming (i.e. linear programming, integer programming). Thanks to the nature of mathematical programming, these methodologies can find the exact optimum, according to the various solution evaluation perspectives they have. However, dependence on mathematical programming might also mean that such methodologies will require too much memory from the computer, and also too much execution time, when large-scale optimization problems are considered. A common strategy to avoid the big memory and execution time requirements of mathematical programming is to use metaheuristic optimization algorithms for solving large problem instances.In this research, we propose an approach for solving medium-to-large-sized robust optimization problem instances. The methodology we propose is a matheuristic (i.e. a hybridization of mathematical programming and metaheuristic). In the matheuristic approach we propose, the mathematical programming part handles the uncertainty, and the metaheuristic part handles the exploration of the solution space. Since the exploration of the solution space is entrusted onto the metaheuristic search, we can obtain practical near-optimal solutions while avoiding the big memory and time requirements that might be brought by pure mathematical programming methods. The mathematical programming part is used for making the metaheuristic favor the solutions which have more protections against the uncertainty. Another important characteristic of the methodology we propose is concurrency with information exchange: we concurrently execute multiple processes of the matheuristic algorithm, each process taking the uncertainty into account with a different degree of conservativeness. During the execution, these processes exchange their best solutions. So, if a process is stuck on a bad solution, it can realize that there is a better solution available thanks to the information exchange, and it can get unstuck. In the end, the solutions of these processes are collected into a solution pool. This solution pool provides the decision maker with alternative solutions with different costs and conservativeness degrees. Having a solution pool available at the end, the decision maker can make the most practical choice according to the problem at hand. In this thesis, we first discuss our studies in the field of robust optimization: a heuristic approach for solving a minimum power multicasting problem in wireless actuator networks under actuator distance uncertainty, and a linear programming approach for solving an aggregate blending problem in the construction industry, where the amounts of components found in aggregates are subject to uncertainty. These studies demonstrate the usage of mathematical programming for handling the uncertainty. We then discuss our studies in the field of matheuristics: a matheuristic approach for solving a large-scale energy management problem, and then a matheuristic approach for solving large instances of minimum power multicasting problem. In these studies, the usage of metaheuristics for handling the large problem instances is emphasized. In our study of solving minimum power multicasting problem, we also incorporate the mechanism of information exchange between different solvers. Later, we discuss the main matheuristic approach that we propose in this thesis. We first apply our matheuristic approach on a well-known combinatorial optimization problem: capacitated vehicle routing problem, by using an ant colony optimization as the metaheuristic part. Finally, we discuss the generality of the methodology that we propose: we suggest that it can be used as a general framework on various combinatorial optimization problems, by choosing the most appropriate metaheuristic algorithm according to the nature of the problem

Exact and Heuristic Hybrid Approaches for Scheduling and Clustering Problems

This thesis deals with the design of exact and heuristic algorithms for scheduling and clustering combinatorial optimization problems. All the works are linked by the fact that all the presented methods arebasically hybrid algorithms, that mix techniques used in the world of combinatorial optimization. The algorithms are all efficient in practice, but the one presented in Chapter 4, that has mostly theoretical interest. Chapter 2 presents practical solution algorithms based on an ILP model for an energy scheduling combinatorial problem that arises in a smart building context. Chapter 3 presents a new cutting stock problem and introduce a mathematical formulation and a heuristic solution approach based on a heuristic column generation scheme. Chapter 4 provides an exact exponential algorithm, whose importance is only theoretical so far, for a classical scheduling problem: the Single Machine Total Tardiness Problem. The relevant aspect is that the designed algorithm has the best worst case complexity for the problem, that has been studied for several decades. Furthermore, such result is based on a new technique, called Branch and Merge, that avoids the solution of several equivalent sub-problems in a branching algorithm that requires polynomial space. As a consequence, such technique embeds in a branching algorithm ideas coming from other traditional computer science techniques such as dynamic programming and memorization, but keeping the space requirement polynomial. Chapter 5 provides an exact approach based on semidefinite programming and a matheuristic approach based on a quadratic solver for a fractional clustering combinatorial optimization problem, called Max-Mean Dispersion Problem. The matheuristic approach has the peculiarity of using a non-linear MIP solver. The proposed exact approach uses a general semidefinite programming relaxation and it is likely to be extended to other combinatorial problems with a fractional formulation. Chapter 6 proposes practical solution methods for a real world clustering problem arising in a smart city context. The solution algorithm is based on the solution of a Set Cover model via a commercial ILP solver. As a conclusion, the main contribution of this thesis is given by several approaches of practical or theoretical interest, for two classes of important combinatorial problems: clustering and scheduling. All the practical methods presented in the thesis are validated by extensive computational experiments, that compare the proposed methods with the ones available in the state of the art

Fixed cardinality stable sets

Given an undirected graph G=(V,E) and a positive integer k in {1, ..., |V|}, we initiate the combinatorial study of stable sets of cardinality exactly k in G. Our aim is to instigate the polyhedral investigation of the convex hull of fixed cardinality stable sets, inspired by the rich theory on the classical structure of stable sets. We introduce a large class of valid inequalities to the natural integer programming formulation of the problem. We also present simple combinatorial relaxations based on computing maximum weighted matchings, which yield dual bounds towards finding minimum-weight fixed cardinality stable sets, and particular cases which are solvable in polynomial time.publishedVersio

Stochastic Service Network Design for Intermodal Freight Transportation

In view of the accelerating climate change, greenhouse gas emissions from freight transportation must be significantly reduced over the next decades. Intermodal transportation can make a significant contribution here. During the transportation process, different modes of transportation are combined, enabling a modal shift to environmentally friendly alternatives such as rail and inland waterway transportation. However, at the same time, the organization of several modes is more complex compared to the unimodal case (where, for example, only trucks are employed). In particular, an efficient management of uncertainties, such as fluctuating transportation demand volumes or delays, is required to realize low costs and transportation times, thereby ensuring the attractiveness of intermodal transportation for a further modal shift. Stochastic service network design can explicitly consider such uncertainities in the planning in order to increase the performance of intermodal transportation. Decisions for the network design as well as for the mode choice are defined by mathematical optimization models, which originate from operations research and include relevant uncertainities by stochastic parameters. As central research gap, this dissertation addresses important operational constraints and decision variables of real-life intermodal networks, which have not been considered in these models so far and, in consequence, strongly limit their application in everyday operations. The resulting research contribution are two new variants of stochastic service network design models: The "stochastic service network design with integrated vehicle routing problem" integrates corresponding routing problems for road vehicles into the planning of intermodal networks. This new variant ensures a cost- and delay-minimal mode choice in the case of uncertain transportation times. The "stochastic service network design with short-term schedule modifications" deals with modifications of intermodal transportation schedules in order to adapt them to fluctuating demand as best as possible. For both new model variants, heuristic solution methods are presented which can efficiently solve even large network instances. Extensive case studies with real-world data demonstrate significant savings potentials compared to deterministic models as well as (simplified) stochastic models that already exist in literature

Development of a hybrid algorithm for bi-level bi-objective optimization, and application to hydrogen supply chain deployment and design

The present master thesis is based on the recently presented doctoral thesis of Dr. Victor Hugo Cantu Medrano, addressing multiobjective optimization problems in Process Engineering with several alternative resolution methods using Evolutionary Computation. In his thesis, a new algorithm to find the optimal design of the Hydrogen Supply Chain while minimizing economic costs and environmental impact is presented. For its resolution, the algorithm divides the problem into two subproblems or levels. The first level deals with the design of the HSC structure (sizing and location of the facilities). A second level that solves the subproblem corresponding to the operation of the supply chain (production and transportation). The technique used for its resolution is a hybridization of the MOEA SMS-EMOA, for the first level, with a linear programming solver that uses a scalarization function to address the two objectives considered in the second level. In this line, this master thesis consists of developing an extension of this same algorithm with the objective of taking advantage of all the information generated in the second level to increase its efficiency. To achieve this, the second level is executed several times for each execution of the first level, using each time a different vector of weights in the scalarization function. But this new logic implies the readaptation of the whole algorithm. First, the Hydrogen Supply Chain problem is presented and the technique for solving the original algorithm is discussed. Subsequently, the necessary modifications to the MOEA are presented in order to be able to apply the new approach to the algorithm. With the new algorithm implemented, a study is carried out for the definition of the weight vectors and different scalarization functions are studied to try to increase its efficiency. Finally, the results obtained with the new algorithm and those of the original algorithm are compared to determine whether the new version is capable of solving the same problems using fewer computational resourcesCette thèse de master est basée sur la thèse de doctorat récemment soutenue par Dr Víctor Hugo Cantú Medrano, dans laquelle il expérimente plusieurs méthodes de résolution alternatives à l'aide méthodes évolutionnaires pour résoudre les problèmes d'optimisation multiobjectifs dans le domaine du génie des procédés. Dans sa thèse, le Dr Cantú présente un nouvel algorithme permettant de trouver la conception optimale de la chaîne d'approvisionnement en hydrogène tout en minimisant les coûts économiques et l'impact environnemental. Pour sa résolution, l'algorithme divise le problème en deux sous-problèmes ou niveaux. Le premier niveau traite de la conception de la structure de la chaîne logistique hydrogène (dimensionnement et emplacement des installations). Un second niveau résout le sous-problème correspondant à l'exploitation de la chaîne logistique (production et transport). La technique utilisée pour sa résolution est une hybridation du MOEA SMS-EMOA, pour le premier niveau, avec un solveur de programmation linéaire qui utilise une fonction de scalarisation pour traiter les deux objectifs considérés dans le second niveau. Dans cette lignée, ce mémoire de master consiste à développer une extension de ce même algorithme avec l'objectif de tirer profit de toute l'information générée dans le deuxième niveau pour augmenter son efficacité. Pour ce faire, le second niveau est exécuté plusieurs fois pour chaque exécution du premier niveau, en utilisant à chaque fois un vecteur de poids différent dans la fonction de scalarisation. Mais cette nouvelle logique implique la réadaptation de l'ensemble de l'algorithme. Tout d'abord, le problème de la chaîne logistique hydrogène est présenté et la technique de résolution de l'algorithme original est discutée. Ensuite, les modifications nécessaires au MEOA sont présentées afin de pouvoir appliquer la nouvelle approche à l'algorithme. Avec le nouvel algorithme implémenté, une étude est réalisée pour la définition des vecteurs de poids et différentes fonctions de scalarisation sont étudiées pour essayer d'augmenter son efficacité. Enfin, les résultats obtenus avec le nouvel algorithme et ceux de l'algorithme original sont comparés pour déterminer si la nouvelle version est capable de résoudre les mêmes problèmes en utilisant moins de ressources informatiquesEste Trabajo Final de Master parte de la tesis doctoral recientemente presentada del doctor Víctor Hugo Cantú Medrano, donde se abordan problemas de optimización multiobjetivo en Ingeniería de Procesos experimentando con varios métodos de resolución alternativos haciendo uso de la Computación Evolutiva. En su tesis, el doctor Cantú presenta un nuevo algoritmo para encontrar el diseño óptimo de la Hydrogen Supply Chain minimizando los costes económicos y el impacto ambiental. Para su resolución, el algoritmo divide el problema en dos subproblemas o niveles. Un primer nivel que aborda el diseño de la estructura de la HSC (dimensionamiento y ubicación de las instalaciones). Un segundo nivel que resuelve el subproblema correspondiente a la operación de la cadena de suministro (producción y transporte). La técnica empleada para su resolución es una hibridación del MOEA SMS-EMOA, para el primer nivel, con un solver de programación lineal que utiliza una función de escalarización para tratar los dos objetivos considerados en el segundo nivel. En esta línea, este trabajo consiste en desarrollar una extensión de este mismo algoritmo con el objetivo de aprovechar toda la información que se genera en el segundo nivel para aumentar su eficiencia. Para lograrlo se ejecuta varias veces el segundo nivel por cada ejecución del primer nivel, utilizando cada vez un vector de pesos diferente en la función de escalarización. Pero esta nueva lógica implica la readaptación de todo el algoritmo. En primer lugar, se presenta el problema de la Hydrogen Supply Chain y se discute la técnica de resolución del algoritmo original. Posteriormente se presentan las modificaciones necesarias en el MOEA para poder aplicar el nuevo enfoque al algoritmo. Ya con el nuevo algoritmo implementado se realiza un estudio para la definición de los vectores de peso y se estudian diferentes funciones de escalarización para tratar de aumentar su eficiencia. Por último, se comparan los resultados obtenidos con el nuevo algoritmo y los del original para determinar si la nueva versión es capaz de resolver los mismos problemas utilizando un menor número de recursos computacionalesAquest Treball Final de Màster té el seu origen en la tesis doctoral recentment presentada del doctor Víctor Hugo Cantú Medrano, en la qual s’aboren problemes d’optimització multiobjectiu en enginyeria de processos, experimentant amb diversos mètodes de resolució alternatius fent ús de la Computació Evolutiva. En la seva tesis, el doctor Cantú presenta un nou algorisme per a trobar el disseny òptim de la Hydrogen Supply Chain minimitzant els costos econòmics i l’impacte ambiental. Per a la seva resolució, l’algoritme divideix el problema en dos subproblemes o nivells. Un primer nivell aborda el disseny de l’estructura.de la HSC (dimensionament i ubicació de les instal·lacions). Un segon nivell resol el subproblema corresponent a l’operació de la cadena de subministrament (producció i transport). La tècnica empleada per a la seva resolució és una hibridació del MOEA SMS-EMOA, per al primer nivell amb un solver de programació lineal que utilitza una funció d’escalarització per a tractar els dos objectius considerats en el segon nivell. En aquesta línia, aquest treball consisteix a desenvolupar una extensió d’aquest mateix algorisme amb l’objectiu d’aprofitar tota la informació que es genera en el segon nivell per a augmentar la seva eficiència. Per a aconseguir-ho s’executa diverses vegades el segon nivell per cada execució del primer nivell, utilitzant cada vegada un vector de pesos diferent en la funció d’escalarització. Però aquesta nova lògica implica la readaptació de tot l’algorisme. En primer lloc, es presenta el problema de la Hydrogen Supply Chain i es discuteix la tècnica de resolució de l’algorisme original. Posteriorment es presenten les modificacions necessàries en el MOEA per a poder aplicar el nou enfocament a l’algorisme. Ja amb el nou algorisme implementat es realitza un estudi per a la definició dels vectors de pes i s’estudien diferents funcions d’escalarització per a tractar d’augmentar la seva eficiència. Ja amb el nou algorisme implementat es realitza un estudi per a la definició dels vectors de pes i s’estudien diferents funcions d’escalarització per a tractar d’augmentar la seva eficiència. Finalment, es comparen els resultats obtinguts amb el nou algorisme i els de l’original per tal de determinar si es possible obtenir els mateixos resultats fent us d’un menor número de recursos computacionalsObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.3 - Per a 2030, duplicar la taxa mundial de millora de l’eficiència energètic