Hypervolume based metaheuristics for multiobjective optimization

The purpose of multiobjective optimization is to find solutions that are optimal regarding several goals. In the branch of vector or Pareto optimization all these goals are considered to be of equal importance, so that compromise solutions that cannot be improved regarding one goal without deteriorating in another are Paretooptimal. A variety of quality measures exist to evaluate approximations of the Paretooptimal set generated by optimizers, wherein the hypervolume is the most significant one, making the hypervolume calculation a core problem of multiobjective optimization. This thesis tackles that challenge by providing a new hypervolume algorithm from computational geometry and analyzing the problem’s computational complexity. Evolutionary multiobjective optimization algorithms (EMOA) are state-of-the-art methods for Pareto optimization, wherein the hypervolume-based algorithms belong to the most powerful ones, among them the popular SMS-EMOA. After its promising capabilities have already been demonstrated in first studies, this thesis is dedicated to deeper understand the underlying optimization process of the SMS-EMOA and similar algorithms, in order to specify their performance characteristics. Theoretical analyses are accomplished as far as possible with established and newly developed tools. Beyond the limitations of rigorous scrutiny, insights are gained via thorough experimental investigation. All considered problems are continuous, whereas the algorithms are as well applicable to discrete problems. More precisely, the following topics are concerned. The process of approaching the Pareto-optimal set of points is characterized by the convergence speed, which is analyzed for a general framework of EA with hypervolume selection on several classes of bi-objective problems. The results are achieved by a newly developed concept of linking single and multiobjective optimization. The optimization on the Pareto front, that is turning the population into a set with maximal hypervolume, is considered separately, focusing on the question under which circumstances the steady-state selection of exchanging only one population member suffices to reach a global optimum. We answer this question for different bi-objective problem classes. In a benchmarking on so-called many-objective problems of more than three objectives, the qualification of the SMS-EMOA is demonstrated in comparison to other EMOA, while also studying their cause of failure. Within the mentioned examinations, the choice of the hypervolume’s reference point receives special consideration by exposing its influence. Beyond the study of the SMS-EMOA with default setup, it is analyzed to what extent the performance can be improved by parameter tuning of the EMOA anent to certain problems, focusing on the influence of variation operators. Lastly, an optimization algorithm based on the gradient of the hypervolume is developed and hybridized with the SMS-EMOA

Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm

The introduction of learning to the search mechanisms of optimization algorithms has been nominated as one of the viable approaches when dealing with complex optimization problems, in particular with multi-objective ones. One of the forms of carrying out this hybridization process is by using multi-objective optimization estimation of distribution algorithms (MOEDAs). However, it has been pointed out that current MOEDAs have an intrinsic shortcoming in their model-building algorithms that hamper their performance. In this work, we put forward the argument that error-based learning, the class of learning most commonly used in MOEDAs is responsible for current MOEDA underachievement. We present adaptive resonance theory (ART) as a suitable learning paradigm alternative and present a novel algorithm called multi-objective ART-based EDA (MARTEDA) that uses a Gaussian ART neural network for model-building and a hypervolume-based selector as described for the HypE algorithm. In order to assert the improvement obtained by combining two cutting-edge approaches to optimization an extensive set of experiments are carried out. These experiments also test the scalability of MARTEDA as the number of objective functions increases.This work was supported by projects Projects CICYT TIN2011-28620-C02- 01, CICYT TEC2011-28626-C02-02, CAM CONTEXTS (S2009/TIC-1485) and DPS2008-07029-C02-02.Publicad

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

ParadisEO-MOEO: A Software Framework for Evolutionary Multi-Objective Optimization

This chapter presents ParadisEO-MOEO, a white-box object-oriented software framework dedicated to the flexible design of metaheuristics for multi-objective optimization. This paradigm-free software proposes a unified view for major evolutionary multi-objective metaheuristics. It embeds some features and techniques for multi-objective resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the problems they are intended to solve. This separation confers a maximum design and code reuse. This general-purpose framework provides a broad range of fitness assignment strategies, the most common diversity preservation mechanisms, some elitistrelated features as well as statistical tools. Furthermore, a number of state-of-the-art search methods, including NSGA-II, SPEA2 and IBEA, have been implemented in a user-friendly way, based on the fine-grained ParadisEO-MOEO components

Peeking beyond peaks:Challenges and research potentials of continuous multimodal multi-objective optimization

Multi-objective (MO) optimization, i.e., the simultaneous optimization of multiple conflicting objectives, is gaining more and more attention in various research areas, such as evolutionary computation, machine learning (e.g., (hyper-)parameter optimization), or logistics (e.g., vehicle routing). Many works in this domain mention the structural problem property of multimodality as a challenge from two classical perspectives: (1) finding all globally optimal solution sets, and (2) avoiding to get trapped in local optima. Interestingly, these streams seem to transfer many traditional concepts of single-objective (SO) optimization into claims, assumptions, or even terminology regarding the MO domain, but mostly neglect the understanding of the structural properties as well as the algorithmic search behavior on a problem's landscape. However, some recent works counteract this trend, by investigating the fundamentals and characteristics of MO problems using new visualization techniques and gaining surprising insights. Using these visual insights, this work proposes a step towards a unified terminology to capture multimodality and locality in a broader way than it is usually done. This enables us to investigate current research activities in multimodal continuous MO optimization and to highlight new implications and promising research directions for the design of benchmark suites, the discovery of MO landscape features, the development of new MO (or even SO) optimization algorithms, and performance indicators. For all these topics, we provide a review of ideas and methods but also an outlook on future challenges, research potential and perspectives that result from recent developments.</p

A Unified Model for Evolutionary Multiobjective Optimization and its Implementation in a General Purpose Software Framework: ParadisEO-MOEO

This paper gives a concise overview of evolutionary algorithms for multiobjective optimization. A substantial number of evolutionary computation methods for multiobjective problem solving has been proposed so far, and an attempt of unifying existing approaches is here presented. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual global model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. The presented model is then incorporated into a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. This package has proven its validity and flexibility by enabling the resolution of many real-world and hard multiobjective optimization problems

Antecipação na tomada de decisão com múltiplos critérios sob incerteza

Orientador: Fernando José Von ZubenTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: A presença de incerteza em resultados futuros pode levar a indecisões em processos de escolha, especialmente ao elicitar as importâncias relativas de múltiplos critérios de decisão e de desempenhos de curto vs. longo prazo. Algumas decisões, no entanto, devem ser tomadas sob informação incompleta, o que pode resultar em ações precipitadas com consequências imprevisíveis. Quando uma solução deve ser selecionada sob vários pontos de vista conflitantes para operar em ambientes ruidosos e variantes no tempo, implementar alternativas provisórias flexíveis pode ser fundamental para contornar a falta de informação completa, mantendo opções futuras em aberto. A engenharia antecipatória pode então ser considerada como a estratégia de conceber soluções flexíveis as quais permitem aos tomadores de decisão responder de forma robusta a cenários imprevisíveis. Essa estratégia pode, assim, mitigar os riscos de, sem intenção, se comprometer fortemente a alternativas incertas, ao mesmo tempo em que aumenta a adaptabilidade às mudanças futuras. Nesta tese, os papéis da antecipação e da flexibilidade na automação de processos de tomada de decisão sequencial com múltiplos critérios sob incerteza é investigado. O dilema de atribuir importâncias relativas aos critérios de decisão e a recompensas imediatas sob informação incompleta é então tratado pela antecipação autônoma de decisões flexíveis capazes de preservar ao máximo a diversidade de escolhas futuras. Uma metodologia de aprendizagem antecipatória on-line é então proposta para melhorar a variedade e qualidade dos conjuntos futuros de soluções de trade-off. Esse objetivo é alcançado por meio da previsão de conjuntos de máximo hipervolume esperado, para a qual as capacidades de antecipação de metaheurísticas multi-objetivo são incrementadas com rastreamento bayesiano em ambos os espaços de busca e dos objetivos. A metodologia foi aplicada para a obtenção de decisões de investimento, as quais levaram a melhoras significativas do hipervolume futuro de conjuntos de carteiras financeiras de trade-off avaliadas com dados de ações fora da amostra de treino, quando comparada a uma estratégia míope. Além disso, a tomada de decisões flexíveis para o rebalanceamento de carteiras foi confirmada como uma estratégia significativamente melhor do que a de escolher aleatoriamente uma decisão de investimento a partir da fronteira estocástica eficiente evoluída, em todos os mercados artificiais e reais testados. Finalmente, os resultados sugerem que a antecipação de opções flexíveis levou a composições de carteiras que se mostraram significativamente correlacionadas com as melhorias observadas no hipervolume futuro esperado, avaliado com dados fora das amostras de treinoAbstract: The presence of uncertainty in future outcomes can lead to indecision in choice processes, especially when eliciting the relative importances of multiple decision criteria and of long-term vs. near-term performance. Some decisions, however, must be taken under incomplete information, what may result in precipitated actions with unforeseen consequences. When a solution must be selected under multiple conflicting views for operating in time-varying and noisy environments, implementing flexible provisional alternatives can be critical to circumvent the lack of complete information by keeping future options open. Anticipatory engineering can be then regarded as the strategy of designing flexible solutions that enable decision makers to respond robustly to unpredictable scenarios. This strategy can thus mitigate the risks of strong unintended commitments to uncertain alternatives, while increasing adaptability to future changes. In this thesis, the roles of anticipation and of flexibility on automating sequential multiple criteria decision-making processes under uncertainty are investigated. The dilemma of assigning relative importances to decision criteria and to immediate rewards under incomplete information is then handled by autonomously anticipating flexible decisions predicted to maximally preserve diversity of future choices. An online anticipatory learning methodology is then proposed for improving the range and quality of future trade-off solution sets. This goal is achieved by predicting maximal expected hypervolume sets, for which the anticipation capabilities of multi-objective metaheuristics are augmented with Bayesian tracking in both the objective and search spaces. The methodology has been applied for obtaining investment decisions that are shown to significantly improve the future hypervolume of trade-off financial portfolios for out-of-sample stock data, when compared to a myopic strategy. Moreover, implementing flexible portfolio rebalancing decisions was confirmed as a significantly better strategy than to randomly choosing an investment decision from the evolved stochastic efficient frontier in all tested artificial and real-world markets. Finally, the results suggest that anticipating flexible choices has lead to portfolio compositions that are significantly correlated with the observed improvements in out-of-sample future expected hypervolumeDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO

International audienceThis paper presents a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. A concise overview of evolutionary algorithms for multiobjective optimization is given. A substantial number of methods has been proposed so far, and an attempt of conceptually unifying existing approaches is presented here. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. This model is then incorporated into the ParadisEO-MOEO software framework. This framework has proven its validity and high flexibility by enabling the resolution of many academic, real-world and hard multiobjective optimization problems