Non-elitist Evolutionary Multi-objective Optimizers Revisited

Since around 2000, it has been considered that elitist evolutionary multi-objective optimization algorithms (EMOAs) always outperform non-elitist EMOAs. This paper revisits the performance of non-elitist EMOAs for bi-objective continuous optimization when using an unbounded external archive. This paper examines the performance of EMOAs with two elitist and one non-elitist environmental selections. The performance of EMOAs is evaluated on the bi-objective BBOB problem suite provided by the COCO platform. In contrast to conventional wisdom, results show that non-elitist EMOAs with particular crossover methods perform significantly well on the bi-objective BBOB problems with many decision variables when using the unbounded external archive. This paper also analyzes the properties of the non-elitist selection.Comment: This is an accepted version of a paper published in the proceedings of GECCO 201

Evolutionary multiobjective optimization for automatic agent-based model calibration: A comparative study

This work was supported by the Spanish Agencia Estatal de Investigacion, the Andalusian Government, the University of Granada, and European Regional Development Funds (ERDF) under Grants EXASOCO (PGC2018-101216-B-I00), SIMARK (P18-TP-4475), and AIMAR (A-TIC-284-UGR18). Manuel Chica was also supported by the Ramon y Cajal program (RYC-2016-19800).The authors would like to thank the ``Centro de Servicios de Informática y Redes de Comunicaciones'' (CSIRC), University of Granada, for providing the computing resources (Alhambra supercomputer).Complex problems can be analyzed by using model simulation but its use is not straight-forward since modelers must carefully calibrate and validate their models before using them. This is specially relevant for models considering multiple outputs as its calibration requires handling different criteria jointly. This can be achieved using automated calibration and evolutionary multiobjective optimization methods which are the state of the art in multiobjective optimization as they can find a set of representative Pareto solutions under these restrictions and in a single run. However, selecting the best algorithm for performing automated calibration can be overwhelming. We propose to deal with this issue by conducting an exhaustive analysis of the performance of several evolutionary multiobjective optimization algorithms when calibrating several instances of an agent-based model for marketing with multiple outputs. We analyze the calibration results using multiobjective performance indicators and attainment surfaces, including a statistical test for studying the significance of the indicator values, and benchmarking their performance with respect to a classical mathematical method. The results of our experimentation reflect that those algorithms based on decomposition perform significantly better than the remaining methods in most instances. Besides, we also identify how different properties of the problem instances (i.e., the shape of the feasible region, the shape of the Pareto front, and the increased dimensionality) erode the behavior of the algorithms to different degrees.Spanish Agencia Estatal de InvestigacionAndalusian GovernmentUniversity of GranadaEuropean Commission PGC2018-101216-B-I00 P18-TP-4475 A-TIC-284-UGR18Spanish Government RYC-2016-1980

Recognizing Sets in Evolutionary Multiobjective Optimization, Journal of Telecommunications and Information Technology, 2012, nr 1

Among Evolutionary Multiobjective Optimization Algorithms (EMOA) there are many which find only Paretooptimal solutions. These may not be enough in case of multimodal problems and non-connected Pareto fronts, where more information about the shape of the landscape is required. We propose a Multiobjective Clustered Evolutionary Strategy (MCES) which combines a hierarchic genetic algorithm consisting of multiple populations with EMOA rank selection. In the next stage, the genetic sample is clustered to recognize regions with high density of individuals. These regions are occupied by solutions from the neighborhood of the Pareto set. We discuss genetic algorithms with heuristic and the concept of well-tuning which allows for theoretical verification of the presented strategy. Numerical results begin with one example of clustering in a single-objective benchmark problem. Afterwards, we give an illustration of the EMOA rank selection in a simple two-criteria minimization problem and provide results of the simulation of MCES for multimodal, multi-connected example. The strategy copes with multimodal problems without losing local solutions and gives better insight into the shape of the evolutionary landscape. What is more, the stability of solutions in MCES may be analyzed analytically

Pareto or non-Pareto: Bi-criterion evolution in multi-objective optimization

It is known that Pareto dominance has its own weaknesses as the selection criterion in evolutionary multi-objective optimization. Algorithms based on Pareto dominance can suffer from slow convergence to the optimal front, inferior performance on problems with many objectives, etc. Non-Pareto criterion, such as decomposition-based criterion and indicator-based criterion, has already shown promising results in this regard, but its high selection pressure may lead the algorithm to prefer some specific areas of the problem’s Pareto front, especially when the front is highly irregular. In this paper, we propose a bi-criterion evolution framework of Pareto criterion and non-Pareto criterion, which attempts to make use of their strengths and compensates for each other’s weaknesses. The proposed framework consists of two parts, Pareto criterion evolution and non-Pareto criterion evolution. The two parts work collaboratively, with an abundant exchange of information to facilitate each other’s evolution. Specifically, the non-Pareto criterion evolution leads the Pareto criterion evolution forward and the Pareto criterion evolution compensates the possible diversity loss of the non-Pareto criterion evolution. The proposed framework keeps the freedom on the implementation of the non-Pareto criterion evolution part, thus making it applicable for any non-Pareto-based algorithm. In the Pareto criterion evolution, two operations, population maintenance and individual exploration, are presented. The former is to maintain a set of representative nondominated individuals, and the latter is to explore some promising areas which are undeveloped (or not well-developed) in the non-Pareto criterion evolution. Experimental results have shown the effectiveness of the proposed framework. The bi-criterion evolution works well on seven groups of 42 test problems with various characteristics, including those where Pareto-based algorithms or non-Paretobased algorithms strugg- e

Otimização multiobjetivo com estimação de distribuição guiada por tomada de decisão multicritério

Orientadores: Fernando José Von Zuben, Guilherme Palermo CoelhoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Considerando as meta-heurísticas estado-da-arte para otimização multiobjetivo (MOO, do inglês Multi-Objective Optimization), como NSGA-II, NSGA-III, SPEA2 e SMS-EMOA, apenas um critério de preferência por vez é levado em conta para classificar soluções ao longo do processo de busca. Neste trabalho, alguns dos critérios de seleção adotados por esses algoritmos estado-da-arte, incluindo classe de não-dominância e contribuição para a métrica de hipervolume, são utilizados em conjunto por uma técnica de tomada de decisão multicritério (MCDM, do inglês Multi-Criteria Decision Making), mais especificamente o algoritmo TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), responsável por ordenar todas as soluções candidatas. O algoritmo TOPSIS permite o uso de abordagens baseadas em múltiplas preferências, ao invés de apenas uma como na maioria das técnicas híbridas de MOO e MCDM. Cada preferência é tratada como um critério com uma importância relativa determinada pelo tomador de decisão. Novas soluções candidatas são então amostradas por meio de um modelo de distribuição, neste caso uma mistura de Gaussianas, obtido a partir da lista ordenada de soluções candidatas produzida pelo TOPSIS. Essencialmente, um operador de roleta é utilizado para selecionar um par de soluções candidatas de acordo com o seu mérito relativo, adequadamente determinado pelo TOPSIS, e então uma novo par de soluções candidatas é gerado a partir de perturbações Gaussianas centradas nas correspondentes soluções candidatas escolhidas. O desvio padrão das funções Gaussianas é definido em função da distância das soluções no espaço de decisão. Também foram utilizados operadores para auxiliar a busca a atingir regiões potencialmente promissoras do espaço de busca que ainda não foram mapeadas pelo modelo de distribuição. Embora houvesse outras opções, optou-se por seguir a estrutura do algoritmo NSGA-II, também adotada no algoritmo NSGA-III, como base para o método aqui proposto, denominado MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Assim, os aspectos distintos da proposta, quando comparada com o NSGA-II e o NSGA-III, são a forma como a população de soluções candidatas é ordenada e a estratégia adotada para gerar novos indivíduos. Os resultados nos problemas de teste ZDT mostram claramente que nosso método é superior aos algoritmos NSGA- II e NSGA-III, e é competitivo com outras meta-heurísticas bem estabelecidas na literatura de otimização multiobjetivo, levando em conta as métricas de convergência, hipervolume e a medida IGDAbstract: Considering the state-of-the-art meta-heuristics for multi-objective optimization (MOO), such as NSGA-II, NSGA-III, SPEA2 and SMS-EMOA, only one preference criterion at a time is considered to properly rank candidate solutions along the search process. Here, some of the preference criteria adopted by those state-of-the-art algorithms, including non-dominance level and contribution to the hypervolume, are taken together as inputs to a multi-criteria decision making (MCDM) strategy, more specifically the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), responsible for sorting all candidate solutions. The TOPSIS algorithm allows the use of multiple preference based approaches, rather than focusing on a particular one like in most hybrid algorithms composed of MOO and MCDM techniques. Here, each preference is treated as a criterion with a relative relevance to the decision maker (DM). New candidate solutions are then generated using a distribution model, in our case a Gaussian mixture model, derived from the sorted list of candidate solutions produced by TOPSIS. Essentially, a roulette wheel is used to choose a pair of the current candidate solutions according to the relative quality, suitably determined by TOPSIS, and after that a new pair of candidate solutions is generated as Gaussian perturbations centered at the corresponding parent solutions. The standard deviation of the Gaussian functions is defined in terms of the parents distance in the decision space. We also adopt refreshing operators, aiming at reaching potentially promising regions of the search space not yet mapped by the distribution model. Though other choices could have been made, we decided to follow the structural conception of the NSGA-II algorithm, also adopted in the NSGA-III algorithm, as basis for our proposal, denoted by MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Therefore, the distinctive aspects, when compared to NSGA-II and NSGA-III, are the way the current population of candidate solutions is ranked and the strategy adopted to generate new individuals. The results on ZDT benchmarks show that our method is clearly superior to NSGA-II and NSGA-III, and is competitive with other wellestablished meta-heuristics for multi-objective optimization from the literature, considering convergence to the Pareto front, hypervolume and IGD as performance metricsMestradoEngenharia de ComputaçãoMestre em Engenharia Elétrica2016/21031-0FAPESPCAPE

Scalarized Preferences in Multi-objective Optimization

Multikriterielle Optimierungsprobleme verfügen über keine Lösung, die optimal in jeder Zielfunktion ist. Die Schwierigkeit solcher Probleme liegt darin eine Kompromisslösung zu finden, die den Präferenzen des Entscheiders genügen, der den Kompromiss implementiert. Skalarisierung – die Abbildung des Vektors der Zielfunktionswerte auf eine reelle Zahl – identifiziert eine einzige Lösung als globales Präferenzenoptimum um diese Probleme zu lösen. Allerdings generieren Skalarisierungsmethoden keine zusätzlichen Informationen über andere Kompromisslösungen, die die Präferenzen des Entscheiders bezüglich des globalen Optimums verändern könnten. Um dieses Problem anzugehen stellt diese Dissertation eine theoretische und algorithmische Analyse skalarisierter Präferenzen bereit. Die theoretische Analyse besteht aus der Entwicklung eines Ordnungsrahmens, der Präferenzen als Problemtransformationen charakterisiert, die präferierte Untermengen der Paretofront definieren. Skalarisierung wird als Transformation der Zielmenge in diesem Ordnungsrahmen dargestellt. Des Weiteren werden Axiome vorgeschlagen, die wünschenswerte Eigenschaften von Skalarisierungsfunktionen darstellen. Es wird gezeigt unter welchen Bedingungen existierende Skalarisierungsfunktionen diese Axiome erfüllen. Die algorithmische Analyse kennzeichnet Präferenzen anhand des Resultats, das ein Optimierungsalgorithmus generiert. Zwei neue Paradigmen werden innerhalb dieser Analyse identifiziert. Für beide Paradigmen werden Algorithmen entworfen, die skalarisierte Präferenzeninformationen verwenden: Präferenzen-verzerrte Paretofrontapproximationen verteilen Punkte über die gesamte Paretofront, fokussieren aber mehr Punkte in Regionen mit besseren Skalarisierungswerten; multimodale Präferenzenoptima sind Punkte, die lokale Skalarisierungsoptima im Zielraum darstellen. Ein Drei-Stufen-Algorith\-mus wird entwickelt, der lokale Skalarisierungsoptima approximiert und verschiedene Methoden werden für die unterschiedlichen Stufen evaluiert. Zwei Realweltprobleme werden vorgestellt, die die Nützlichkeit der beiden Algorithmen illustrieren. Das erste Problem besteht darin Fahrpläne für ein Blockheizkraftwerk zu finden, die die erzeugte Elektrizität und Wärme maximieren und den Kraftstoffverbrauch minimiert. Präferenzen-verzerrte Approximationen generieren mehr Energie-effiziente Lösungen, unter denen der Entscheider seine favorisierte Lösung auswählen kann, indem er die Konflikte zwischen den drei Zielen abwägt. Das zweite Problem beschäftigt sich mit der Erstellung von Fahrplänen für Geräte in einem Wohngebäude, so dass Energiekosten, Kohlenstoffdioxidemissionen und thermisches Unbehagen minimiert werden. Es wird gezeigt, dass lokale Skalarisierungsoptima Fahrpläne darstellen, die eine gute Balance zwischen den drei Zielen bieten. Die Analyse und die Experimente, die in dieser Arbeit vorgestellt werden, ermöglichen es Entscheidern bessere Entscheidungen zu treffen indem Methoden angewendet werden, die mehr Optionen generieren, die mit den Präferenzen der Entscheider übereinstimmen

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

Computer Systems, Imagery and Medi