A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

[EN] In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdateP(Q,epsilon)D(xy), Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant number RTI2018-096904-B-I00), by the Generalitat Valenciana regional government through project AICO/2019/055 and by the Universitat Politecnica de Valencia (grant number SP20200109).Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Martínez Iranzo, MA. (2021). A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization. Mathematics. 9(9):1-28. https://doi.org/10.3390/math9090999S1289

On the detection of nearly optimal solutions in the context of single-objective space mission design problems

When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions – in the design space – but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e–approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design

Multi-Objective Archiving

Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.Comment: 21 pages, 4 figures, journa

Evolutionary Algorithms in Engineering Design Optimization

Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc

Bio-inspired optimization algorithms for multi-objective problems

Orientador : Aurora Trinidad Ramirez PozoCoorientador : Roberto Santana HermidaTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 06/03/2017Inclui referências : f. 161-72Área de concentração : Computer ScienceResumo: Problemas multi-objetivo (MOPs) são caracterizados por terem duas ou mais funções objetivo a serem otimizadas simultaneamente. Nestes problemas, a meta é encontrar um conjunto de soluções não-dominadas geralmente chamado conjunto ótimo de Pareto cuja imagem no espaço de objetivos é chamada frente de Pareto. MOPs que apresentam mais de três funções objetivo a serem otimizadas são conhecidos como problemas com muitos objetivos (MaOPs) e vários estudos indicam que a capacidade de busca de algoritmos baseados em Pareto é severamente deteriorada nesses problemas. O desenvolvimento de otimizadores bio-inspirados para enfrentar MOPs e MaOPs é uma área que vem ganhando atenção na comunidade, no entanto, existem muitas oportunidades para inovar. O algoritmo de enxames de partículas multi-objetivo (MOPSO) é um dos algoritmos bio-inspirados adequados para ser modificado e melhorado, principalmente devido à sua simplicidade, flexibilidade e bons resultados. Para melhorar a capacidade de busca de MOPSOs, seguimos duas linhas de pesquisa diferentes: A primeira foca em métodos de líder e arquivamento. Trabalhos anteriores apontaram que esses componentes podem influenciar no desempenho do algoritmo, porém a seleção desses componentes pode ser dependente do problema. Uma alternativa para selecioná-los dinamicamente é empregando hiper-heurísticas. Ao combinar hiper-heurísticas e MOPSO, desenvolvemos um novo framework chamado H-MOPSO. A segunda linha de pesquisa também é baseada em trabalhos anteriores do grupo que focam em múltiplos enxames. Isso é feito selecionando como base o framework multi-enxame iterado (I-Multi), cujo procedimento de busca pode ser dividido em busca de diversidade e busca com múltiplos enxames, e a última usa agrupamento para dividir um enxame em vários sub-enxames. Para melhorar o desempenho do I-Multi, exploramos duas possibilidades: a primeira foi investigar o efeito de diferentes características do mecanismo de agrupamento do I-Multi. A segunda foi investigar alternativas para melhorar a convergência de cada sub-enxame, como hibridizá-lo com um algoritmo de estimativa de distribuição (EDA). Este trabalho com EDA aumentou nosso interesse nesta abordagem, portanto seguimos outra linha de pesquisa, investigando alternativas para criar versões multi-objetivo de um dos EDAs mais poderosos da literatura, chamado estratégia de evolução baseada na adaptação da matriz de covariância (CMA-ES). Para validar o nosso trabalho, vários estudos empíricos foram conduzidos para investigar a capacidade de busca das abordagens propostas. Em todos os estudos, nossos algoritmos investigados alcançaram resultados competitivos ou melhores do que algoritmos bem estabelecidos da literatura. Palavras-chave: multi-objetivo, algoritmo de estimativa de distribuição, otimização por enxame de partículas, multiplos enxames, híper-heuristicas.Abstract: Multi-Objective Problems (MOPs) are characterized by having two or more objective functions to be simultaneously optimized. In these problems, the goal is to find a set of non-dominated solutions usually called Pareto optimal set whose image in the objective space is called Pareto front. MOPs presenting more than three objective functions to be optimized are known as Many-Objective Problems (MaOPs) and several studies indicate that the search ability of Pareto-based algorithms is severely deteriorated in such problems. The development of bio-inspired optimizers to tackle MOPs and MaOPs is a field that has been gaining attention in the community, however there are many opportunities to innovate. Multi-objective Particle Swarm Optimization (MOPSO) is one of the bio-inspired algorithms suitable to be modified and improved, mostly due to its simplicity, flexibility and good results. To enhance the search ability of MOPSOs, we followed two different research lines: The first focus on leader and archiving methods. Previous works have pointed that these components can influence the algorithm performance, however the selection of these components can be problem-dependent. An alternative to dynamically select them is by employing hyper-heuristics. By combining hyper-heuristics and MOPSO, we developed a new framework called H-MOPSO. The second research line, is also based on previous works of the group that focus on multi-swarm. This is done by selecting as base framework the iterated multi swarm (I-Multi) algorithm, whose search procedure can be divided into diversity and multi-swarm searches, and the latter employs clustering to split a swarm into several sub-swarms. In order to improve the performance of I-Multi, we explored two possibilities: the first was to further investigate the effect of different characteristics of the clustering mechanism of I-Multi. The second was to investigate alternatives to improve the convergence of each sub-swarm, like hybridizing it to an Estimation of Distribution Algorithm (EDA). This work on EDA increased our interest in this approach, hence we followed another research line by investigating alternatives to create multi-objective versions of one of the most powerful EDAs from the literature, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In order to validate our work, several empirical studies were conducted to investigate the search ability of the approaches proposed. In all studies, our investigated algorithms have reached competitive or better results than well established algorithms from the literature. Keywords: multi-objective, estimation of distribution algorithms, particle swarm optimization, multi-swarm, hyper-heuristics

Archivers for the representation of the set of approximate solutions for MOPs

International audienceIn this paper we address the problem of computing suitable representations of the set of approximate solutions of a given multi-objective optimization problem via stochastic search algorithms. For this, we will propose different archiving strategies for the selection of the candidate solutions maintained by the generation process of the stochastic search process, and investigate them further on analytically and empirically. For all archivers we will provide upper bounds on the approximation quality as well as on the cardinality of the limit solution set. We conclude this work by a comparative study on some test problems in order to visualize the effect of all novel archiving strategies

“Oluşumlar, dönüşümler, bozunumlar” Moskova nonkoformist sanatçıları ve işleri peşinde komün oda ve mimarisinin izini sürmek 1975-1991

This thesis traces the evolution of communal room from a collective to private space through practices of an underground art circle that emerged during the second half of the 1970s in Soviet Moscow, namely Soviet Nonconformist artists. The Soviet project of the communal apartment was a revolutionary experiment of collective living. Initiated with the ideal of designing "socialism in one building," it turned into an institution of social control, the base for establishing status-quo and a micro-cosmos where Soviet communal bodies were shaped between the 1920s and late 1950s. Following the transformation of communal apartments into private rooms during Khrushchev's Thaw in the late 1950s, these new private rooms were transformed into zones of freedom by newly flourishing underground culture in major cities of the Soviet Union. Starting from the 1960s, especially Moscow and Leningrad, witnessed private rooms to be appropriated as spaces for the underground activities of various intellectual fields. This thesis aims to decode the dynamics, aesthetics, and architecture of post-thaw Soviet communal rooms in between privacy-collectivity, and officiality-unofficiality by tracing "Moscow Nonconformists" through three generations that were formed, reformed, and deformed between the years 1975-1991. In two parallel analysis, on networks and artworks of Nonconformist artists, it is aimed to trace the architectural history of the communal room both in Moscow and through artists exhibitions in the West as the context, the muse and the object of their artistic genre, while documenting the room's intertwined journey with artists' biographies and networks.Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Architecture