A convergence acceleration operator for multiobjective optimisation

A novel multiobjective optimisation accelerator is introduced that uses direct manipulation in objective space together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions

Proposal and Comparative Study of Evolutionary Algorithms for Optimum Design of a Gear System

This paper proposes a novel metaheuristic framework using a Differential Evolution (DE) algorithm with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Both algorithms are combined employing a collaborative strategy with sequential execution, which is called DE-NSGA-II. The DE-NSGA-II takes advantage of the exploration abilities of the multi-objective evolutionary algorithms strengthened with the ability to search global mono-objective optimum of DE, that enhances the capability of finding those extreme solutions of Pareto Optimal Front (POF) difficult to achieve. Numerous experiments and performance comparisons between different evolutionary algorithms were performed on a referent problem for the mono-objective and multi-objective literature, which consists of the design of a double reduction gear train. A preliminary study of the problem, solved in an exhaustive way, discovers the low density of solutions in the vicinity of the optimal solution (mono-objective case) as well as in some areas of the POF of potential interest to a decision maker (multi-objective case). This characteristic of the problem would explain the considerable difficulties for its resolution when exact methods and/or metaheuristics are used, especially in the multi-objective case. However, the DE-NSGA-II framework exceeds these difficulties and obtains the whole POF which significantly improves the few previous multi-objective studies.Fil: Méndez Babey, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

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

Progressive Preference Articulation for Decision Making in Multi-Objective Optimisation Problems

This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articu- lation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algo- rithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA). WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation. Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the pro- posed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest

CMA-PAES: Pareto archived evolution strategy using covariance matrix adaptation for multi-objective optimisation

The quality of Evolutionary Multi-Objective Optimisation (EMO) approximation sets can be measured by their proximity, diversity and pertinence. In this paper we introduce a modular and extensible Multi-Objective Evolutionary Algorithm (MOEA) capable of converging to the Pareto-optimal front in a minimal number of function evaluations and producing a diverse approximation set. This algorithm, called the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES), is a form of (μ + λ) Evolution Strategy which uses an online archive of previously found Pareto-optimal solutions (maintained by a bounded Pareto-archiving scheme) as well as a population of solutions which are subjected to variation using Covariance Matrix Adaptation. The performance of CMA-PAES is compared to NSGA-II (currently considered the benchmark MOEA in the literature) on the ZDT test suite of bi-objective optimisation problems and the significance of the results are analysed using randomisation testing. © 2012 IEEE

Faster Evolutionary Multi-Objective Optimization via GALE, the Geometric Active Learner

Goal optimization has long been a topic of great interest in computer science. The literature contains many thousands of papers that discuss methods for the search of optimal solutions to complex problems. In the case of multi-objective optimization, such a search yields iteratively improved approximations to the Pareto frontier, i.e. the set of best solutions contained along a trade-off curve of competing objectives.;To approximate the Pareto frontier, one method that is ubiquitous throughout the field of optimization is stochastic search. Stochastic search engines explore solution spaces by randomly mutating candidate guesses to generate new solutions. This mutation policy is employed by the most commonly used tools (e.g. NSGA-II, SPEA2, etc.), with the goal of a) avoiding local optima, and b) expand upon diversity in the set of generated approximations. Such blind mutation policies explore many sub-optimal solutions that are discarded when better solutions are found. Hence, this approach has two problems. Firstly, stochastic search can be unnecessarily computationally expensive due to evaluating an overwhelming number of candidates. Secondly, the generated approximations to the Pareto frontier are usually very large, and can be difficult to understand.;To solve these two problems, a more-directed, less-stochastic approach than standard search tools is necessary. This thesis presents GALE (Geometric Active Learning). GALE is an active learner that finds approximations to the Pareto frontier by spectrally clustering candidates using a near-linear time recursive descent algorithm that iteratively divides candidates into halves (called leaves at the bottom level). Active learning in GALE selects a minimally most-informative subset of candidates by only evaluating the two-most different candidates during each descending split; hence, GALE only requires at most, 2Log2(N) evaluations per generation. The candidates of each leaf are thereafter non-stochastically mutated in the most promising directions along each piece. Those leafs are piece-wise approximations to the Pareto frontier.;The experiments of this thesis lead to the following conclusion: a near-linear time recursive binary division of the decision space of candidates in a multi-objective optimization algorithm can find useful directions to mutate instances and find quality solutions much faster than traditional randomization approaches. Specifically, in comparative studies with standard methods (NSGA-II and SPEA2) applied to a variety of models, GALE required orders of magnitude fewer evaluations to find solutions. As a result, GALE can perform dramatically faster than the other methods, especially for realistic models