2,027 research outputs found
MOEA/D with Adaptive Weight Adjustment
Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.</jats:p
A decomposition-based multiobjective evolutionary algorithm with angle-based adaptive penalty
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.A multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and optimizes them in a collaborative manner. In MOEA/D, decomposition mechanisms are used to push the population to approach the Pareto optimal front (POF), while a set of uniformly distributed weight vectors are applied to maintain the diversity of the population. Penalty-based boundary intersection (PBI) is one of the approaches used frequently in decomposition. In PBI, the penalty factor plays a crucial role in balancing convergence and diversity. However, the traditional PBI approach adopts a fixed penalty value, which will significantly degrade the performance of MOEA/D on some MOPs with complicated POFs. This paper proposes an angle-based adaptive penalty (AAP) scheme for MOEA/D, called MOEA/D-AAP, which can dynamically adjust the penalty value for each weight vector during the evolutionary process. Six newly designed benchmark MOPs and an MOP in the wastewater treatment process are used to test the effectiveness of the proposed MOEA/D-AAP. Comparison experiments demonstrate that the AAP scheme can significantly improve the performance of MOEA/D
Desenvolvimento de um Algoritmo de Decomposição Híbrido Bioinspirado Baseado em Baleias e Estratégias de Evolução Diferencial para Otimização Multiobjetivo
A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.Um Problema de Otimização Multiobjetivo (POM) requer a otimização de várias funções objetivo simultaneamente, geralmente conflitantes entre si. Um dos algoritmos mais eficientes para resolver POMs é o MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), que decompõe um POM em subproblemas de otimização monobjetivo, isto é, com uma única função objetivo a ser minimizada, e os resolve usando informações de subproblemas vizinhos. Variantes do MOEA/D com outros operadores evolutivos surgiram ao longo dos anos, melhorando sua eficiência em diversos POMs. Recentemente foi proposto o IWOA (Improved Whale Optimization Algorithm), um algoritmo de otimização bioinspirado no método de caça das baleias hibridizado com Evolução Diferencial que apresentou ótimos resultados em problemas de otimização monobjetivo. Esse trabalho propõe o algoritmo MOEA/D-IWOA, que extende o IWOA para resolver POMs associando características dos seus operadores evolutivos ao MOEA/D. Experimentos computacionais para analisar o desempenho do MOEA/D-IWOA em POMs benchmark foram realizados e os resultados comparados aos obtidos pelos algoritmos bem conhecidos da literatura, a saber, MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2) e Indicator-Based Evolutionary Algorithm (IBEA) nos indicadores Hypervolume e Inverted Generational Distance Plus (IGD+). O MOEA/D-IWOA se mostrou competitivo, com bom perfil de desempenho, além de apresentar os melhores resultados em alguns POMs
Decomposition-Based-Sorting and Angle-Based-Selection for Evolutionary Multiobjective and Many-Objective Optimization
Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail
MOEA/D with Tabu Search for multiobjective permutation flow shop scheduling problems
Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) decomposes a multiobjective optimisation problem into a number of single-objective problems and optimises them in a collaborative manner. This paper investigates how to use Tabu Search (TS), a well-studied single objective heuristic to enhance MOEA/D performance. In our proposed approach, the TS is applied to these subproblems with the aim to escape from local optimal solutions. The experimental studies have shown that MOEA/D with TS outperforms the classical MOEA/D on multiobjective permutation flow shop scheduling problems. It also have demonstrated that use of problem specific knowledge can significantly improve the algorithm performance
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