Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems

Liu, Hailin; Gu, Fangqing; Zhang, Qingfu

doi:10.1109/tevc.2013.2281533

Cited by 710 publications

(310 citation statements)

References 18 publications

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“…Liu et al [8] introduced several hard-to-converge problems with considerably deceptive properties and strong variable linkages. As a testing example, we choose the three-objective MOP6 to distinguish the difference between diversityfirst sorting and convergence-first sorting.…”

Section: Results On a Hard Three-objective Problemmentioning

confidence: 99%

Convergence Versus Diversity in Multiobjective Optimization

Jiang

Yang

2016

Lecture Notes in Computer Science

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Abstract. Convergence and diversity are two main goals in multiobjective optimization. In literature, most existing multiobjective optimization evolutionary algorithms (MOEAs) adopt a convergencefirst-and-diversity-second environmental selection which prefers nondominated solutions to dominated ones, as is the case with the popular nondominated sorting based selection method. While convergence-first sorting has continuously shown effectiveness for handling a variety of problems, it faces challenges to maintain well population diversity due to the overemphasis of convergence. In this paper, we propose a general diversity-first sorting method for multiobjective optimization. Based on the method, a new MOEA, called DBEA, is then introduced. DBEA is compared with the recently-developed nondominated sorting genetic algorithm III (NSGA-III) on different problems. Experimental studies show that the diversity-first method has great potential for diversity maintenance and is very competitive for many-objective optimization.

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Section: Results On a Hard Three-objective Problemmentioning

confidence: 99%

Convergence Versus Diversity in Multiobjective Optimization

Jiang

Yang

2016

Lecture Notes in Computer Science

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“…At each iteration of MOMAD, a PLS procedure and multiple scalarized single-objective local search procedures are conducted. Liu et al [11] propose the MOEA/D-M2M algorithm, which decomposes the original problem into a number of sub-problems by setting weight vectors in the objective space. In MOEA/D-M2M, each sub-problem corresponds to a sub-population and all sub-populations evolve in a collaborative way.…”

Section: Related Work and Positioningmentioning

confidence: 99%

Using Parallel Strategies to Speed up Pareto Local Search

Shi

Zhang

Derbel

et al. 2017

Lecture Notes in Computer Science

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Abstract. Pareto Local Search (PLS) is a basic building block in many state-of-the-art multiobjective combinatorial optimization algorithms. However, the basic PLS requires a long time to find high-quality solutions. In this paper, we propose and investigate several parallel strategies to speed up PLS. These strategies are based on a parallel multi-search framework. In our experiments, we investigate the performances of different parallel variants of PLS on the multiobjective unconstrained binary quadratic programming problem. Each PLS variant is a combination of the proposed parallel strategies. The experimental results show that the proposed approaches can significantly speed up PLS while maintaining about the same solution quality. In addition, we introduce a new way to visualize the search process of PLS on twoobjective problems, which is helpful to understand the behaviors of PLS algorithms.

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“…The representative EMOAs are MOEA/D-M2M [37] and MOEA/DD [38]. The motivation of this category is to balance convergence and diversity in each subspace.…”

Section: Introductionmentioning

confidence: 99%

An R2 Indicator and Decomposition Based Steady-State Evolutionary Algorithm for Many-Objective Optimization

Liu

Huang

et al. 2018

Mathematical Problems in Engineering

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An 2 indicator based selection method is a major ingredient in the formulation of indicator based evolutionary multiobjective optimization algorithms. The existing classical indicator based selection methodologies have demonstrated an excellent performance to solve low-dimensional optimization problems. However, the 2 indicator based evolutionary multiobjective optimization algorithms encounter enormous challenges in high-dimensional objective space. Our main purpose is to explore how to extend the 2 indicator to handle many-objective optimization problems. After analyzing the 2 indicator, the objective space partition strategy, and the decomposition method, we propose a steady-state evolutionary algorithm based on the 2 indicator and the decomposition method, named, 2-MOEA/D, to obtain well-converged and well-distributed Pareto front. The main contribution of this paper contains two aspects. (1) The convergence and diversity for the 2 indicator based selection are analyzed. Two improper selection situations will be properly solved via applying the decomposition method. (2) According to the position of a new individual in the steady-state evolutionary algorithm, two different objective space partition strategies and the corresponding selection methods are proposed. Extensive experiments are conducted on a variety of benchmark test problems, and the experimental results demonstrate that the proposed algorithm has competitive performance in comparison with several tailored algorithms for many-objective optimization.

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Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems

Cited by 710 publications

References 18 publications

Convergence Versus Diversity in Multiobjective Optimization

Convergence Versus Diversity in Multiobjective Optimization

Using Parallel Strategies to Speed up Pareto Local Search

An R2 Indicator and Decomposition Based Steady-State Evolutionary Algorithm for Many-Objective Optimization

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