Journal Article10.1109/tevc.2022.3201890
Decomposition-based Multi-objective Optimization Algorithms with Adaptively Adjusting Weight Vectors and Neighborhoods
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TL;DR: In this paper , a decomposition-based multi-objective optimization algorithm with adaptively adjusting weight vectors and neighborhoods (MOEA/D-AAWN) is developed, where the evolutionary direction of each subproblem is analyzed and the Sparsity function (Spa) is proposed to measure the population density on the PF.
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Abstract: The decomposition-based multi-objective optimization algorithm (MOEA/D) is an effective method of solving a multi-objective optimization problem (MOP). The main idea of MOEA/D is that the objectives are weighted through different vectors to form different subproblems, and an optimal solution set is obtained by co-evolution in a certain neighborhood. However, with the increase of objectives, the number of non-dominated solutions increases exponentially, resulting in the deteriorated capability of searching for optimal solutions. In addition, for an optimization problem with the complex Pareto front(PF), the selection pressure of non-dominated solutions is insufficient. To make evolution more efficient, a decomposition-based multi-objective optimization algorithm with adaptively adjusting weight vectors and neighborhoods (MOEA/D-AAWN) is developed in this paper. Firstly, the evolutionary direction of each subproblem is analyzed and the Sparsity function (Spa) is proposed to measure the population density on the PF. By using Spa, a method of generating uniform vectors is presented to improve the diversity of solutions. Besides, a method of adaptively adjusting neighborhoods is given. It adjusts neighborhoods according to the number of iterations and the Spa value of its corresponding subproblem. In this way, the computational resource can be effectively allocated, leading to the improvement in evolutionary efficiency. The proposed algorithm is applied to solve a series of benchmark optimization instances, and the experimental results show that the proposed algorithm outperforms comparison algorithms in runtime, convergence, and diversity.
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References
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TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
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TL;DR: A reference-point-based many-objective evolutionary algorithm that emphasizes population members that are nondominated, yet close to a set of supplied reference points is suggested that is found to produce satisfactory results on all problems considered in this paper.
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TL;DR: This paper provides a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions and shows that elitism is shown to be an important factor for improving evolutionary multiobjectives search.
Comparison of multiobjective evolutionary algorithms: empirical results
Eckart Zitzler,Kalyanmoy Deb,Lothar Thiele +2 more
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TL;DR: In this article, the authors provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions, each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front.
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