A Rough-to-Fine Evolutionary Multiobjective Optimization Algorithm
This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified <inline-formula> <tex-math notatio...
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| Vydané v: | IEEE transactions on cybernetics Ročník 52; číslo 12; s. 13472 - 13485 |
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| Hlavní autori: | , , , |
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| Jazyk: | English |
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01.12.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 2168-2267, 2168-2275, 2168-2275 |
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| Abstract | This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-means algorithm on <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(M \log N) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm. |
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| AbstractList | This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified [Formula Omitted]-means algorithm on [Formula Omitted] uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is [Formula Omitted], where [Formula Omitted] is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm. This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-means algorithm on <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is <inline-formula> <tex-math notation="LaTeX">\mathcal {O}(M \log N) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm. This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified k -means algorithm on N uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is O(M logN) , where M is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm.This article presents a rough-to-fine evolutionary multiobjective optimization algorithm based on the decomposition for solving problems in which the solutions are initially far from the Pareto-optimal set. Subsequently, a tree is constructed by a modified k -means algorithm on N uniform weight vectors, and each node of the tree contains a weight vector. Each node is associated with a subproblem with the help of its weight vector. Consequently, a subproblem tree can be established. It is easy to find that the descendant subproblems are refinements of their ancestor subproblems. The proposed algorithm approaches the Pareto front (PF) by solving a few subproblems in the first few levels to obtain a rough PF and gradually refining the PF by involving the subproblems level-by-level. This strategy is highly favorable for solving problems in which the solutions are initially far from the Pareto set. Moreover, the proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of dealing with a new candidate solution is O(M logN) , where M is the number of objectives. Empirical studies demonstrate the efficacy of the proposed algorithm. |
| Author | Cheung, Yiu-Ming Gu, Fangqing Zheng, Minyi Liu, Hai-Lin |
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| SubjectTerms | Approximation algorithms Complexity Decomposition Diversity reception Empirical analysis evolutionary algorithm Evolutionary algorithms Evolutionary computation incremental multiobjective optimization Multiple objective analysis Optimization Optimization algorithms Pareto optimization Pareto optimum Problem solving Sociology Sorting Statistics tree-like weight design |
| Title | A Rough-to-Fine Evolutionary Multiobjective Optimization Algorithm |
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