Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory
In this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergen...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8451639 |
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| _version_ | 1832550046467358720 |
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| author | Jiandong Duan Jing Wang Xinghua Liu Gaoxi Xiao |
| author_facet | Jiandong Duan Jing Wang Xinghua Liu Gaoxi Xiao |
| author_sort | Jiandong Duan |
| collection | DOAJ |
| description | In this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergence analysis of MOLFA is to investigate whether a Pareto optimal solution can be reached when the optimal charge population state is obtained, the development of a charge population state is analyzed to achieve the goal of this paper. Based on the martingale theory, the MOLFA convergence analysis is carried out in terms of the supermartingale convergence theorem, which shows that the MOLFA can reach the global optimum with probability one. Finally, the effectiveness of the proposed MOLFA is verified by a numerical simulation example. |
| format | Article |
| id | doaj-art-0f126221a0fa4bb887c8611799a5773d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0f126221a0fa4bb887c8611799a5773d2025-02-03T06:07:41ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/84516398451639Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale TheoryJiandong Duan0Jing Wang1Xinghua Liu2Gaoxi Xiao3School of Electrical Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Electrical Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Electrical Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang, SingaporeIn this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergence analysis of MOLFA is to investigate whether a Pareto optimal solution can be reached when the optimal charge population state is obtained, the development of a charge population state is analyzed to achieve the goal of this paper. Based on the martingale theory, the MOLFA convergence analysis is carried out in terms of the supermartingale convergence theorem, which shows that the MOLFA can reach the global optimum with probability one. Finally, the effectiveness of the proposed MOLFA is verified by a numerical simulation example.http://dx.doi.org/10.1155/2020/8451639 |
| spellingShingle | Jiandong Duan Jing Wang Xinghua Liu Gaoxi Xiao Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory Complexity |
| title | Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory |
| title_full | Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory |
| title_fullStr | Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory |
| title_full_unstemmed | Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory |
| title_short | Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory |
| title_sort | multiobjective lightning flash algorithm design and its convergence analysis via martingale theory |
| url | http://dx.doi.org/10.1155/2020/8451639 |
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