| 摘要: |
| 针对多目标进化的特点,提出了用擂台赛法则(arena's principle,简称AP)构造多目标Pareto最优解集的方法,论证了构造方法的正确性,分析了其时间复杂度为O(rmN)(0＜m/N＜1).理论上,当AP与Deb的算法以及Jensen的算法比较时(它们的时间复杂度分别为O(rN2)和O(Nlog(r-1)N)),AP优于Deb的算法;当目标数r较大时(如r≥5),AP优于Jensen的算法;此外,当m/N较小时(如m/N≤50%),AP的效率与其他两种算法比较具有优势.对比实验结果表明,AP具有比其他两种算法更好的CPU时间效率.在应用中,AP可以被集成到任何基于Pareto的MOEA中,并能在较大程度上提高MOEA的运行效率. |
| 关键词: 多目标进化 擂台赛法则 非支配集构造方法 Pareto最优解集 运行效率 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60435010, 69974043 (国家自然科学基金); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education (教育部留学回国人员科研启动基金); the Natural Science Foundation of Hu'nan Province of China under Grant Nos.01JJY2060, 05JJ30125 (湖南省自然科学基金); the SRF of Hu'nan Provincial Education Department (湖南省教育厅重点科研项) |
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| An Approach of Constructing Multi-Objective Pareto Optimal Solutions Using Arena's Principle |
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ZHENG Jin-Hua,JIANG Hao,KUANG Da,SHI Zhong-Zhi
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| Abstract: |
| This paper proposes an approach, namely the arena’s principle (AP), to construct the Pareto optimal solutions by utilizing features of the multi-objective evolution. It is proved that the AP works correctly and its computational complexity is O(rmN) (0<1). Theoretically, when AP is compared with Deb’s algorithm and Jensen’s algorithm (their computational complexity are O(rN2) and O(Nlog(r-1)N) respectively), AP is better than Deb’s, and is also better than Jensen’s when the objective number r is relatively large (such as r≥5). Moreover, AP performs better than the other two algorithms when m/N is relatively small (such as m/N≤50%). Experimental results indicate that AP performs better than the other two algorithms on the CPU time efficiency. In applications, AP can be integrated into any Pareto-based MOEA to improve its running efficiency. |
| Key words: multi-objective evolution arena’s principle non-dominated set Pareto optimal solutions running efficiency |
