【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.更多还原

【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<m/N<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.更多还原