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中文摘要：
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D（rN^2）和O（Nlog^（r-1）N）），AP优于Deb的算法；当目标教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．
英文摘要：
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（rN^2） 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.
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