北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (10): 1910-1917.doi: 10.13700/j.bh.1001-5965.2014.0706

• 算法与应用 • 上一篇    下一篇

基于子目标进化的高维多目标优化算法

雷宇曜, 姜文志, 刘立佳, 马向玲   

  1. 海军航空工程学院兵器科学与技术系, 烟台 264001
  • 收稿日期:2014-11-17 修回日期:2015-02-13 出版日期:2015-10-20 发布日期:2015-11-02
  • 通讯作者: 姜文志(1964-),男,山东莱州人,教授,ytjwz@sohu.com,主要研究方向为武器装备与作战指挥一体化技术. E-mail:ytjwz@sohu.com
  • 作者简介:雷宇曜(1984-),男,陕西丹凤人,博士研究生,2669116897@qq.com
  • 基金资助:
    国防预研项目(2014CX-C201-FW);国家自然科学基金青年科学基金(61002006)

Many-objective optimization based on sub-objective evolutionary algorithm

LEI Yuyao, JIANG Wenzhi, LIU Lijia, MA Xiangling   

  1. Department of Ordnance Science and Technology, Naval Aeronautical and Astronautical University, Yantai 264001, China
  • Received:2014-11-17 Revised:2015-02-13 Online:2015-10-20 Published:2015-11-02

摘要: 多目标优化问题是工程应用中的常见问题,已有的方法在解决3个目标以上的高维优化问题时效果欠佳.如何进行有效的个体选择是求解高维多目标优化问题的关键.针对该问题,提出了求解高维多目标优化问题的子目标进化算法.从理论上证明了多目标优化问题Pareto非支配解的求取,可通过子目标函数值排序,先行选择进化种群中部分非支配解;然后,根据排序信息有选择性地比较进化种群中的元素,减少了比较次数,从而快速获得非支配解集.同时,提出归一化函数差值的Minkowski距离"k近邻"距离计算方法,在进化过程中应用到密度函数中,加速了收敛速度.同当前求解高维多目标优化的算法,在对标准测试函数的计算性能上进行比较,统计结果显示了所提算法在性能上的优势.

关键词: 高维多目标优化, 子目标进化算法, Pareto非支配解集, Minkowski距离, 遗传算法

Abstract: many-objective optimization is widely used in engineering area. There are some flaws to deal with many-objective optimization problem which the number of objectives exceeded three. The method which could chose proper individual solution is very crucial to solve high-dimension many-objective optimization problem. A sub-objective evolutionary algorithm (SOEA) was put forward to solve this problem. It was given in an abstract way to get the non-dominance solutions of high-dimension many-objective optimization problem. Firstly, the value of sub-objective function was sorted, and then partial Pareto non-dominance solutions of evolutional set were obtained quickly. By using the information of sorting, it could reduce the times of solution comparison in evolutional set and could get the solutions quickly. A uniform difference Minkowski distance algorithm and "k-neighbor" strategy were applied to compute fitness function. By using this method, it could improve the convergence speed to approach Pareto non-dominance solutions. Compared with the algorithms which can solve many-objective optimization problem for computing standard testing functions, it was showed the better performance of the SOEA algorithm.

Key words: many-objective optimization, sub-objective evolutionary algorithm, Pareto non-dominance solution set, Minkowski distance, genetic algorithm

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