基于子目标进化的高维多目标优化算法

Many-objective optimization based on sub-objective evolutionary algorithm

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.

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 prob- lem. 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. First- ly, the value of sub-objective function was sorted, and then partial Pareto non-dominance solutions of evolu- tional set were obtained quickly. By using the information of sorting, it could reduce the times of solution com- parison in evolutional set and could get the solutions quickly. A uniform difference Minkowski distance algo- rithm 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.