基于子目标进化的高维多目标优化算法

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 based on sub-objective evolutionary algorithm

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.