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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.
Multi-objective optimization is a common problem in engineering applications, and the existing methods are not effective in solving high-dimensional optimization problems with more than three objectives. How to choose effective individuals is the key to solving high-dimensional multi-objective optimization problems. In this paper, we propose a sub-target evolutionary algorithm for solving high-dimensional multi-objective optimization problems.Finally, we prove that the Pareto non-dominated solution of multi-objective optimization problem can be obtained by sorting sub-objective function values, Then, according to the sorted information, the elements in the evolutionary population are selectively compared and the number of comparison times is reduced, so that the non-dominated solution set can be quickly obtained. Meanwhile, the Minkowski distance "k-nearest neighbor The distance calculation method is applied to the density function in the evolutionary process to accelerate the convergence rate.Compared with the current algorithms for solving high-dimensional multi-objective optimization, the calculation performance of the standard test function is compared, and the statistical results show that the proposed algorithm Performance advantages.