一种新的混合演化多目标优化算法

在KKT(Karush-Kuhn-Tucker)条件下,m维的连续多目标优化问题的Pareto解集在决策空间是一个(m-1)维的流形(manifold)。随着算法的迭代,当前种群将分布在流形的周围。为充分利用这一规则特性(regularity property)以解决具有复杂PS(Pareto set)的多目标优化问题,本文提出一种基于差分算子和分布估计算子的混合子代生成算法。首先,引入一个参数来指示当前种群的收敛程度,即当前种群解个体所构成的数据的协方差矩阵的前(m-1)个特征值的和与所有特征值的和的比,比值越大,收敛程度越高;进而,根据不同比值,自适应调节差分算子和分布估计算子生成新解的数量。将该算法在tec09系列测试函数上进行仿真实验,并与RM-MEDA、NSGA-II-DE两个算法进行对比,实验结果表明,RM-MEDA/DE算法优于与之比较的其他算法。

A New Hybrid Evolutionary Multi-objective Optimization Algorithm

From the Karush-Kuhn-Tucher condition, it can be induced that, in the decision space, the Pareto set of a m-D continuous multi-objective optimization problem is a piecewise continuous (m-1)-D manifold. To take full advantage of this regularity property to solve multi-objective optimization problem with a complex Pareto Set (PS), this paper proposes a new algorithm, named RM-MEDA/DE, which hybridizes differential evolution (DE) and estimation of distribution (EDA). Firstly, a new parameter is employed, which is the ratio of the sum of the first (m-1) largest eigenvalue of the populations covariance matrix to the sum of the whole eigenvalue, to illustrate the degree of convergence of the population. The bigger the ratio is the higher the convergence will be. The number of new solution generated by two methods is adjusted by the parameter. The proposed algorithm is validated on nine tec09 problems. Systematic experiments have shown that RM-MEDA/DE outperforms two other state-of-the-art algorithms , namely, RM-MEDA and NSGA-II-DE.