一种基于目标空间转换权重求和的超多目标进化算法

权重求和是基于分解的超多目标进化算法中常用的方法, 相比其他方法具有计算简单、搜索效率高等优点, 但难以有效处理帕累托前沿面(Pareto optimal front, PF)为非凸型的问题. 为充分发挥权重求和方法的优势, 同时又能处理好PF为非凸型的问题, 本文提出了一种基于目标空间转换权重求和的超多目标进化算法, 简称NSGAIII-OSTWS. 该算法的核心是将各种问题的PF转换为凸型曲面, 再利用权重求和方法进行优化. 具体地, 首先利用预估PF的形状计算个体到预估PF的距离; 然后, 根据该距离值将个体映射到目标空间中预估凸型曲面与理想点之间的对应位置; 最后, 采用权重求和函数计算出映射后个体的适应值, 据此实现对问题的进化优化. 为验证NSGAIII-OSTWS的有效性, 将NSGAIII-OSTWS与7个NSGAIII的变体, 以及9个具有代表性的先进超多目标进化算法在WFG、DTLZ和LSMOP基准问题上进行对比, 实验结果表明NSGAIII-OSTWS具备明显的竞争性能.

A Many-objective Evolutionary Algorithm Based on Weighted Sum of Objective Space Transformation

The weighted sum method is a common decomposition method in many-objective evolutionary algorithm based on decomposition. Compared with other methods, it has the advantages of computationally easy and high search efficiency. However, it is difficult for this method to handle the problem with nonconvex Pareto optimal front (PF) effectively. To take full advantage of the weighted sum method and effectively handle the problem with nonconvex PF at the same time, a many-objective evolutionary algorithm based on weighted sum of objective space transformation is proposed, namely NSGAIII-OSTWS. The core of the NSGAIII-OSTWS is to transform the PF of various problems into convex surfaces, and then apply the weighted sum method to optimize the transformed problem. Specifically, the distance between the individual and the estimated PF is calculated firstly. Then all individuals are mapped into the corresponding location between the estimated convex surface and the ideal point according to their distance value. Finally, the fitness values of all mapped individuals are calculated by weighted sum function, and then the evolutionary optimization of the problem is proceeded. In order to verify the effectiveness of NSGAIII-OSTWS, seven variants of NSGAIII, and nine representative advanced many-objective evolutionary algorithms are compared on the WFG, DTLZ and LSMOP benchmark problems. The experimental results show that NSGAIII-OSTWS has obviously competitive performance compared with the comparison algorithms.