一种多目标优化问题的理想灰色粒子群算法

Grey particle swarm optimization based on TOPSIS for multi-objective optimization problems

针对逼近理想解的排序方法对Pareto前端的距离跟踪以及灰色关联度能够很好地分析非劣解集曲线与Pareto最优解集曲线的相似性,提出了一种求解多目标优化问题的理想灰色粒子群算法。该算法利用理想解理论与灰色关联度理论来求解粒子与理想解之间的相对适应度和灰色关联度系数,把两者的和定义为相对理想度,通过相对理想度来判别粒子的优劣,以确定个体极值和全局极值。通过四组不同类型的基准函数测试算法性能,并与目标加权法和灰色粒子群算法比较分析,结果表明该算法能够较好地收敛到Pareto最优解集,不但具有较好的收敛性和分布均匀性,而且算法的复杂度并没有增加。

A grey particle swarm optimization algorithm based on TOPSIS for solving multi-objective optimization problems,which proposed by taking advantage of technique for order preference by similarity to ideal solution （ TOPSIS） trace Pareto front for distance and grey correlation degree distinguish similarity between curves of non-inferior solution sets and curves of Pareto front solution sets. The algorithm took advantage of TOPSIS theory and grey correlation degree theory to acquire relative fitness coefficient and gray correlation coefficient,and defined their sum as relatively ideal degree,which distinguished advantages and disadvantages of particles and determines individual extreme and global extreme. Validated the algorithm using four different types benchmark cases. The experimental results show that grey particle swarm optimization based on TOPSIS,compared with objective weighting method and grey PSO algorithms,it can find many Pareto optimal solutions distributed onto the Pareto front and do not increase the complexity of the algorithm.