基于ε占优的正交多目标差分演化算法研究

Research on an ε-Domination Based Orthogonal Differential Evolution Algorithm for Multi-Objective Optimization

演化多目标优化是目前演化计算中热门研究方向之一.但是,要设计一种高效、鲁棒的演化多目标优化算法,使其找到接近最优和完整的非劣解集是一项很困难的任务.为了能有效求解多目标优化问题,提出了一种新的多目标差分演化算法.新算法具有如下特征:1)利用正交实验设计和连续空间量化的方法产生初始群体,使得初始群体中的个体可以均匀分布于搜索空间,并且可以使好的个体在演化过程中得到利用;2)采用Archive群体保存非劣解,并利用ε占优方法更新Archive群体,从而可以使算法较快获得分布很好的Pareto解集;3)为了加快算法收敛,提出一种基于随机选择和精英选择的混合选择机制.通过8个标准测试函数对新算法进行测试,并与其他一些多目标演化算法进行比较,其结果表明新算法可以有效逼近真实Pareto前沿且分布均匀,并且在收敛性和多样性的求解精度和稳定性上与其他算法相当.同时,通过实验的方法验证了新算法改进之处的有效性,并进一步讨论了差分演化算法中CR取值和混合选择机制中选择控制参数λ取值对算法性能的影响.

Evolutionary multi-objective optimization （EMO） has become a very popular topic in the last few years. However, to design an efficient and effective EMO algorithm to find the near-optimal and near-complete Pareto front is a challenging task. In this paper, a novel differential evolution algorithm is proposed to solve multi-objective optimization problems （MOPs） efficiently. The proposed approach uses an archive population to retain the obtained non-dominated solutions; also it adopts the orthogonal design method with quantization technique to generate an initial population of points that are scattered uniformly over the feasible solution space, so that the algorithm can evenly scan the feasible solution space to locate good points for further exploration in subsequent iterations. Moreover, it is based on the ε-dominance concept to obtain a good distribution of Pareto-optimal solutions in a small computational time. To make the algorithm converge faster, the new approach employs a hybrid selection mechanism in which a random selection and an elitist selection are interleaved. Experiments on eight benchmark problems of diverse complexities show that the new approach is able to obtain a good distribution in all cases. Compared with several other state-of-the-art evolutionary algorithms, it achieves not only comparable results in terms of convergence and diversity metrics, but also a considerable reduction of the computational effort. Furthermore, the influences of different CR value and the parameter value of hybrid selection mechanism on the performance of the algorithm are discussed experimentally.