混合分解和强度帕累托多目标进化算法

在多目标进化优化中，使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低，使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略，提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿；然后,利用强度帕累托策略使解集均匀分布在帕累托前沿，利用解集重置分解策略中的权重向量集，使其适配于特定的帕累托前沿；最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准，将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优，在5个基准问题上接近于最优，且无论MOP的帕累托前沿是简单或复杂、连续或不连续的，该算法均能生成分布均匀的解集。

Hybrid decomposition and strength Pareto multi-objective evolutionary algorithm

In multi-objective evolutionary optimization, Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) with decomposition strategy is of low computational complexity, while Strength Pareto Evolutionary Algorithm-2 (SPEA2) 〖BP(〗with strength Pareto strategy 〖BP)〗can generate solution sets distributed uniformly. By combining these two strategies, a novel multi-objective evolutionary algorithm was proposed for solving Multi-objective Optimization Problem (MOP) with complex and discontinuous Pareto fronts in this paper. In the proposed algorithm, decomposition strategy was firstly used to make the solution set quickly approach the Pareto front; then strength Pareto strategy was used to make the solution set uniformly distributed along the Pareto front, and the weight vector set in decomposition strategy was rearranged based on this solution set, with a consequence of the weight vector set adapted to a particular Pareto front; and finally, decomposition strategy was used again to make the solution set further approach the Pareto front. In terms of Inverted Generational Distance (IGD) metric, the novel algorithm was compared with three state-of-art algorithms, MOEA/D, SPEA2 and paλ-MOEA/D on twelve benchmark problems. The experimental results indicate that the performance of the proposed algorithm is optimal on seven benchmark problems, and is approximately optimal on five benchmark problems. Moreover, the algorithm can generate uniformly distributed solution sets whether Pareto fronts of MOP are simple or complex, continuous or discontinuous.