Abstract:

Aiming at the disadvantages of slow convergence and easily falling into local optimum of Differential Evolution （DE） algorithm， a DE algorithm based on multi-population adaptation and historically successful parameters was proposed. Firstly， all individuals were divided into elite， medium and inferior subpopulations according to fitness value， and different mutation strategies were used for different subpopulations to improve the balance between exploitation and exploration of the algorithm. Secondly， a new mutation strategy was proposed for inferior subpopulation to improve diversity of the algorithm. Thirdly， in order to further improve the balance between exploitation and exploration of the algorithm， the range of candidate parents of random individuals in each strategy was limited， which gave full play to the advantages of different individuals and the performance of the algorithm was improved. Finally， in order to strengthen the development of the algorithm， the historical successful parameters were used to guide the adaptive selection of parameters， and make the parameters keep moving in a good direction. Based on 30 test functions of CEC2014 test set， comparative experiments were carried out. Experimental results show that in 30-dimensional and 50-dimensional problems， compared with OLELS-DE （efficient Differential Evolution algorithm based on Orthogonal Learning and Elites Local Search mechanisms for numerical optimization）， the proposed algorithm has the rank level of Friedman test improved by 8.62% and 22.55% respectively. It can be seen that the performance and solution accuracy of the proposed algorithm are better， and the proposed algorithm can deal with global numerical optimization problems effectively.

Key words: Differential Evolution (DE), multi-population, historically successful parameter, multi-strategy adaptation, parameter adaptation

摘要：

针对差分进化（DE）算法收敛缓慢、易陷入局部最优的缺点，提出一种基于多种群自适应和历史成功参数的DE算法。首先，所有个体按适应度值被分为精英、中庸、劣势这3个子种群，并对不同子种群使用不同的变异策略，从而加强了算法开发性和探索性之间的平衡；其次，对劣势子种群提出一种新的变异策略提高算法的多样性；再次，为了进一步加强开发性与探索性之间的平衡，限定每种策略中随机个体的候选父母范围，从而发挥不同个体之间的优势，进而提高算法的性能；最后，为了加强算法的开发性，使用历史成功参数指导参数的自适应选择，从而引领参数一直向着好的方向前进。基于CEC2014测试集的30个测试函数进行了比较实验，实验结果表明，在30维、50维问题上，相较于OLELS-DE（efficient Differential Evolution algorithm based on Orthogonal Learning and Elites Local Search mechanisms for numerical optimization），所提算法的Friedman检验的秩次等级分别提高了8.62%和22.55%。可见，所提算法的性能与求解精度更优，能有效处理全局数值优化的问题。

关键词: 差分进化, 多种群, 历史成功参数, 多策略自适应, 参数自适应