Abstract: In order to improve the convergence and distribution in solving the large-dimensional multi-objective optimization problem(MOP)with differential evolution algorithm(DE), a multi-objective differential evolution algorithm based on the population self-adaptive adjustment(PSAMODE)is proposed. A population expansion strategy is designed for DE, which generates some new individuals to search optimal non dominated solutions in decision space; a population shrinking strategy is also designed, which depends on the degree of contribution of the non dominated solutions to elimination of poor individuals to reduce the computational load. Meanwhile, it sets aside some space to the new disturbance individuals with population diversity. The proposed method is introduced to elite learning strategies to prevent trapping into local convergence. Some typical multi-objective optimization functions are tested to verify this method. Simulation results show that compared with other algorithms, PSAMODE has obvious advantages, superior performance and ensure a good convergence. To obtain the Pareto optimal solution set, the proposed method has a more uniform distribution and wider coverage, especially suitable for high-dimensional complex solution of the multi-objective optimization problem.

Key words: multi-objective optimization, population expansion strategy, population shrinking strategy, differential evolution algorithm, elite learning strategy

摘要： 为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。

关键词: 多目标优化, 种群扩增, 种群缩减, 差分进化算法, 精英学习策略