混合约束多峰优化问题的一个协同共轭进退粒子群算法  

A cooperative conjugate advance-retreat particle swarm optimization algorithm for hybrid constrained multimodal optimization problems

作　　者：陈相兵[1] 陈晨[2] 闵心畅[3] CHEN Xiang-Bing;CHEN Chen;MIN Xin-Chang(Division of Mathematics,Sichuan University Jinjiang College,Meishan 620860,China;College of Science,Civil Aviation Flight University of China,Guanghan 618307,China;School of Mathematics,Sichuan University,Chengdu 610044,China)

机构地区：[1]四川大学锦江学院数学教学部,眉山620860 [2]中国民用航空飞行学院理学院,广汉618307 [3]四川大学数学学院,成都610044

出　　处：《四川大学学报（自然科学版）》2023年第1期32-38,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技计划(2022JDRC0068,2021JDRC0080);四川省教育厅项目(18ZB0363);中国民用航空飞行学院校级项目(J2021-058)。

摘　　要：为解决混合(等式和不等式)约束的多峰优化问题(MOPs),本文在粒子群算法框架下提出了粒子优度比较准则和局部协同与共轭进退寻优两种迭代进化策略.优度比较准则在适应度和约束违反度的双重限制下指导粒子高效地执行进化策略,局部协同策略可使粒子能通过局部抱团收敛到多个全局最优解,而共轭进退寻优策略则提升了寻优的速度和精度.基于优度比较准则与两种进化策略的有效结合,本文设计了一个协同共轭进退粒子群(CCARPSO)算法,以充分融合粒子群算法的全局搜索能力和共轭进退法的局部快速寻优能力.数值仿真表明,该算法能有效解决复杂约束MOPs和非线性方程组的多根问题,在广义Logistic分布的参数估计中有全局优化能力和较高的计算精度.This paper aims at the multimodal optimization problems(MOPs)with equality and inequality constraints.A new algorithm is proposed following the particle swarm optimization idea.This algorithm consists of a superiority comparison criterion and two iterative evolutionary strategies.The superiority comparison criterion guides the particles on how to evolute according to the constructed constraint violation degree and the fitness(i.e.,the objective function value).The local cooperation strategy ensures that all particles can converge to multiple global optimal solutions through local clustering.The conjugate advance-retreat optimization strategy improves the speed and precision of optimization.Our algorithm,named cooperative conjugate advance-retreat particle swarm optimization(CCARPSO)algorithm,integrates the global searching ability of PSO and the local fast optimization capability of conjugate advance-retreat method.In numerical simulations,the algorithm effectively solves MOPs with complex constraints and nonlinear equations with multiple solutions,and has high global optimization ability and calculation accuracy in estimating parameters of the generalized Logistic distribution.

关 键 词：多峰优化 优度比较 局部协同 共轭方向 进退法 粒子群 

分 类 号：O29[理学—应用数学]