关键词: 优化,进化计算,种群动力学,生物地理学优化算法,Lotka-Volterra模型

Abstract: A population dynamics-based optimization algorithm with global convergence is constructed based on 3populations Lotka-Volterra model．In the algorithm,each population is just an alternative solution of an optimization problem,and each mutual relation among 3populations,which includes the competition,mutual-benefit,predator-prey and their arbitrary combinations,is expressed into a graph,and its associated Lotka-Volterra model is established,and each mutual relation among 3populations responds to an evolution operator,whose mathematical expression is just the discrete expression of its associated Lotka-Volterra model,furthermore,in order to solve much complicated optimization problems,the mergence,mutation and selection behaviour of populations are used to construct evolution operators．The features of all constructed operators can ensure population suitability index(PSI)of each population to keep either to stay unchanged or to transfer toward better states,therefore the global convergence is ensured,and during evolution process of populations,each population’s transferring from one state to another realizes the search for the optimum solution．The stability condition of a reducible stochastic matrix was applied to prove the global convergence of the algorithm．The case study shows that the algorithm is efficient.

Key words: Optimization,Evolutionary computation,Population dynamics,Biogeography-based optimization,Lotka-Volterra model