基于3种群Lotka-Volterra模型的种群动力学函数优化算法  

Population Dynamics Optimization Based on 3 Populations Lotka-Volterra Model

作　　者：黄光球[1] 赵魏娟[1] 陆秋琴[1] 

机构地区：[1]西安建筑科技大学管理学院,西安710055

出　　处：《计算机科学》2013年第8期214-219,共6页Computer Science

基　　金：陕西省科学技术研究发展计划项目(2011K06-08);陕西省教育厅科技计划项目(12JK0789);陕西重点学科建设专项资金项目(E08001);陕西房地产技术经济及管理研究(E08005)资助

摘　　要：基于3种群Lotka-Volterra模型构造出了可全局收敛的种群动力学优化算法。在该算法中,每个种群对应着优化问题的一个试探解;基于3种群间的每种相互作用关系,提出了相应的图形表示方法以及对应的Lotka-Volterra模型构建方法,种群间的相互作用关系包括竞争关系、互惠共存关系、捕食-被食关系或者它们间的任意组合;3种群间的每种相互作用关系均对应着一种种群进化算子,该算子的数学表达式就是其对应的Lotka-Volterra模型的离散化表达式;另外,为了求解更复杂的优化问题求解,将种群融合、突变和选择等行为也构造成操作算子。所有算子的特性可以确保整个种群的适应度指数要么保持原状不变,要么向好的方向转移,从而确保了算法的全局收敛性;在种群演变过程中,种群从一种状态转移到另一种状态实现了种群对优化问题最优解的搜索。应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性。测试结果表明本算法是高效的。A population dynamics-based optimization algorithm with global convergence is constructed based on 3 popu- lations Lotka-Volterra model. In the algorithm, each population is just an alternative solution of an optimization prob- lem, and each mutual relation among 3 populations, 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 3 populations responds to an evolution operator, whose mathematical expression is just the dis- crete 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 so- lution. The stability condition of a reducible stochastic matrix was applied to prove the global convergence of the algo- rithm. The case study shows that the algorithm is efficient.

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 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]