基于编码转换的离散演化算法设计与应用

为了求解离散域上的组合优化问题，借鉴遗传算法（GA）、二进制粒子群优化（BPSO）和二进制差分演化（HBDE）中的映射方法，给出了一种基于映射变换思想设计离散演化算法（DisEA）的实用方法——编码转换法（ETM）。为了说明ETM的实用性与有效性，首先，基于ETM给出了一个离散粒子群优化算法（DisPSO）；然后，分别利用BPSO，HBDE和DisPSO等基于ETM构造的演化算法求解集合联盟背包问题和折扣{0-1}背包问题.通过与GA的计算结果比较指出，BPSO，HBDE和DisPSO的求解性能均优于GA，说明基于ETM提出的DisEA在求解背包问题方面具有良好的性能.由此表明，利用ETM方法设计DisEA是一种实用的有效方法。

In order to solve a combinatorial optimization problem in discrete domains by using evolutionary algorithms, this study draws lessons from the design concept of genetic algorithm (GA), binary particle swarm optimization (BPSO) and binary differential evolution with hybrid encoding (HBDE), to propose a simple and practical method for designing discrete evolution algorithm (DisEA) based on the idea of mapping transformation. This method is named encoding transformation method (ETM). For illustrating the practicability of ETM, a discrete particle swarm optimization (DisPSO) algorithm based on ETM is presented. For showing the feasibility and effectiveness of ETM, GA, BPSO, HBDE and DisPSO are used to solve the set union knapsack problem (SUKP) and the discounted {0-1} knapsack problem (D{0-1}KP), respectively. The results show that for SUKP and D{0-1}KP, the discrete evolutionary algorithms based on ETM, i.e. BPSO, HBDE and DisPSO have better performance than GA. This indicates that the design of DisEA based on ETM is not only a feasible method, but also a very practical and efficient method.