用于结构优化设计的改进多目标群搜索算法

摘要

在多目标群搜索算法(multi-objective group search optimization,MGSO)基本原理的基础上,结合Pareto 最优解理论,提出了基于约束改进的多目标群搜索算法(IMGSO),并应用于多目标的结构优化设计.算法的改进主要有3个方面:第一,引入过渡可行域的概念来处理约束条件;第二,利用庄家法来构造非支配解集;最后,结合禁忌搜索算法和拥挤距离机制来选择发现者,以避免解集过早陷入局部最优,并提高收敛精度.采用IMGSO优化算法分别对平面和空间桁架结构进行了离散变量的截面优化设计,并与MGSO优化算法的计算结果进行了比较,结果表明改进的多目标群搜索优化算法IMGSO与MGSO算法相比具有更好的收敛精度.通过算例表明:IMGSO算法得到的解集中的解能大部分支配MGSO算法的解,在复杂高维结构中IMGSO算法的优越性更加明显,且收敛速度也有一定的提高,可有效应用于多目标的实际结构优化设计.%An improved multi-objective group search optimizer (IMGSO) was presented for multi-objective optimum design. The algorithm was based on the multi-objective group search optimization (MGSO) and combined with Pareto optimal solutions theory. The improvement included three aspects. Firstly, the concept of transition-feasible region was introduced to handle the constrained conditions. Secondly, Dealer's principle was employed to build the non-dominated set. At last, in order to avoid getting into the local optimum untimely and improve the solution precision, the selection of the producer was achieved based on the combination of Tabu search algorithm and crowded mechanism. The IMGSO algorithm was compared with the MGSO by two numerical examples of the design of planar and spatial truss structures with discrete variables. The results show that the solution of the MGSO algorithm is mostly dominated by the IMGSO, and the IMGSO algorithm gets preferable convergence accuracy and obvious advantages for complex problems especially for high-dimensional ones, meanwhile convergence rate is improved to some extent. The proposed IMGSO can be used more effectively for multi-objective practical structural optimal design problems.