离散变量结构优化设计的组合算法<sup>*</sup>

柴山; 孙焕纯

离散变量结构优化设计的组合算法^*

柴山^1,2,
孙焕纯¹

1.
大连理工大学工程力学系, 116023;
2.
山东工程学院, 山东淄博 255012

基金项目: * 山东省自然科学基金

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出版历程
- 收稿日期: 1996-11-28
- 刊出日期: 1997-09-15

A Combinatorial Algorithm for the Discrete Optimization of Structures

Chai Shan^1,2,
Sun Huanchun¹

1.
Dalian University of Technology, Dalian 116023, P. R. China

摘要

摘要: 本文首先给出了离散变量优化设计局部最优解的定义,然后提出了一种综合的组合算法.该算法采用分级优化的方法,第一级优化首先采用计算效率很高且经过随机抽样性能实验表明性能较高的启发式算法─—相对差商法,求解离散变量结构优化设计问题近似最优解 X ;第二级采用组合算法,在 X 的离散邻集内建立离散变量结构优化设计问题的(-1,0.1)规划模型,再进一步将其化为(0,1)规划模型,应用定界组合算法或相对差商法求解该(0,1)规划模型,求得局部最优解.解决了采用启发式算法无法判断近似最优解是否为局部最优解这一长期未得到解决的问题,提高了计算精度,同时,由于相对差商法的高效率与高精度,以上综合的组合算法的计算效率也还是较高的.
- 离散变量 /
- 结构最优化 /
- 组合优化 /
- 局部最优解
Abstract: The definition of local optimum solution of the discrete optimization is first given.and then a comprehensive combinatorial algorithm is proposed in this paper. Two-leveloptimum method is used in the algorithm. In the first level optimization, anapproximate local optimum solution X is found by using the heuristic algorithm,relative difference quotient algorithm. with high computational efficiency and highperformance demonstrated by the performance test of random samples. In the secondlevel, a mathematical model of(-1, 0, 1) programming is established first, and then itis changed into(0, 1) programming model. The local optimum solution X^* will befrom the(0, 1) programming by using the delimitative and combinatorial algorithm orthe relative difference quotient algorithm. By this algorithm, the local optimumsolution can be obtained certainly, and a method is provnded to judge whether or notthe approximate optimum solution obtained by heuristic algorithm is an optimumsolution. The above comprehensive combinatorial algorithm has higher computationalefficiency.
- discrete variables /
- structural optimization /
- combinatorial optimization /
- local optimum solution

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参考文献(6)

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[2]	柴山等,离散变量优化设计的方向差商法,计算结构力学及其应用,3(1994).
[3]	柴山,一类(0,1)规划问题的定界组合算法及其在离散变量结构优化设计中的应用,工程力学,1(1995).
[4]	隋允康等,含梁结构离散断面的优化设计及其对平面框架的程序实现,计算结构力学及其应用,3(1987).
[5]	许强、孙焕纯,离散变量析架结构优化设计的组合算法,大连理工大学学报,6(1991).
[6]	柴山、孙焕纯,寻求离散变量析架结构优化设计(0,1)规划模型可行集的差商向量法,大连理工大学学报.5(1995).