离散变量结构优化设计的组合算法

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．

A Combinatorial Algorithm for the Discrete Optimization of Structures

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-levels optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution X is found by using the heuristic algorithm , relative difference quotient algorithm, with high computational efficiency and high performance demonstrated by the performance test of random samples. In the second level, a mathematical model of (-1, 0, 1) programming is established first,and thed it is changed in to (0,1) programming model. The local optimum solution X#. will be from the (0, 1) programming by using the delimitative and combinatorial algorithm or the relative difference quotient algorithm. By this algorithm, the local optimum solution can be obtained certainly, and a method is provided to judge whether or not the approximate optimum solution obtained by heuristic algorithm is an optimum solution. The above comprehensive combinatorial algorithm has higher computatonal efficiency.