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-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.