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-level optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution 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 then it is changed into (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 computational efficiency.
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Project supported by Natural Science Foundation of Shandong Province
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Shan, C., Huanchun, S. A combinatorial algorithm for the discrete optimization of structures. Appl Math Mech 18, 847–856 (1997). https://doi.org/10.1007/BF00133342
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DOI: https://doi.org/10.1007/BF00133342