The global search algorithms in minimum cost flow problem with concave costs

• Main Authors: Jung-Chien Chen, 陳建榮
• Other Authors: Shangyao Yan
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/35650856338064084785

碩士 === 國立中央大學 === 土木工程研究所 === 90 === The minimum cost transshipment problems are traditionally formulated as a linear cost problem, in order to reduce problem complexity. In reality, the unit cost decreases as the amount transported increases, resulting in a concave cost function. Recently, a research started to use advanced neighborhood search algorithms to solve concave cost network problems in order to find better solutions than traditional heuristics. However, such neighborhood search algorithms easily encounter degeneracy problems, resulting in decreased solution efficiency. It is wonder if such algorithms can explore the whole domain area to find good solutions. This research attempts to develop global search algorithms to solve normal minimum cost network flow problems with concave arc costs. To evaluate global search algorithms and neighborhood search algorithms, we developed two neighborhood search algorithms referring to the threshold accepting algorithm and the great deluge algorithm. The results will hopefully be useful reference for practitioners to solve their real transshipment problems. We first explored the problem characteristics then modified the genetic algorithm (GA) to develop suitable global search algorithms. In details, we designed an efficient coding method to represent network solutions. During various stages of GA, including production, reproduction, selection, crossover, and mutation, we designed methods that are suitable for the characteristics of minimum cost network flow problems with concave arc costs. To evaluate global and neighborhood search algorithms, we designed a randomized network generator to produce many test problems. We employed C++ computer language to code all necessary programs and perform tests on personal computers. The results show that the coding method and other stages in GA performed relatively well in the tests.