Coordination of Cyclic crossover and Bat Algorithm for the Travelling Salesman Problems in Different Environments: A Simulation Approach

Sova Pal, P. Dutta, Indadul Khan, Prasenjit Pramanik, A. K. Maiti, M. Maiti
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Abstract

In this study, the features of cyclic crossover process and K-opt are incorporated in the bat algorithm (BA) to solve the Travelling Salesman Problems (TSP) in different environments. Swap operation and swap sequence are applied for the modification of the different operations of the BA to solve the TSPs. The cyclic crossover operation is applied in a regular interval of iterations on the best found solution and each solution of the final population of BA for the enhancement of the exploration as well as exploitation of the search process. K-Opt operation is applied on the population in each iteration of the BA with some probability for the exploitation. The algorithm is tested with a set of benchmark test instances of the TSPLIB. The algorithm produces exact results for a set of significantly large size problems. For the TSPs in fuzzy environment, a fuzzy simulation approach is proposed to deal with the fuzzy data having linear as well as non-linear membership functions. Also, a rough simulation process is proposed to deal with the TSPs in the rough environment where rough estimation can be done following any type of rough measure. The performance of the algorithm is compared with the state-of-the-art algorithms for the TSPs with crisp cost matrices using different statistical tools.
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不同环境下旅行推销员问题的循环交叉和蝙蝠算法的协调:一种模拟方法
本研究在蝙蝠算法(BA)中加入了循环交叉过程和 K-opt,以解决不同环境下的旅行推销员问题(TSP)。交换操作和交换序列被用于修改 BA 的不同操作,以解决 TSP。循环交叉操作以一定的迭代间隔应用于最佳发现解和 BA 最终群体的每个解,以加强搜索过程的探索和利用。在 BA 的每次迭代中,都会以一定的概率对群体进行 K-Opt 操作,以提高利用率。该算法使用 TSPLIB 的一组基准测试实例进行了测试。该算法对一组规模较大的问题产生了精确的结果。对于模糊环境中的 TSP,提出了一种模糊模拟方法来处理具有线性和非线性成员函数的模糊数据。此外,还提出了一种粗略模拟程序来处理粗略环境中的 TSP,在这种环境中,可以根据任何类型的粗略度量进行粗略估计。利用不同的统计工具,将该算法的性能与具有清晰成本矩阵的 TSP 的最先进算法进行了比较。
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