Seeking Multiple Solutions of Combinatorial optimization Problems: A Proof of Principle Study

Problems with multiple optimal solutions widely exist in the real world. In some applications, it is required to locate multiple optima. However, most studies are dedicated to the continuous multi-solution optimization, while few works contribute to the discrete multi-solution optimization. To promote the multi-solution research in the discrete area, we design a benchmark test suite for multi-solution traveling salesman problems and propose two evaluation indicators. Further, in order to solve the problems, the genetic algorithm is incorporated with a niching technique defined in the discrete space. The proposed algorithm is compared with an existing algorithm. Experimental results demonstrate that the proposed algorithm outperforms the compared algorithm concerning the quality and diversity of obtained solutions.