Symmetry Parallel Search Strategy For Permutation-related Optimization Problems

In this paper, we propose a symmetry parallel search strategy that can be applied to permutation-related combinatorial optimization problems. The proposed symmetry parallel search strategy considers the parity of the permutations and decomposes the solution space into two independent regions, i.e., even and odd permutations. Then, we analyze the relations between the parity of permutations and two representative neighborhood search operators. This allows trajectory-based metaheuristics to keep searching on even or odd permutations without breaking the utility of search operators. For experiments, we take the quadratic assignment problem and two classical trajectory-based metaheuristics as a case study. Experimental results show that the trajectory-based metaheuristics embedded with the symmetry parallel search strategy can achieve a competitive performance.