Modified Grey Wolf Optimization to Solve Traveling Salesman Problem

Abstract

Traveling Salesman Problem (TSP) is arguably the most familiar combinatorial optimization problem. TSP is also a very popular benchmark problem for performance verification of new optimization algorithms even though the algorithms are developed for different problems such as numerical optimization. This paper proposes a new method to solve TSP based on a recently developed optimization method inspired by the hunting and social behavior of the grey wolf pack. Standard Grey Wolf Optimization (GWO) is developed for numerical optimization; GWO is modified and adapted in this study considering Swap Operator (SO) and Swap Sequence (SS) implication for TSP. SS is an arrangement of several SOs in which each SO holds two particular positions in a TSP solution that can be swapped to make a new solution. In the proposed modified GWO, each grey wolf is considered as a TSP solution and SS is considered to update the solution. In every iteration, a new tour is formed by swapping positions indicated by SOs of the SS to the previous solution. The proposed technique is tested on several instances of the benchmark TSP and the final results are compared with the other well-known methods. Experimental results show that the proposed method is a decent technique to resolve TSP.