A New Discrete Whale Optimization Algorithm with a Spiral 3-opt Local Search for Solving the Traveling Salesperson Problem

The whale optimization algorithm is a metaheuristic inspired by the hunting strategy of humpback whales. This paper proposes a new discrete spiral whale optimization algorithm (DSWOA) to solve the traveling salesperson problem (TSP). Our approach uses sequential consecutive crossover and spiral 3-opt search, a modified version of the popular 3-opt local search. Spiral 3-opt search works like the original 3-opt heuristic but only uses part of the tour to generate 3-opt moves. We show that spiral 3-opt achieves results similar to the original 3-opt technique and significantly reduces runtime. We evaluate DSWOA's performance on 19 TSP instances against six benchmark algorithms. Our results suggest that DSWOA produces TSP solutions that are as good or better than our competitors. For five of the six benchmark algorithms, we demonstrated statistically significant improvements.