A discrete cuckoo search algorithm for traveling salesman problem and its application in cutting path optimization

Abstract

The Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem with various industrial applications. This paper proposes a discrete cuckoo search algorithm based on random walk and cluster analysis to solve the traveling salesman problem (TSP). Although the original cuckoo search algorithm is not suitable to solve the TSP, this algorithm is modified to solve the TSP. Lévy flights and random preference walk in the original cuckoo search algorithm are replaced with novel tools, including the local adjustment operator and discrete random walk. The former is utilized to preserve superior solutions found by the algorithm, while the latter is employed to maintain the diversity of the population. For large-scale TSP problems, the k-means algorithm is first utilized to divide cities into k categories for optimization, while random algorithms are adopted to combine them. A simple 2-opt operator is utilized as the local optimization operator to accelerate the algorithm's convergence rate. Multiple groups of standard TSPLIB datasets are chosen to compare the proposed method with state-of-the-art optimization algorithms that also use the 2-opt/k-opt optimization operator. According to the experimental results, the stability and accuracy of the proposed algorithm are superior to the state-of-the-art optimization algorithms. Regarding the solution accuracy, the algorithm improves 0.39%, 0.29%, 0.84%, 0.4%, 0.07% and 2.22% in the optimal solution over discrete cuckoo search (DCS), discrete bat algorithm (DBA), discrete sine–cosine algorithm (DSCA), random-key cuckoo search (RKCS) and discrete spider monkey optimization (DSMO) on the standard test cases, and 0.58%, 0.19%, 0.85%, 0.43%, 0.36% and 5.83% in the average optimal solution. Regarding stability, the variance of the optimal solutions of RKCS, DSMO, and novel discrete differential evolution (NDEE) for 30 independent runs is 38.5, 52.6, and 59.4 times higher than that of the algorithm in this paper. Finally, the proposed algorithm optimizes air knife migration during glass cutting. Accordingly, the path for air knife migration is reduced by 8556 mm.