This paper presents a comparative performance analysis of some metaheuristics such as the African Buffalo Optimization algorithm (ABO), Improved Extremal Optimization (IEO), Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO), Max-Min Ant System (MMAS), Cooperative Genetic Ant System (CGAS), and the heuristic, Randomized Insertion Algorithm (RAI) to solve the asymmetric Travelling Salesman Problem (ATSP). Quite unlike the symmetric Travelling Salesman Problem, there is a paucity of research studies on the asymmetric counterpart. This is quite disturbing because most real-life applications are actually asymmetric in nature. These six algorithms were chosen for their performance comparison because they have posted some of the best results in literature and they employ different search schemes in attempting solutions to the ATSP. The comparative algorithms in this study employ different techniques in their search for solutions to ATSP: the African Buffalo Optimization employs the modified Karp–Steele mechanism, Model-Induced Max-Min Ant Colony Optimization (MIMM-ACO) employs the path construction with patching technique, Cooperative Genetic Ant System uses natural selection and ordering; Randomized Insertion Algorithm uses the random insertion approach, and the Improved Extremal Optimization uses the grid search strategy. After a number of experiments on the popular but difficult 15 out of the 19 ATSP instances in TSPLIB, the results show that the African Buffalo Optimization algorithm slightly outperformed the other algorithms in obtaining the optimal results and at a much faster speed.
Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs