Abstract
In this study, we present the SlGi heuristic to address the no-depot minmax mTSP, comprising both construction and improvement stages. For each stage, we introduce a k-slice method algorithm and a SAG-insertion algorithm. Comparative analysis against clustering algorithms reveals the superior performance of the k-slice method across various data sets. Additionally, we compare minmax distances obtained using the SlGi heuristic with those from ES and MILP algorithms, as well as the optimal minmax distance. Results show that the SlGi heuristic achieves comparable minmax distances to algorithms in the literature and the known optimal solution. Notably, differences between the SlGi heuristic and the known optimal solution decrease with an increasing number of salesmen, accompanied by reduced execution time. Thus, the SlGi heuristic is expected to perfom better with a larger number of salesmen.
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