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Firefly Algorithm (FA) mimics the flashing light characteristic of fireflies to solve optimization problems. An area where its utilization is limited is Travelling Salesman Problem (TSP). There are a number of algorithms utilized to solve the problem; however, there is still scope to do better in terms of solution quality. In this study, stepping ahead FA is proposed to solve the single depot Multiple Travelling Salesman Problem (MTSP) with threshold strategy. Rooted in the discrete FA (dFA), dFA-Step introduces a discrete transformation and threshold strategy to enhance optimization. The algorithm combines a unique stepping ahead mechanism with a threshold acceptance preference operator, achieving a balance between exploration and exploitation. The deterministic threshold acceptance approach facilitates the selection of sub-best solutions while the integration of neighborhood operators, like reverse cyclic permutation and swap transformation, enables exploration of solutions superior and closely aligned with the best solutions. The experimental results are compared with selected novel works from the literature where the results show competitive performance of the proposed algorithm in terms of solution quality. The proposed method gives insight in preference operator and stepping ahead mechanism for other researchers to utilize in discrete domains such as robotics and scheduling.

Single depot Multiple Travelling Salesman Problem solved with Preference based Stepping ahead Firefly Algorithm