Relative distances approach for multi-traveling salesmen problem

Abstract

In this paper, we present a novel approach to addressing the Multi-Traveling Salesman Problem (MTSP), a complex optimization challenge involving the simultaneous fulfillment of multiple tasks such as cargo delivery and warehouse placement by multiple autonomous agents. In general there are two primary objectives to be achieved: minimizing the total path cost and minimizing the maximum cost incurred by agents, also known as makespan. While our primary focus centers on cost minimization, prioritizing this aspect alone often amplifies makespan. Our approach strikes a balance by ensuring that makespan remains within a reasonable threshold. Given the problem’s combinatorial nature, attaining cost-optimal solutions proves infeasible under current constraints. Hence, our emphasis shifts towards swift solution discovery to align with practical applicability. Consequently, we posit that the third pivotal objective is to curtail complexity and expedite solution acquisition, thereby enhancing the problem’s real-world viability. The Multi-Traveling Salesman Problem (MTSP) is typically approached in two distinct phases. In the initial phase, tasks are allocated to salesmen using various methods (such as K-Means or DBSCAN). The second phase involves determining the optimal routes for each salesman, a problem identical to the classic Traveling Salesman Problem (TSP). Our novel heuristic approach integrates these phases into a single method through our relative distance model. This model facilitates the easy addition and removal of tasks within the problem space and enables real-time scheduling.