The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given a set of n goals/targets and m agents, the objective is to find m round trips, such that each target is visited only once and by only one agent, and the total distance of these round trips is minimal. In this paper we describe the Multiagent Planning Problem, a variant of the classical Multiple Traveling Salesmen Problem: given a set of n goals/targets and a team of m agents, m subtours (simple paths) are sought such that each target is visited only once and by only one agent. We optimize for minimumtime rather than minimumtotal distance; therefore the objective is to find the Team Plan in which the longest subtour is as short as possible (a min–max problem). We propose an easy to implement Genetic Algorithm Inspired Descent (GAID) method which evolves a set of subtours using genetic operators. We benchmarked GAID against other evolutionary algorithms and heuristics. GAID outperformed the Ant Colony Optimization and the Modified Genetic Algorithm. Even though the heuristics specifically developed for Multiple Traveling Salesmen Problem (e. g., k-split, bisection) outperformed GAID, these methods cannot solve the Multiagent Planning Problem. GAID proved to be much better than an open-source Matlab Multiple Traveling Salesmen Problem solver.
Kalmár-Nagy, T., Giardini, G., & Bak, B. D. (2017). The multiagent planning problem. Complexity, 2017. https://doi.org/10.1155/2017/3813912