Abstract
The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given a set ofngoals/targets andmagents, the objective is to findmround 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 ofngoals/targets and a team ofmagents,msubtours (simple paths) are sought such that each target is visited only once and by only one agent. We optimize for minimum time rather than minimum total 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.
Highlights
Applications from space exploration [1,2,3] and drone delivery to search and rescue problems [4,5,6,7] have underlined the need to plan a coordinated strategy for a team of vehicles to visit targets
Planning problems have been investigated through Multiple Traveling Salesmen Problem (MTSP) formulations, in [18, 19], where a dynamic mission planning system for multiple mobile robots operating in unstructured environments is presented, or in [20], where the MTSP formulation is used to describe a path planning problem for a team of cooperative vehicles
We compare our method with the results reported in [34], where an Ant Colony Optimization algorithm is compared with the Modified Genetic Algorithm (MGA) of [32]
Summary
Applications from space exploration [1,2,3] and drone delivery to search and rescue problems [4,5,6,7] have underlined the need to plan a coordinated strategy for a team of vehicles to visit targets. We formulate the overall planning problem as finding a near-optimal set of paths that allows the team of agents to visit a given number of targets in the shortest amount of time. A long-term goal of this work is to endow a team of autonomous agents (drones) with the capability of cooperative motion planning In this application, the time available for the solution is limited and real-time algorithms providing. The problem of planning a set of strategies for cooperatively exploring the environment with a fleet of vehicles is modeled as a variant of the classical MTSP, referred to as the Multiagent Planning Problem (MAPP): given n nodes (targets) and m salesmen (agents) located at different depots, the MAPP seeks m tours such that each target is visited only once and by only one agent that minimizes a given cost function (specified by (8) and (9)).
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