Min-Max Tours for Task Allocation to Heterogeneous Agents

TL;DR

This paper addresses a complex task allocation problem for heterogeneous mobile agents, proposing a three-phase approximation algorithm with proven bounds to minimize the maximum tour cost among agents.

Contribution

It introduces a novel three-phase approximation algorithm for a NP-hard task allocation problem with heterogeneous agents and task type constraints.

Findings

Provides a 5-factor approximation algorithm for general case.

Achieves a 4-factor approximation when each agent type is unique.

Demonstrates the algorithm's effectiveness in minimizing maximum tour cost.

Abstract

We consider a scenario consisting of a set of heterogeneous mobile agents located at a depot, and a set of tasks dispersed over a geographic area. The agents are partitioned into different types. The tasks are partitioned into specialized tasks that can only be done by agents of a certain type, and generic tasks that can be done by any agent. The distances between each pair of tasks are specified, and satisfy the triangle inequality. Given this scenario, we address the problem of allocating these tasks among the available agents (subject to type compatibility constraints) while minimizing the maximum cost to tour the allocation by any agent and return to the depot. This problem is NP-hard, and we give a three phase algorithm to solve this problem that provides 5-factor approximation, regardless of the total number of agents and the number of agents of each type. We also show that in the special case where there is only one agent of each type, the algorithm has an approximation factor of 4.