How Many Robots are Enough: A Multi-Objective Genetic Algorithm for the Single-Objective Time-Limited Complete Coverage Problem

Xing Zhou, Huaimin Wang, Bo Ding

Abstract: Complete coverage, which is the foundation of many robotic applications, aims to cover an area as quickly as possible. This study investigates the time-limited version of multi-robot complete coverage problem, that is, to find the least number of robots and allocate tasks properly to them such that they can finish a known mission within the time limit. This version of problem can be tackled straightforwardly based on optimizing the task-allocation to a fixed number of robots and enumerating the number. However, the number-fixed problem is NP-hard and the existing algorithm for the number-fixed problem allows intersecting tasks (possibly causing robots' interference) and endures high approximation factor. In this study, the time-limited complete coverage problem is tackled with a multi-objective approach, instead of enumerating robots' number and optimizing each number-fixed problem one by one. The multi-objective GA, Mofint, at first estimates the lower and upper bounds of the number of robots. It abstracts each task as a weighted node of a graph. Then, Mofint evolves individuals, each individual being a forest containing a certain number (within the bounds) of non-intersecting trees. Mofint can finally obtain higher precision than existing work with less time: the approximation factor for Mofint is 1.1 to 1.5 times the ideal allocation when robots' number is fixed, while for existing work is 1.5 to 2. Due to its higher precision, the least number of robots obtained in the experiments by Mofint is 0.6 times of existing work.