An effective hybrid genetic algorithm for the multi-robot task allocation problem with limited span

Multi-robot task allocation is one of the most interesting multi-robot systems that have gained considerable attention due to various real-world applications. In this paper, we focus on a multi-robot task allocation problem where a set of industrial robots, which are installed on a gantry and have a limited working span, have to jointly perform a set of weld lines in large workpieces. Considering the emphasis on minimizing the processing time of workpieces in industry, the objective of this problem is to minimize the cycle time when scheduling a set of robots to work together efficiently. Following practical applications, we present a mathematical model for small size instances, and for large size instances, we propose an effective hybrid genetic algorithm to solve it because of the significant computational complexity, which includes a specific region division method is used to divide the workpieces into a set of regions where the robots can reach all the weld lines in each region, a dedicated route-based crossover to generate promising offspring solutions, and an effective neighborhood-based local search procedure to improve each offspring solution as much as possible. Extensive experimental results on three benchmark instances show that the algorithm significantly outperforms two refer methods with an average improvement of 6.06% and 4.6%. Additional experiments on real-world instances are presented to verify the algorithm's effectiveness in solving the multi-robot task allocation problem with limited span.