Multi-Robot Routing Problem with Min–Max Objective

In this paper, we study the “Multi-Robot Routing problem” with min–max objective (MRR-MM) in detail. It involves the assignment of sequentially ordered tasks to robots such that the maximum cost of the slowest robot is minimized. The problem description, the different types of formulations, and the methods used across various research communities are discussed in this paper. We propose a new problem formulation by treating this problem as a permutation matrix. A comparative study is done between three methods: Stochastic simulated annealing, deterministic mean-field annealing, and a heuristic-based graph search method. Each method is investigated in detail with several data sets (simulation and real-world), and the results are analysed and compared with respect to scalability, computational complexity, optimality, and its application to real-world scenarios. The paper shows that the heuristic method produces results very quickly with good scalability. However, the solution quality is sub-optimal. On the other hand, when optimal or near-optimal results are required with considerable computational resources, the simulated annealing method proves to be more efficient. However, the res