https://www.mdu.se/

Multi-agent systems have received a tremendous amount of attention in many areas of research and industry, especially in robotics and computer science. With the increased number of agents in missions, the problem of allocation of tasks to agents arose, and it is one of the most fundamental classes of problems in robotics, formally known as the Multi-Robot Task Allocation (MRTA) problem. MRTA encapsulates numerous problem dimensions, and it aims at providing formulations and solutions to various problem configurations, i.e., complex multi-agent missions. One dimension of the MRTA problem has not caught much of the research attention. In particular, problem configurations including Multi-Task (MT) robots have been neglected. However, the increase in computational power, in robotic systems, has allowed the utilization of parallel task execution. This in turn had the benefit of allowing the creation of more complex robotic missions; however, it came at the cost of increased problem complexity. Our contribution to the aforementioned domain can be grouped into three categories. First, we model the problem using two different approaches, Integer Linear Programming and Constraint Programming. With these models, we aim at filling the gap in the literature related to the formal definition of MT robot problem configuration. Second, we introduce the distinction between physical and virtual tasks and their mutual relationship in terms of parallel task execution. This distinction allows the modeling of a wider range of missions while exploiting possible parallel task execution. Finally, we provide a comprehensive performance analysis of both models, by implementing and validating them in CPLEX and CP Optimizer on the set of problems. Each problem consists of the same set of test instances gradually increasing in complexity, while the percentage of virtual tasks in each problem is different. The analysis of the results includes exploration of the scalability of both models and solvers, the effect of virtual tasks on the solvers' performance, and overall solution quality.