Multi-robot task allocation problem with multiple nonlinear criteria using branch and bound and genetic algorithms

Abstract

The paper proposes the formulation of a single-task robot (ST), single-robot task (SR), time-extended assignment (TA), multi-robot task allocation (MRTA) problem with multiple, nonlinear criteria using discrete variables that drastically reduce the computation burden. Obtaining an allocation is addressed by a Branch and Bound (B&B) algorithm in low scale problems and by a genetic algorithm (GA) specifically developed for the proposed formulation in larger scale problems. The GA crossover and mutation strategies design ensure that the descendant allocations of each generation will maintain a certain level of feasibility, reducing greatly the range of possible descendants, and accelerating their convergence to a sub-optimal allocation. The proposed MRTA algorithms are simulated and analyzed in the context of a thermosolar power plant, for which the spatially distributed Direct Normal Irradiance (DNI) is estimated using a heterogeneous fleet composed of both aerial and ground unmanned vehicles. Three optimization criteria are simultaneously considered: distance traveled, time required to complete the task and energetic feasibility. Even though this paper uses a thermosolar power plant as a case study, the proposed algorithms can be applied to any MRTA problem that uses a multi-criteria and nonlinear cost function in an equivalent way. The performance and response of the proposed algorithms are compared for four different scenarios. The results show that the B&B algorithm can find the global optimal solution in a reasonable time for a case with four robots and six tasks. For larger problems, the genetic algorithm approaches the global optimal solution in much less computation time. Moreover, the trade-off between computation time and accuracy can be easily carried out by tuning the parameters of the genetic algorithm according to the available computational power.