Nowadays humanoid robots have generally made dramatic progress, which can form a coalition replacing human work in dangerous environments such as rescue, defense, exploration, etc. In contrast to other types of robots, humanoid robots’ similarity to human make them more suitable for performing such a wide range of tasks. Rescue applications for robots, especially for humanoid robots are exciting. In rescue operating conditions, tasks’ dependencies, tasks’ repetitive accomplishment requirements, robots’ energy consumption, and total tasks’ accomplishment time are key factors. This paper investigates a practical variant of the Multi-Robots Task Allocation (MRTA) problem for humanoid robots as multi-humanoid robots’ task allocation (MHTA) problem. In order to evaluate relevant aspects of the MHTA problem, we proposed a robust Multi-Objective Multi-Humanoid Robots Task allocation (MO-MHTA) algorithm with four objectives, namely energy consumption, total tasks’ accomplishment time, robot’s idle time and fairness were optimized simultaneously in an evolutionary framework in MO-MHTA, which address for the first time. MO-MHTA exhibits multi-objective properties in real-world applications for humanoid robots in two phases. In the first phase, the tasks are partitioned in a fair manner with a proposed constraint k-medoid (CKM) algorithm. In the second phase, a new non-dominated sorting genetic algorithm with special genetic operators is applied. Evaluations based on extensive experiments on the newly proposed benchmark instances with three robust multi-objective evolutionary algorithms (MOEAs) are applied. The proposed algorithm achieves favorable results in comparison to six other algorithms. Besides, the proposed algorithm can be seen as benchmark algorithms for real-world MO-MHTA instances.
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