The team-orienteering problem (TOP) has broad applicability. Examples of possible uses are in factory and automation settings, robot sports teams, and urban search and rescue applications. We chose the rescue domain as a guiding example throughout this paper. Hence, this paper explores a practical variant of TOP with time window (TOPTW) for rescue applications by humanoid robots called TOPTWR. Due to the significant range of algorithm choices and their parameters tuning challenges, the use of hyper-heuristics is recommended. Hyper-heuristics can select, order, or generate different low-level heuristics with different optimization algorithms. In this paper, first, a general multi-objective (MO) solution is defined, with five objectives for TOPTWR. Then a robust and efficient MO and evolutionary hyper-heuristic algorithm for TOPTW based on the humanoid robot's characteristics in the rescue applications (MOHH-TOPTWR) is proposed. MOHH-TOPTWR includes two MO evolutionary metaheuristics algorithms (MOEAs) known as non-dominated sorting genetic algorithm (NSGA-III) and MOEA based on decomposition (MOEA/D). In this paper, new benchmark instances are proposed for rescue applications using the existing ones for TOPTW. The experimental results show that MOHH-TOPTWR in both MOEAs can outperform all the state-of-the-art algorithms as well as NSGA-III and MOEA/D MOEAs.
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