A Hybrid Decomposition-based Multi-objective Evolutionary Algorithm for the Multi-Point Dynamic Aggregation Problem

Abstract: An emerging optimisation problem from the real-world applications, named the multi-point dynamic aggregation (MPDA) problem, has become one of the active research topics of the multi-robot system. This paper focuses on a multi-objective MPDA problem which is to design an execution plan of the robots to minimise the number of robots and the maximal completion time of all the tasks. The strongly-coupled relationships among robots and tasks, the redundancy of the MPDA encoding, and the variable-size decision space of the MO-MPDA problem posed extra challenges for addressing the problem effectively. To address the above issues, we develop a hybrid decomposition-based multi-objective evolutionary algorithm (HDMOEA) using $ \varepsilon $-constraint method. It selects the maximal completion time of all tasks as the main objective, and converted the other objective into constraints. HDMOEA decomposes a MO-MPDA problem into a series of scalar constrained optimization subproblems by assigning each subproblem with an upper bound robot number. All the subproblems are optimized simultaneously with the transferring knowledge from other subproblems. Besides, we develop a hybrid population initialisation mechanism to enhance the quality of initial solutions, and a reproduction mechanism to transmit effective information and tackle the encoding redundancy. Experimental results show that the proposed HDMOEA method significantly outperforms the state-of-the-art methods in terms of several most-used metrics.