A Memetic Algorithm for the Task Allocation Problem on Multi-robot Multi-point Dynamic Aggregation Missions

Multi-Point Dynamic Aggregation (MPDA) is a novel task model to determine task allocation for a multi-robot system. In an MPDA scenario, several robots with different abilities aim to complete a set of tasks cooperatively. The demand of each task is time varying. It increases over time at a certain rate (e.g. the bush fire in Australia). When a robot executes a task, the demand of the task decreases at another certain rate, depending on the robot's ability. In this paper, the objective is to design a task plan for minimising the maximal completed time of all tasks. But coupling cooperative and time-varying characteristics of MPDA brings great challenges to modelling, decoding, and optimisation. In this paper, a multi-permutation encoding is used to represent every robot's visiting sequence of tasks, and an implicit decoding strategy with heuristic rules is designed to simplify the problem from a hybrid variable optimisation to a multi-permutation optimisation. Memetic algorithms for the task allocation of MPDA with two local search methods are designed: equality one-step local search with a better exploration ability and elite multi-step local search with a better exploitation ability. Computational experiments show that the proposed decoding method leads to a better performance given the same computational time budget. Experimental results also show that the proposed memetic algorithms outperform the state-of-the-art method in solving the task planning problems of MPDA.