Dual learning based Pareto evolutionary algorithm for a kind of multi-objective task assignment problem

The task assignment problem (TAP) involves assigning a set of tasks to a set of agents subject to the processing capacity of each agent. The objective is to minimize the total assignment cost and total communication cost. This paper focuses on a special kind of multi-objective TAP (MOTAP). MOTAP differs from TAP in that it optimizes the total cost and agent load balance. MOTAP has many real-life applications and is however NP-hard. To solve the problem, a dual learning-based Pareto evolutionary algorithm (DLPEA) is proposed. The primary highlights of this work are two-fold: a new mathematical model of MOTAP and a dual learning-based search model of DLPEA. For the mathematical model, we propose the MOTAP model for the first time and a problem-specific repair method for infeasible solutions. For the search framework, a statistical learning method with shift-based density estimation is proposed to evaluate the convergence and diversity of the population, enabling the selection of high-quality individuals. We additionally present a probability learning mechanism with a clustering technique to extract valuable information about elite individuals based on which meaningful population can be predicted. Results of experiments on 180 benchmark instances show that the proposed algorithm competes favorably with state-of-the-art methods.