A Discrete Differential Evolution Algorithm for the Multi-Objective Generalized Assignment Problem

In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the multi-objective generalized assignment problem (mGAP), which is basically concerned with finding the optimal assignment of jobs to agents such that each job is assigned to exactly one agent, subject to capacity constraint of agents, and aims to optimize multiple objective functions simultaneously, such as minimizing cost, minimizing time, and maximizing profit. First, the mGAP is described and a standard multi-objective mathematical programming model for nnGAP is given. Second, the DDE is presented, in which individuals are represented as the integer encoding scheme, and a novel integer-encoding-based dynamic mutation operator is employed to generate new candidate solutions. Furthermore, a sequential selection operator for dealing with multiple objectives is embedded in the proposed DDE. Finally, an extensive computational study is carried out by comparison with the enumeration algorithm and genetic algorithm, the results show that the proposed DDE is an effective algorithm for mGAR