Multi-objective swarm intelligence (MOSI) metaheuristics were proposed to solve multi-objective optimization problems (MOPs) that consists of two or more conflict objectives, in which improving an objective leads to the degradation of the other. The MOSI algorithms are based on the integration of single objective algorithms and multi-objective optimization (MOO) approach. The MOO approaches include scalarization, Pareto dominance, decomposition and indicator-based. In this paper, the status of MOO research and state-of-the-art MOSI algorithms namely, multi-objective particle swarm, artificial bee colony, firefly algorithm, bat algorithm, gravitational search algorithm, grey wolf optimizer, bacterial foraging and moth-flame optimization algorithms have been reviewed. These reviewed algorithms were mainly developed to solve continuous MOPs. The review is based on how the algorithms deal with objective functions using MOO approaches, the benchmark MOPs used in the evaluation and performance metrics. Furthermore, it describes the advantages and disadvantages of each MOO approach and provides some possible future research directions in this area. The results show that several MOO approaches have not been used in most of the proposed MOSI algorithms. Integrating other different MOO approaches may help in developing more effective optimization algorithms, especially in solving complex MOPs. Furthermore, most of the MOSI algorithms have been evaluated using MOPs with two objectives, which clarifies open issues in this research area.
Multi-objective optimization for oil-gas production process based on compensation model of comprehensive energy consumption using improved evolutionary algorithm
