A multiple search strategies based grey wolf optimizer for solving multi-objective optimization problems

In this paper, a novel multi-objective grey wolf optimizer (MOGWO) based on multiple search strategies (i.e., adaptive chaotic mutation strategy, boundary mutation strategy, and elitism strategy) which we shall call MMOGWO is proposed to solve multi-objective optimization problems (MOPs). The algorithm uses a fixed-sized external archive that is adaptively maintained according to a grid-based approach to preserve the non-dominated solutions found during the search process. Then, the archive is used to define the social hierarchy and simulate the hunting behaviors of grey wolves. In the proposed algorithm, an adaptive chaotic mutation strategy based on a chaotic cubic map and modified generational distance (GD) is applied to the archive to dynamically adjust the convergence speed and balance the exploration and exploitation. To prevent the population diversity loss, a boundary mutation strategy based on the concept of multi-level parallel is employed to manage boundary constraint violations. Moreover, a non-dominated sorting and crowding distance-based elitism strategy is also incorporated into the algorithm for exploiting more potential Pareto optimal solutions and preserve the diversity of solutions in the approximated set. The proposed algorithm is evaluated on a wide range of multi-objective optimization problems (MOPs), and compared with other state-of-the-art multi-objective optimization algorithms in terms of often-used performance metrics with the help of statistical analysis, average ranks test and Wilcoxon Signed-Rank Test (WSRT). It is revealed by the experimental results that the algorithm is highly competitive and significantly outperforms other well-known algorithms on most of the test problems. On obtaining satisfactory performance for test problems, to investigate the performance of the MMOGWO for solving real-world optimization problems with various constraints, MMOGWO is further applied to handle the multi-objective optimal scheduling problem (MOOSP) of cascade hydropower stations (CHSs) based on a novel constraints handling method designed in this paper. Simulation results indicate that, compared with other algorithms, MMOGWO can produce better quality solutions and it can be considered as a promising alternative tool to deal with multi-objective real-life engineering problems with complex constraints by equipping with constraints handling methods.