For multi-objective optimization problems with irregular Pareto Fronts, most widely used decomposition methods in MOEA/D (multi-objective evolutionary algorithms based on decomposition) have shown to be lack of the ability to balance the diversity and the convergence to track the true Pareto Fronts during the search. This research investigates the recently proposed grid-based decomposition methods, which reflect the inherent characteristics of the neighborhood structure in the solution to address the issues of diversity and convergence. The performance of the grid-based decomposition method, however, depends on the size of its grid segmentation, and its time complexity increases with the number of grids. In order to improve the computational efficiency, we propose a new concept of Pareto Front grid to guide the search in MOEA. In order to reduce the computing time, a new nadir point estimation strategy based on statistical analysis has been proposed to estimate the whole population. In addition, based on the idea of knee point, a novel grid-based knee point selection method is proposed in the environmental selection of the next generation. Finally, a grid-based decomposition multi-objective evolutionary algorithm with Pareto Front Grid (PFG-MOEA) is proposed. Extensive experimental analysis demonstrates the effectiveness of the proposed PFG-MOEA against state-of-the-art multi-objective evolution algorithms. As the extension of the CDG-MOEA (Constrained Decomposition approach with Grids MOEA) algorithm in the literature, PFG-MOEA can obtain better performance by consuming much less computing time.
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