Frequency-domain Assisted Multitask Differential Evolution Algorithm for Operational Optimization of Coal Mine Integrated Energy Systems

The operational optimization problem of coal mine integrated energy systems features large-scale variables, strong constraints, and multiple objectives. Especially, its ramp constraints introduce significant temporal coupling between decision variables. To address the limitations of existing constrained multi-objective evolutionary algorithms in handling temporal coupling variables, we propose a frequency-domain assisted multi-task differential evolution algorithm. Specifically, for the first time, we present a method for constructing auxiliary task based on frequency-domain decision variables. The frequency-domain representation of decision variables simultaneously possesses global correlation and low-dimensional characteristics. It not only produces solutions more readily satisfy temporal constraints, but also substantially reduce the dimensionality of search space, thereby improving the auxiliary population’s search efficiency. Furthermore, a Gaussian random field-based initialization method for main and auxiliary populations is proposed to generate high-quality initial individuals whose variable values satisfy temporal continuity; and a novel adaptive frequency-domain differential evolution strategy is designed to enhance the search efficiency and diversity of the auxiliary population. Finally, the proposed algorithm is applied to a mine in Shanxi Province, China. The experimental results show that the algorithm is able to obtain a set of optimal solutions with good distribution and convergence in a short time, and it shows improvements of at least 8.5% in HV value and 1.6-3 times in Spread performance over 12 state-of-the-art algorithms.