Machine learning-enhanced vector ordinal optimization for multi-objective stochastic unit commitment

The high penetration of renewable power generation introduces new challenges to the economic and stable operation of power systems. The security-constrained unit commitment (SCUC) problem is an important mixed-integer programming (MIP) problem solved within a limited time by independent system operators every day. To address the uncertainty associated with renewable power, there is a growing need for fast solutions to stochastic multi-objective SCUC (MO-SCUC), which considers both operational cost and spinning reserve capacity. In this paper, we propose a fast solution method based on vector ordinal optimization (VOO) to effectively obtain good enough solutions for MO-SCUC. We first propose a method for efficiently generating high-quality initial solutions for integer variables, which includes a machine learning-based probability-guided sampling method and analytical feasibility conditions derived from the problem structure. Then, VOO is applied to rapidly select good enough solutions. Our method can quickly determine the values of integer variables in MO-SCUC, transforming the computational burden from large-scale MIP problems into a few small-scale linear programming problems that can be solved in parallel. Furthermore, to enhance the performance of VOO, we propose a hybrid approach that integrates VOO with existing multi-objective evolutionary methods to efficiently obtain approximately Pareto optimal solutions. Experimental results on the IEEE 30-bus and 118-bus systems show that the proposed VOO-M method achieves speedups of 35 $$\sim$$ 210 times compared to traditional methods using the commercial solver Gurobi, with solution quality degradation of less than 15% relative to these methods. The VOO+NSGA-II hybrid method further improves performance, achieving speedups of 4 $$\sim$$ 31 times while outperforming the Weighted-sum method in solution quality by 0.53% $$\sim$$ 3.05%. Moreover, our method exhibits high computational efficiency and scales effectively to larger problems.