The integration of renewable energy sources and unpredictable demand has increased the complexity of electricity markets, challenging traditional capacity market-clearing models that restrict bidding to non-decreasing curves. This study proposes that allowing both non-decreasing and non-increasing bidding strategies enhances market flexibility and efficiency. To validate this, a hybrid optimization algorithm Lagrange Multiplier-based Dynamic Beetle Antenna Swarm Optimization (LM-DBASO) is developed. The capacity market clearing problem is formulated as a nonlinear, large-scale, multi-objective optimization task incorporating efficiency, reliability, and fairness. A weighted-sum scalarization method enables tractability, with priorities embedded into a single objective function. LM method ensures constraint satisfaction, while the DBASO component provides adaptive global search. Unlike penalty-based methods, LM-DBASO maintains feasibility throughout the search process. The model is implemented in PyTorch for scalability and computational efficiency. A game-theoretic perspective approximates Nash equilibrium through iterative convergence, ensuring that no generator can unilaterally improve its outcome. Simulation results demonstrate the model's effectiveness, achieving an efficiency ratio of 98%, electricity conception ratio of 99%, and system security ratio of 95%. The proposed approach improves bidding rationality, accelerates market clearing, and enhances societal welfare, making LM-DBASO a robust solution for modern electricity market challenges.
YuanYuan et al. (Tue,) studied this question.