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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.<\/jats:p>","DOI":"10.1177\/18724981251389330","type":"journal-article","created":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T18:22:46Z","timestamp":1763490166000},"page":"3758-3775","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on the design and optimization model of capacity market clearing mechanism based on lagrange multiplier method"],"prefix":"10.1177","volume":"19","author":[{"given":"Cao","family":"Yuanyuan","sequence":"first","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Yabin","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zou","family":"Peng","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhao","family":"Jianghui","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Duan","family":"Yaohui","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhang","family":"Chao","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Yumin","sequence":"additional","affiliation":[{"name":"Shanxi Power Exchanger Center Co., Ltd, Market Department, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2025,11,18]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2020.106635"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.3390\/su16062390"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/JPHOTOV.2021.3104149"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2021.3096971"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSTE.2021.3117313"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIA.2022.3218271"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3390\/en16207061"},{"key":"e_1_3_2_9_2","first-page":"1357","article-title":"Local energy and planned ramping product joint market based on a distributed optimization method","volume":"7","author":"Zhang Z","year":"2021","unstructured":"Zhang Z, Li F, Park SW, et\u00a0al. 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