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Aiming to address power consumption issues of various equipment in metro stations and the inefficiency of peak shaving and valley filling in the power supply system, this study presents an economic optimization scheduling method for the multi-modal "source-network-load-storage" system in metro stations. The proposed method, called the Improved Gray Wolf Optimization Algorithm (IGWO), utilizes objective evaluation criteria to achieve economic optimization. First, construct a mathematical model of the "sourcenet-work-load-storage" joint system with the metro station at its core. This model should consider the electricity consumption within the station. Secondly, a two-layer optimal scheduling model is established, with the upper model aiming to optimize peak elimination and valley filling, and the lower model aiming to minimize electricity consumption costs within a scheduling cycle. Finally, this paper introduces the IGWO optimization approach, which utilizes meta-models and the Improved Gray Wolf Optimization Algorithm to address the nonlinearity and computational complexity of the two-layer model. The analysis shows that the proposed model and algorithm can improve the solution speed and minimize the cost of electricity used by about 5.5% to 8.7% on the one hand, and on the other hand, it improves the solution accuracy, and at the same time effectively realizes the peak shaving and valley filling, which provides a proof of the effectiveness and feasibility of the new method. [ABSTRACT FROM AUTHOR]

We presented an image space branch-and-bound algorithm for globally minimizing the sum of linear ratios problem. In the algorithm, a new linearizing technique was proposed for deriving the linear relaxation problem. An image space region reduction technique was constructed for improving the convergence speed of the algorithm. Moreover, by analyzing the computational complexity of the algorithm, the maximum iterations of the algorithm were estimated, and numerical experimental results showed the potential computing benefits of the algorithm. Finally, a practical application problem in education investment was solved to verify the usefulness of the proposed algorithm. [ABSTRACT FROM AUTHOR]