An ${\ell}_{0}$ -Norm Minimization for Energy-Efficient Timetabling in Subway Systems

Abstract

In this paper, a sparse optimization model with 0-norm and the squared 2-norm as the objective function is proposed for energy-efficient timetabling in subway systems by means of improving the regenerative braking energy utilization. Optimality analysis is addressed for the proposed sparse optimization problem. Specifically, the local minimizer is shown to be a KKT point without any additional constraint qualification. Moreover, based on the hard-thresholding operator, we yield an explicit formula for the Lagrangian dual problem for the proposed non-convex discontinuous optimization problem and achieve the strong duality under the stationarity condition. To evaluate the effectiveness of our proposed model for the energy-efficient timetabling, we design a hard-thresholding based alternating direction method of multipliers for solving the proposed model. The case study on Beijing Metro Yizhuang Line is conducted and the comparison to some recent existing approaches illustrates the effectiveness of our model in terms of energy saving rate and the efficiency of our proposed algorithm in terms of computation time. INDEX TERMS 0-norm minimization, hard-thresholding operator, energy-efficient timetabling, optimality analysis, alternating direction method of multipliers. ZIYAN LUO was born in Hunan, China, in 1983. She received the Ph.D. degree in operations research and cybernetics from

Multi‐view side information‐incorporated tensor completion

“…The decomposition rule of the subdifferential remains to be proved as stated in the first equality in (15). Exploiting [Corollary 10.9] 40 combined with $$$ \hat{\partial}{\left\Vert \mathcal{E}\right\Vert}_0=\partial {\left\Vert \mathcal{E}\right\Vert}_0 $$$ and $$$ \hat{\partial}{\delta}_{\Omega}\left(\mathscr{H}\right)=\partial {\delta}_{\Omega}\left(\mathscr{H}\right) $$$, we get the inclusion By imitating the proof of expression (23) in Reference 48 (Theorem 1), the required conclusion is obtained by This completes the proof.…”

An effective utilization scheme for regenerative braking energy based on power regulation with a genetic algorithm

“…Optimizing the train timetable is an inexpensive option [20]. By adjusting the train timetable, the regenerative braking energy can be utilized by the accelerating trains in the same power arm [4,21]. However, the flexibility of the scheme is poor, and the energy-saving effect is not significant due to operational constraints and service requirements [22].…”