文献类型：期刊文献

英文题名：Cardinality-Constrained Bilevel Capacity Expansion

作者：Guo, Lei[1]; Li, Jiayang[2]

机构：[1] School of Business, East China University of Science and Technology, China; [2] Department of Data and Systems Engineering, The University of Hong Kong, Hong Kong

年份：2025

外文期刊名：arXiv

收录：EI(收录号：20250402001)

语种：英文

外文关键词：Constraint theory - Expansion - Location - Numerical methods - Operations research

摘要：As a fundamental problem in transportation and operations research, the bilevel capacity expansion problem (BCEP) has been extensively studied for decades. In practice, BCEPs are commonly addressed in two stages: first, preselect a small set of links for expansion; then, optimize their capacities. However, this sequential and separable approach can lead to suboptimal solutions as it neglects the critical interdependence between link selection and capacity allocation. In this paper, we propose to introduce a cardinality constraint into the BCEP to limit the number of expansion locations rather than fixing such locations beforehand. This allows us to search over all possible link combinations within the prescribed limit, thereby enabling the joint optimization of both expansion locations and capacity levels. The resulting cardinality-constrained BCEP (CCBCEP) is computationally challenging due to the combination of a nonconvex equilibrium constraint and a nonconvex and discontinuous cardinality constraint. To address this challenge, we develop a penalized difference-of-convex (DC) approach that transforms the original problem into a sequence of tractable subproblems by exploiting its inherent DC structure and the special properties of the cardinality constraint. We prove that the method converges to approximate Karush–Kuhn–Tucker (KKT) solutions with arbitrarily prescribed accuracy. Numerical experiments further show that the proposed approach consistently outperforms alternative methods for identifying practically feasible expansion plans investing only a few links, both in solution quality and computational efficiency. Copyright ? 2025, The Authors. All rights reserved.