Benders Subproblem Decomposition for Bilevel Problems with Convex Follower
针对上层含整数变量、下层满足强对偶的双层优化问题，提出一种专用Benders分解方法，将子问题分解为两个可顺序求解的上下层问题，并在能源市场等应用中验证了计算优势。
Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications, such as pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel optimization problems in which the upper level problem features some integer variables and the lower level problem enjoys strong duality. We propose a dedicated Benders decomposition method for solving this class of bilevel problems, which decomposes the Benders subproblem into two more tractable, sequentially solvable problems that can be interpreted as the upper and lower level problems. We show that the Benders subproblem decomposition carries over to an interesting extension of bilevel problems, which connects the upper level solution with the lower level dual solution, and discuss some special cases of bilevel problems that allow sequence-independent subproblem decomposition. Several novel schemes for generating numerically stable cuts, finding a good incumbent solution, and accelerating the search tree are discussed. A computational study demonstrates the computational benefits of the proposed method over a state-of-the-art, bilevel-tailored, branch-and-cut method; a commercial solver; and the standard Benders method on standard test cases and the motivating applications in sequential energy markets.