A New Computational Approach for Solving Linear Bilevel Programs Based on Parameter-Free Disjunctive Decomposition

TL;DR

This paper introduces a novel disjunctive decomposition algorithm for linear bilevel programs that avoids the NP-hard big-M parameter computation, ensuring optimal solutions with promising computational performance.

Contribution

The paper proposes a parameter-free disjunctive decomposition method for linear bilevel programs, eliminating the need for big-M calculations and guaranteeing optimality.

Findings

Algorithm avoids NP-hard big-M computation.

Ensures optimal solutions for linear bilevel programs.

Demonstrates promising computational performance.

Abstract

Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its Karush-Kuhn-Tucker optimality conditions and linearizes the complementary slackness conditions using the big-M technique. Although the approach is straightforward, it requires finding the big-M whose computation is recently shown to be NP-hard. This paper presents a disjunctive-based decomposition algorithm which does not need finding the big-Ms whereas guaranteeing that obtained solution is optimal. Our experience shows promising performance of our algorithm.