Logic-based Benders decomposition for large-scale optimization

TL;DR

This paper introduces Logic-based Benders decomposition (LBBD), a flexible large-scale optimization technique that generalizes classical Benders decomposition, enabling more complex subproblems and diverse applications.

Contribution

It presents the fundamental theory of LBBD, compares it with classical Benders, and demonstrates its application through case studies and a comprehensive literature survey.

Findings

LBBD generalizes classical Benders decomposition.

It effectively solves large-scale planning and scheduling problems.

The survey covers diverse applications of LBBD across domains.

Abstract

Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming problem. It is amenable to a wide variety large-scale problems that decouple or otherwise simplify when certain decision variables are fixed. This chapter presents the basic theory of LBBD and explains how classical Benders decomposition is a special case. It also describes branch and check, a variant of LBBD that solves the master problem only once. It illustrates in detail how Benders cuts and subproblem relaxations can be developed for some planning and scheduling problems. It then describes the role of LBBD in three large-scale case studies. The chapter concludes with an extensive survey of the LBBD literature, organized by problem domain, to allow the reader to explore how Benders cuts have been developed for a wide range of applications.