A Brief Tour of Logic and Optimization

TL;DR

This paper surveys the deep connections between logic and optimization, highlighting practical methods like decision diagrams, Benders decomposition, and constraint programming integration, emphasizing their theoretical foundations and applications.

Contribution

It provides an informal overview of how various logical frameworks underpin and enhance optimization techniques, with a focus on practical methods derived from these connections.

Findings

Decision diagrams facilitate optimization processes.

Logic-based Benders decomposition improves problem-solving.

Integration of constraint programming with optimization enhances practical solutions.

Abstract

This paper is an informal survey of some of the deep connections between logic and optimization. It covers George Boole's probability logic, decision diagrams, logic and cutting planes, first order predicate logic, default and nonmonotonic logics, logic and duality, and finite-domain constraint programming. There is particular emphasis on practical optimization methods that stem from these connections, including decision-diagram based methods, logic-based Benders decomposition, and integration of CP and optimization technologies. The paper is a slight revision of an invited article for the INFORMS Optimization Society Newsletter in observance of the 2018 Khachian Award.