Work

Branch-and-Bound versus Lift-and-Project Relaxations in Combinatorial Optimization

Year: 2025

Type: article

Abstract: In this note, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis by streamlining the definition of branch-and-bound. We introduce “skewed k -trees” which give a hierarchy of relaxations that is incomparable to that of Sherali-Adams, and we show that it is much better for some instances. We also give an example where lift-and-project does very well and branch-and-bound does not. Finally, we study the set of branch-and-bound trees of height at most k and “squeeze” their effectiveness between two well-known lift-and-project procedures.

Source: Mathematical Programming

DOI: 10.1007/s10107-025-02248-7

Authors: Gérard Cornuéjols, Yatharth Dubey

Institutions: Carnegie Mellon University, University of Illinois Urbana-Champaign

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Carnegie Mellon University, Office of Naval Research, Office of Naval Research Global