Branch-and-Bound Methods: A Survey

TLDR

Branch‑and‑bound methods are applied in many fields beyond mathematical programming. The paper describes the essential features of branch‑and‑bound for constrained optimization and reviews several specific applications. Branch‑and‑bound is applied to integer linear programming, nonlinear programming, the traveling‑salesman problem, and the quadratic assignment problem, with discussion of computational trade‑offs and comparison to dynamic programming. The study compares branch‑and‑bound to dynamic programming, highlighting trade‑offs between computation time and storage.

Abstract

The essential features of the branch-and-bound approach to constrained optimization are described, and several specific applications are reviewed. These include integer linear programming (Land-Doig and Balas methods), nonlinear programming (minimization of nonconvex objective functions), the traveling-salesman problem (Eastman and Little, et al. methods), and the quadratic assignment problem (Gilmore and Lawler methods). Computational considerations, including trade-offs between length of computation and storage requirements, are discussed and a comparison with dynamic programming is made. Various applications outside the domain of mathematical programming are also mentioned.