Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection

Abstract

The branch-and-bound algorithm based on decision diagrams is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on pruning inequalities given by rough upper bounds and local bounds — two additional filtering techniques recently introduced. Computational experiments show that the pruning brought by this caching mechanism allows for significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0340 ), as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0340 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .