The Quadratic Unconstrained Binary Optimization Problem

The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others.This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.

Auteur

Abraham P. Punnen is a professor in the department of Mathematics at Simon Fraser University, Burnaby, Canada. His primary research interest is in combinatorial optimization and published extensively in this area. He, jointly with G. Gutin, edited the popular book "The Traveling Salesman Problem and Its Variations" (Springer, 2007).

Contenu

Introduction to QUBO.- Applications and Computational Advances for Solving the QUBO Model.- Complexity and Polynomially Solvable Special Cases of QUBO.- The Boolean Quadric Polytope.- Autarkies and Persistencies for QUBO.- Mathematical Programming Models and ExactAlgorithms.- The Random QUBO.- Fast Heuristics and Approximation Algorithms.- Metaheuristic Algorithms.- The Bipartite QUBO.- QUBO Software.