Quantum Relaxation for Solving Multiple Knapsack Problems

TL;DR

This paper explores a hybrid quantum-classical approach using relaxations and QRAC-inspired methods to solve large constrained optimization problems like multi-knapsack, demonstrating potential advantages over traditional quantum algorithms.

Contribution

It introduces a novel hybrid quantum-classical method leveraging relaxations and QRAC concepts for constrained optimization, addressing scalability and real-world problem application.

Findings

Effective handling of knapsack constraints via relaxations.

Comparison shows potential advantages over QAOA.

Successful application to a large procurement problem.

Abstract

Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are unconstrained (such as Max-Cut). In this study, we investigate a hybrid quantum-classical method for constrained optimization problems, particularly those with knapsack constraints that occur frequently in financial and supply chain applications. Our proposed method relies firstly on relaxations to local quantum Hamiltonians, defined through commutative maps. Drawing inspiration from quantum random access code (QRAC) concepts, particularly Quantum Random Access Optimizer (QRAO), we explore QRAO's potential in solving large constrained optimization problems. We employ classical techniques like Linear Relaxation as a presolve mechanism to handle constraints and cope further with scalability. We compare our approach with QAOA and present the final results for a real-world procurement optimization problem: a significant sized multi-knapsack-constrained problem.