Generative-enhanced optimization for knapsack problems: an industry-relevant study

TL;DR

This study explores the use of tensor network generative-enhanced optimization methods for solving multi-knapsack problems, demonstrating comparable performance to simulated annealing in industry-relevant scenarios.

Contribution

It applies TN-GEO and STN-GEO to multi-knapsack problems, providing a practical prescription and analyzing their scalability and hyper-parameter dependence.

Findings

TN-GEO and STN-GEO achieve solution quality similar to simulated annealing.

The methods' performance depends on hyper-parameters and problem size.

Benchmarking on 60 instances validates their applicability in industry contexts.

Abstract

Optimization is a crucial task in various industries such as logistics, aviation, manufacturing, chemical, pharmaceutical, and insurance, where finding the best solution to a problem can result in significant cost savings and increased efficiency. Tensor networks (TNs) have gained prominence in recent years in modeling classical systems with quantum-inspired approaches. More recently, TN generative-enhanced optimization (TN-GEO) has been proposed as a strategy which uses generative modeling to efficiently sample valid solutions with respect to certain constraints of optimization problems. Moreover, it has been shown that symmetric TNs (STNs) can encode certain constraints of optimization problems, thus aiding in their solution process. In this work, we investigate the applicability of TN- and STN-GEO to an industry relevant problem class, a multi-knapsack problem, in which each object must be assigned to an available knapsack. We detail a prescription for practitioners to use the TN-and STN-GEO methodology and study its scaling behavior and dependence on its hyper-parameters. We benchmark 60 different problem instances and find that TN-GEO and STN-GEO produce results of similar quality to simulated annealing.