Technology Category
Constraint Satisfaction and Optimization: Constraint OptimizationSearch and Optimization: Combinatorial OptimizationReasoning under Uncertainty: Stochastic Optimization
Generative-enhanced optimization for knapsack problems: an industry-relevant study
🤖 AI Summary
This paper addresses the multidimensional knapsack problem (MKP)—an NP-hard constrained optimization problem pervasive in logistics and manufacturing. We propose Tensor Network Generative Enhanced Optimization (TN-GEO) and its symmetric variant, Symmetric TN-GEO (STN-GEO). STN-GEO is the first method to explicitly encode MKP’s assignment constraints via symmetric tensor networks, integrating generative sampling with a quantum-inspired optimization framework to efficiently produce high-quality feasible solutions. Extensive evaluation on 60 industrial-scale instances demonstrates that STN-GEO matches simulated annealing in solution quality while improving the sampling efficiency of constraint-satisfying solutions by an order of magnitude. The approach exhibits strong hyperparameter robustness and favorable scalability. By unifying interpretable tensor-based modeling with combinatorial optimization, STN-GEO establishes a generalizable, principled tensor-network paradigm for constrained discrete optimization.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Optimizing knapsack problems with generative-enhanced methods
Applying tensor networks for industry-relevant optimization
Benchmarking TN-GEO against simulated annealing
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses Tensor Networks for optimization
Applies generative-enhanced sampling techniques
Encodes constraints with Symmetric Tensor Networks
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