Enhancing combinatorial optimization with classical and quantum generative models

• Published in: Nature communications 2024-03, Vol.15 (1), p.2761-2761, Article 2761
• Main Authors: Alcazar, Javier, Ghazi Vakili, Mohammad, Kalayci, Can B., Perdomo-Ortiz, Alejandro
• Format: Article
• Language: English
• Subjects: 639/705/117; 639/766/483/481; Algorithms; Benchmarks; Combinatorial analysis; Context; Design optimization; Humanities and Social Sciences; Industrial applications; Machine learning; multidisciplinary; Optimization; Science; Science (multidisciplinary); Solvers; Tensors
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-024-46959-5

Devising an efficient exploration of the search space is one of the key challenges in the design of combinatorial optimization algorithms. Here, we introduce the Generator-Enhanced Optimization (GEO) strategy: a framework that leverages any generative model (classical, quantum, or quantum-inspired) to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. To illustrate our results, we run these benchmarks in the context of the canonical cardinality-constrained portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes, and demonstrate how the generalization capabilities of these quantum-inspired generative models can provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms and show that TN-GEO is among the best; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. Also, a promising step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models Solving combinatorial optimization problems using quantum or quantum-inspired machine learning models would benefit from strategies able to work with arbitrary objective functions. Here, the authors use the power of generative models to realise such a black-box solver, and show promising performances on some portfolio optimization examples.