Numerical analysis of quantization‐based optimization

• Published in: ETRI journal Vol. 46; no. 3; pp. 367 - 378
• Main Authors: Seok, Jinwuk, Cho, Chang Sik
• Format: Journal Article
• Language: English
• Published: Electronics and Telecommunications Research Institute (ETRI) 01.06.2024
• Subjects: combinatorial optimization; global optimization; number theory; quantization; quantum annealing
• ISSN: 1225-6463; 2233-7326
• DOI: 10.4218/etrij.2023-0083

We propose a number‐theory‐based quantized mathematical optimization scheme for various NP‐hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization‐based optimization proposal also depends on stochastic features (i.e., the white‐noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization‐based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes. Effective combinatorial optimization algorithms for solving NP‐hard problems are essential for using machine learning to overcome engineering challenges. Conventional algorithms such as simulated annealing and quantum annealing suffer from low convergence speeds and poor optimization performance for NP‐hard problems. Now, researchers from ETRI, Korea, have developed a novel quantization‐based optimization algorithm using number theory, which significantly outperforms conventional algorithms and finds feasible solutions even where conventional algorithms fail, marking a significant achievement.