Quantization-Based Optimization: Alternative Stochastic Approximation of Global Optimization

TL;DR

This paper introduces a novel global optimization algorithm based on quantizing the energy levels of an objective function, leveraging stochastic analysis to ensure convergence under Lipschitz conditions, and demonstrating superior performance on NP-hard problems.

Contribution

It presents a new quantization-based stochastic approximation method that guarantees global convergence without relying on local Hessian conditions.

Findings

Outperforms traditional methods on NP-hard problems

Ensures global convergence under Lipschitz continuity

Effective in solving the traveling salesman problem

Abstract

In this study, we propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. According to the white noise hypothesis for a quantization error with a dense and uniform distribution, we can regard the quantization error as i.i.d. white noise. From stochastic analysis, the proposed algorithm converges weakly only under conditions satisfying Lipschitz continuity, instead of local convergence properties such as the Hessian constraint of the objective function. This shows that the proposed algorithm ensures global optimization by Laplace's condition. Numerical experiments show that the proposed algorithm outperforms conventional learning methods in solving NP-hard optimization problems such as the traveling salesman problem.