Quantization-Based Optimization: Alternative Stochastic Approximation of Global Optimization
This provides a more robust optimization approach for NP-hard problems, though it appears incremental relative to existing stochastic approximation methods.
The authors tackled NP-hard global optimization problems by developing a quantization-based algorithm that treats quantization errors as i.i.d. white noise, enabling weak convergence under Lipschitz continuity instead of stricter local constraints. Numerical experiments demonstrated that this algorithm outperforms conventional methods on problems like the traveling salesman problem.
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.