Article
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Simulated Annealing driven by the Free-Energy: The SAFE Algorithm
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Version 1
: Received: 16 July 2024 / Approved: 16 July 2024 / Online: 17 July 2024 (04:41:48 CEST)
How to cite: Barua, A.; Hatzikirou, H. Simulated Annealing driven by the Free-Energy: The SAFE Algorithm. Preprints 2024, 2024071353. https://doi.org/10.20944/preprints202407.1353.v1 Barua, A.; Hatzikirou, H. Simulated Annealing driven by the Free-Energy: The SAFE Algorithm. Preprints 2024, 2024071353. https://doi.org/10.20944/preprints202407.1353.v1
Abstract
Optimization techniques are pivotal across various scientific domains, typically involving solving problems among feasible alternatives based on specific goals, alternatives, or constraints. In mathematical optimization, traditional methods like Simulated Annealing (SA) do not guarantee finding global minima/optima, especially in cases that contain high dimensions in objective functions. This paper introduces a novel approach where a free-energy driven self-adaptive SA algorithm is designed to handle such cases by incorporating free-energy costs within the Metropolis-Hastings framework. This algorithm not only dynamically adjusts to the changing dimensions of the objective function, but it also enhances a faster optimization process. Furthermore, as examples we demonstrate its capability on a convex unimodal function and the non-convex Rastrigin function, revealing faster convergence to search global minima compared to standard SA algorithm. At last, parameter estimation of noisy exponential data has been executed by our Simulated Annealing driven by the Free-Energy (SAFE) algorithm. Our results suggest that this novel approach may significantly improve optimization speed and accuracy, providing a robust tool for complex multidimensional optimization problems.
Keywords
Free-energy; Simulated Annealing; Mathematical Optimization; Monte-Carlo Methods; Convergence
Time; Parameter Estimation;
Time; Parameter Estimation;
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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