Toscano Rosario, Lyonnet Patrick
Laboratoire de Tribologie et de Dynamique des Systèmes, Ecole Nationale d'Ingénieurs de Saint-Etienne, Saint-Etienne Cedex 2, France.
IEEE Trans Syst Man Cybern B Cybern. 2009 Oct;39(5):1231-44. doi: 10.1109/TSMCB.2009.2014777. Epub 2009 Mar 24.
The main objective of this paper is to present a new optimization approach, which we call heuristic Kalman algorithm (HKA). We propose it as a viable approach for solving continuous nonconvex optimization problems. The principle of the proposed approach is to consider explicitly the optimization problem as a measurement process designed to produce an estimate of the optimum. A specific procedure, based on the Kalman method, was developed to improve the quality of the estimate obtained through the measurement process. The efficiency of HKA is evaluated in detail through several nonconvex test problems, both in the unconstrained and constrained cases. The results are then compared to those obtained via other metaheuristics. These various numerical experiments show that the HKA has very interesting potentialities for solving nonconvex optimization problems, notably concerning the computation time and the success ratio.
本文的主要目标是提出一种新的优化方法，我们称之为启发式卡尔曼算法（HKA）。我们将其作为解决连续非凸优化问题的一种可行方法提出。该方法的原理是将优化问题明确视为一个旨在产生最优估计的测量过程。基于卡尔曼方法开发了一种特定程序，以提高通过测量过程获得的估计质量。通过几个非凸测试问题，在无约束和有约束情况下详细评估了HKA的效率。然后将结果与通过其他元启发式方法获得的结果进行比较。这些各种数值实验表明，HKA在解决非凸优化问题方面具有非常有趣的潜力，特别是在计算时间和成功率方面。
