Heuristic Kalman Algorithm for Solving Optimization Problems

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.