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A new heuristic approach for non-convex optimization problems. (English) Zbl 1198.90331

Summary: In this work a new optimization method, called the heuristic Kalman algorithm (HKA), is presented. This new algorithm is proposed as an alternative approach for solving continuous, non-convex optimization problems. The principle of HKA is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum. A specific procedure, based on the Kalman estimator, was developed to improve the quality of the estimate obtained through the measurement process. The main advantage of HKA, compared to other metaheuristics, lies in the small number of parameters that need to be set by the user. Further, it is shown that HKA converges almost surely to a near-optimal solution. The efficiency of HKA was evaluated in detail using several non-convex test problems, both in the unconstrained and constrained cases. The results were then compared to those obtained via other metaheuristics. The numerical experiments show that HKA is a promising approach for solving non-convex optimization problems, particularly in terms of computation time and success ratio.

MSC:

90C26 Nonconvex programming, global optimization
90C59 Approximation methods and heuristics in mathematical programming
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