A new global optimization algorithm based on space-filling curve and auxiliary function approach and its applications

Global optimization is a topic of great interest because of the many practical problems in real life. This article focuses on the unconstrained global minimization of multi-modal continuously differentiable functions, an important subclass of global optimization problems. In order to solve these problems, we develop a new global optimization technique that utilizes two fundamental concepts. The first one is the reducing dimension technique, which uses space-filling curves, while the second one involves utilizing an auxiliary function approach. We propose a new continuously differentiable auxiliary function with direct control of the slope and present the theory behind it. The auxiliary function method is combined with the space-filling curve methodology. We construct a new global optimization algorithm based on the proposed auxiliary function, space-filling curves, and local searches. We implement a comprehensive numerical test procedure to evaluate the numerical stabilization and efficiency of the proposed algorithm. For this purpose, the proposed algorithm is applied to test problems, and the obtained numerical results are compared with the results obtained by some recently proposed algorithms. Moreover, the proposed algorithm is applied to two different economic load dispatch problems, and promising results are obtained.