Globally Convergent Hybridization of Particle Swarm Optimization Using Line Search-Based Derivative-Free Techniques

The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are often not available. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical A. Serani (&) M. Diez E.F. Campana CNR-INSEAN, Via di Vallerano 139, Rome, Italy e-mail: [email protected] M. Diez e-mail: [email protected] E.F. Campana e-mail: [email protected] G. Fasano Department of Management, University Ca’ Foscari of Venice, S. Giobbe, Cannaregio 873, Venice, Italy e-mail: [email protected] D. Peri CNR-IAC, Via dei Taurini 19, Rome, Italy e-mail: [email protected] A. Serani U. Iemma Department of Engineering, Roma Tre University, Via Vito Volterra 62, Rome, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2015 X.-S. Yang (ed.), Recent Advances in Swarm Intelligence and Evolutionary Computation, Studies in Computational Intelligence 585, DOI 10.1007/978-3-319-13826-8_2 25 properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a specific test function and for two real-world optimization problems in ship hydrodynamics.