DEPP - Differential Evolution Parallel Program

Optimization is a mathematical problem often found in science and engineering.Currently, however, there is no general method to face this problem.Solutions are generally addressed by two approaches, both iterative: (a) quasi-Newton methods (Griva, Nash, & Sofer, 2009) and (b) heuristic methods (Coley, 1999;Feoktistov, 2006).Each one has advantages depending on the problem to be optimized.Quasi-Newton methods, in general, converge faster then heuristic methods provided the function to be optimized (the objective function) is smooth.Heuristic methods, on the other hand, are more appropriate to deal with noisy objective functions, to handle failures in the calculation of the objective function and are less susceptible to be retained in local optimum than quasi-Newton methods.Among the heuristic methods, Differential Evolution (DE) (Price, Storn, & Lampinen, 2005; Storn & Price, 1997) had emerged as a simple and efficient method for finding the global maximum.This method is based on the principles of biological evolution.To combine the robustness of heuristic methods with the high convergence speed of quasi-Newton methods, Loris Vincenzi and Marco Savoia (Vincenzi & Savoia, 2015) proposed coupling Differential Evolution heuristic with Response Surfaces (Khuri & Cornell, 1996;Myers, Montgomery, & Anderson-Cook, 2009).Fitting Response Surfaces during optimization and finding their optima mimics quasi-Newton methods.The authors showed that this approach reduced significantly the effort to solve some problems within a given tolerance (in general, more than 50% compared to the original heuristic method).