New Criteria for Comparing Global Stochastic Derivative-Free Optimization Algorithms

For many situations, the function that best models a situation or data set can have a derivative that may be difficult or impossible to find, leading to difficulties in obtaining information about the optimal values of the function. Thus, numerical methods for finding these important values without the direct involvement of the derivative have been developed, making the representation and interpretation of the results for these algorithms of importance to the researchers using them. This is the motivation to use and compare between derivative-free optimization (DFO) algorithms. The comparison methods developed in this paper were tested using three global solvers: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA) on a set of 26 n-dimensional test problems of varying convexity, continuity, differentiability, separability, and modality. Each solver was run 100 times per problem at 2, 20, 50 and 100 dimensions. The formulation for each algorithm used comes from the MATLAB Optimization Toolbox, unedited or revised. New criteria for comparing DFO solver performance are introduced in terms defined as Speed, Accuracy, and Efficiency, taken at different levels of precision and dimensionality. The numerical results for these benchmark problems are analyzed using these methods.