New Criteria for Comparing Global Stochastic Derivative-Free Optimization Algorithms

Jonathan Mccart,Ahmad Almomani

doi:10.14569/ijacsa.2019.0100781

Abstract

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.

Highlights

When deciding which algorithm is most appropriate to use on a given problem, it is crucial to have a detailed and encompassing description of how the algorithm will perform when applied in different contexts
Genetic Algorithm (GA) showed a gradual reduction in success from 20 to 100 dimensions, coming through as the algorithm which was most robust to changes in dimensionality for G1
Just as we examined the Accuracy plots for G4 to gain insight into the average solution capability of each algorithm, we look to Efficiency values for G4 shown in Fig. 9 to get an indication as to how well the successful attempts at finding the optimal were completed

Summary

Introduction

When deciding which algorithm is most appropriate to use on a given problem, it is crucial to have a detailed and encompassing description of how the algorithm will perform when applied in different contexts. Important is that the description of the algorithm is comprised of measures which can be universally applied to any other algorithm and used as an objective basis for comparison between many algorithms. The parameters we will be mainly focused on comparing across are dimension and problem type. These are two areas that substantially influence solver performance, which makes knowing the details on how exactly these areas impact performance important in the improvement of these solvers as well as the development of solvers with similar characteristics that are capable of circumventing the discovered weaknesses to these parameters

Objectives

Results

Conclusion