Fifty Collected Test Functions

Abstract

This study collects fifty test functions. This collection includes test problems from Deb ’s test and problem toolkit, ZDT and DTLZ test suites, Van Veldhuizen’s test suite, and other examples from the literature. For each test function, the Pareto-optimal set in the parameter space and the Pareto-optimal front in the fitness space are determined by using NSGA-II. We specify the main features of the Pareto-optimal sets for these test functions. The Pareto-optimal sets can be connected or disconnected, separable, unimodal of multimodal, symmetric and scalable. The Pareto-optimal fronts may have particular shapes such as a curve, a single point or a surface. The Paretooptimal fronts can be connected or disconnected, and entirely or partially with convex or nonconvex.

Keywords: Connected Pareto-optimal front, Constrained test function, Convex function, Disconnected Pareto-optimal front, Multimodal function, Near Paretooptimal front, Nonconvex function, NSGA-II software, Scalable function, Separable function, Symmetric Pareto-optimal front, Test function, Test suites, Unconstrained test function, Unimodal function.