Source-linked AI summary
Test Problems in Optimization
Xin-She Yang
TL;DR
The paper addresses how to validate and compare optimization algorithms without a mandatory test-function list. It provides a selected set of bounded test problems spanning diverse properties, including convex, unimodal, multimodal, nonsmooth, singular, and stochastic cases.
Problem
Optimization algorithms need standard test functions for performance comparison, but no mandatory list exists and diverse functions are needed to assess different optimization capabilities.
Method
The paper provides a selected appendix of commonly used test functions, specifying each function, its bounded search domain, and its optimal solution or objective value.
Results
The collection covers functions with varied landscapes and properties, including convex and unimodal functions, multimodal functions, nonsmooth or singular optima, and stochastic components.
Takeaways & Limitations
New optimization algorithms should be tested on a subset of functions with diverse properties to determine which types of optimization they solve efficiently.
Abstract
from arXiv · showhide
Test functions are important to validate new optimization algorithms and to compare the performance of various algorithms. There are many test functions in the literature, but there is no standard list or set of test functions one has to follow. New optimization algorithms should be tested using at least a subset of functions with diverse properties so as to make sure whether or not the tested algorithm can solve certain type of optimization efficiently. Here we provide a selected list of test problems for unconstrained optimization.