A Benchmark of 25 Nonlinear Functions with Domain-Induced Discontinuity for Global Optimization

TL;DR

This paper introduces a challenging benchmark of 25 nonlinear optimization problems with domain-induced discontinuities, designed to evaluate and compare global optimization algorithms in complex landscapes.

Contribution

The paper presents the CPC Benchmark, a novel test suite with embedded infeasible regions and discontinuities, facilitating rigorous performance assessment of diverse optimization methods.

Findings

Many functions have extremely small feasible regions.

Algorithms exhibit high sensitivity near feasibility boundaries.

The benchmark effectively discriminates between different optimization algorithms.

Abstract

A benchmark of 25 nonlinear optimization problems with domain-induced discontinuity is proposed to support the performance evaluation of global optimization algorithms under feasibility-scarce and structurally discontinuous landscapes. Referred to as the CPC Benchmark (Challenging Problems for Computation), the test suiteconsists of functions that are continuous on their natural domains, while infeasible regions and undefined evaluations are implicitly embedded in the objective, creating substantial challenges for global minimization. Six representative algorithms from diverse methodological paradigms are assessed to examine the structural complexity and discriminative capability of the benchmark. Numerical results show that many functions possess extremely small feasible regions and strong precision sensitivity near feasibility boundaries, complicating initialization, feasibility discovery, and reliable objective assessment. The findings demonstrate that the CPC benchmark provides clear discriminative power across algorithmic paradigms and offers a rigorous, software-oriented testbed for advancing research in global optimization.