Benchmark sets are extremely important for evaluating and developing global optimization algorithms and related solvers. A new test set named PCC benchmark is proposed especially for optimization problems of nonlinear curve fitting for the first time, with the aspiration of helping developers to investigate and compare the performance of different global optimization solvers, as well as more effective optimization algorithms could be developed. Compared with the well-known classical nonlinear curve fitting benchmark set given by the National Institute of Standards and Technology (NIST) of USA, the most distinguishable features of the PCC benchmark are small problem dimensions, unconstrained with free search domain and high level of difficulty for obtaining global optimization solutions, which make the PCC benchmark be not only suitable for validating the effectiveness of different global optimization algorithms, but also more ideal for verifying and comparing various related solvers. Seven of the world's leading global optimization solvers, including Baron, Antigone, Couenne, Lingo, Scip, Matlab-GA and 1stOpt, are employed to test NIST and PCC benchmark thoroughly in terms of both effectiveness and efficiency. The results showed that the NIST benchmark is relatively simple and not suitable for global optimization testing, meanwhile the PCC benchmark is a unique, challenging and effective test dataset for global optimization.

翻译：基准测试集对于评估和开发全局优化算法及相关求解器至关重要。本文首次提出专用于非线性曲线拟合优化问题的PCC基准测试集，旨在帮助研究者探究和比较不同全局优化求解器的性能，进而开发更有效的优化算法。与美国国家标准与技术研究院（NIST）的经典非线性曲线拟合基准测试集相比，PCC基准测试集最显著的特征包括：问题维度小、无约束自由搜索域以及获取全局优化解的难度极高。这些特性使得PCC基准测试集不仅适用于验证不同全局优化算法的有效性，更理想地适用于比较各类相关求解器。本研究采用Baron、Antigone、Couenne、Lingo、Scip、Matlab-GA及1stOpt等七种世界领先的全局优化求解器，从求解有效性和计算效率两个维度对NIST与PCC基准测试集进行了全面测试。结果表明：NIST基准测试集较为简单，不适用于全局优化测试；而PCC基准测试集则是一套独特、具有挑战性且有效的全局优化测试数据集。