A New Challenging Curve Fitting Benchmark Test Set for Global Optimization

Abstract: 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.