A New Challenging Curve Fitting Benchmark Test Set for Global Optimization Solvers

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 problem of nonlinear curve fitting for the first time, with the aspiration of investigating and comparing the performance of different global optimization solvers. 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 important features of the PCC benchmark are small problem dimensions, free search domain and high level of difficulty for obtaining global optimization solutions, which makes the PCC benchmark be not only suitable for validating the effectiveness of various global optimization algorithms, but also more ideal for verifying and comparing various solvers with global optimization solving capabilities. Based on PCC and NIST benchmark, seven of the world's leading global optimization solvers, including Baron, Antigone, Couenne, Lingo, Scip, Matlab GA and 1stOpt, are thoroughly tested and compared in terms of both effectiveness and efficiency. The results showed that the NIST benchmark is relatively simple and not suitable for global optimization testing, while the PCC benchmark is a unique, challengeable and effective test dataset for testing and verifying global optimization algorithms and related solvers. 1stOpt solver gives the overall best performance in both NIST and PCC benchmark.