Benchmarking Powell’s Legacy: Performance of Five Derivative-Free Solvers in pdfo on the bbob Test Suite

The pdfo library by Tom M. Ragonneau and Zaikun Zhang makes the five derivative-free solvers BOBYQA, COBYLA, LINCOA, NEWUOA, and UOBYQA—originally written by Michael J. D. Powell—available in Python. In this paper, we are comparing their performance on the bbob test suite with three other solvers from the COCO data archive: CMA-ES from pycma, SLSQP and BFGS from scipy. We also compare the original solvers, written by Powell in Fortran 77, with the current pdfo versions, which saw multiple bug fixes and code improvements by Ragonneau and Zhang. For the latter comparison, we do not see large effects on performance between the Fortran 77 version and the current pdfo version. The only notable exception is the Bent Cigar function where we observe differences by a factor of 2–5 for BOBYQA, LINCOA, and NEWUOA. Compared to the other baseline algorithms, BOBYQA, LINCOA and NEWUOA perform very similarly over all bbob functions, being about a factor of 5 slower than SLSQP and BFGS while UOBYQA—as the best-performing pdfo solver—outperforms SLSQP and BFGS for larger budgets when compared over all 24 bbob functions. The linear surrogate of COBYLA, on the contrary, is clearly worse over all functions than the other algorithms.