Tuning differential evolution for cheap, medium, and expensive computational budgets

This paper presents a parameter tuning study of Differential Evolution (DE) algorithms, including both standard DE as well as variants of the state-of-the-art adaptive DE, SHADE for both cheap and expensive optimization scenarios. Using the algorithm configuration tool SMAC, the DE variants are tuned independently for three different scenarios: expensive (102 × D evaluations), medium (104 × D evaluations), cheap (10⁵ × D evaluations), where D is the benchmark problem dimensionality. Each of these tuned parameter settings is then tested under both cheap and expensive scenarios, which enables us to analyze the effect of both the tuning and test scenario on the performance of the tuned algorithm. We evaluate restarting variants of DE (R-DE), as well as restarting variants of SHADE (R-SHADE) and L-SHADE (RL-SHADE). For the parameter tuning phase, we use the CEC2014 benchmarks as training problems, and for the testing phase, we use all 24 problems from the BBOB benchmark set. We also compare these DE variants with state-of-the-art restart CMA-ES variants (HCMA, BIPOP-CMA-ES, and IPOP-CMA-ES). For both cheap and expensive scenarios, DE algorithms perform very well for low-dimensional problems. In particular, for the expensive scenario, the simple, restarting DE (R-DE) performs quite well, and on the cheap scenario, RL-SHADE performs well.