Efficient Surrogate Assisted Optimization for Constrained Black-Box Problems

Modern real-world optimization problems are often high dimensional and subject to many constraints. These problems are typically expensive in terms of cost and computational time. In order to optimize such problems, conventional constraintbased solvers require a high number of function evaluations which are not affordable in practice. Employment of fast surrogate models to approximate objective and constraint functions is a known approach for efficient optimization. The performance of the RBF interpolation is not dependent on the dimensionality of the optimization tasks. This is why in the area of surrogate-assisted optimization a lot of attention is devoted to RBF modeling. As an example for such a solver, COBRA is a constrained based efficient optimizer that outperforms many other algorithms on a large number of benchmarks. COBRA-R is a variant of COBRA extended with several algorithms such as a different initialization method and a novel repair technique. In this thesis, after investigating the strengths and weaknesses of COBRA-R, we introduced several extensions to enhance the overall performance of COBRA-R. Our investigation showed that the RBF surrogates cannot provide a suitable model for steep functions. Therefore, problems with steep objective or constraint functions have to be modified in order to be optimized with the COBRA-R approach. Additionally, the performance of COBRA-R is highly sensitive to the correct selection of a parameter called DRC. Also, the surrogate models appeared to be wrong for the problems with highly varying input ranges. Moreover, it was observed that sometimes a bad initial design could cause an early stagnation. The extended COBRA-R called self-adaptive COBRA-R intends to overcome these mentioned obstacles by including three extra steps: 1. Rescaling the input space to [0, 1] (if it is necessary). 2. Automatic parameter/function(s) adaptation according to the information gained from the initial population. 3. Random start mechanism to avoid occasional bad solutions due to a few unfortunate initial designs. We evaluate our approach by using 11 G-problems and a high dimensional automotive problem (MOPTA08) as benchmark. We also report negative results where SACOBRA-R still shows a bad behavior and gives indications for possible improvements.