Constrained Optimization with a Limited Number of Function Evaluations

In real-world optimization often constraints must be respected, restricting the number of feasible solutions. Therefore algorithms and strategies have been proposed to repair constraint-violating solutions or to avoid extensive search in infeasible regions. Such constraint handling methods are well-known from the literature, but most algorithms have the drawback that they require a large number of function evaluations. This can be especially problematic for real-world optimization tasks, which often incorporate expensive simulations. Up to now, only little work has been devoted to efficient constraint-based optimization (severely reduced number of function evaluations). A possible solution in that regard is to use surrogate models for the objective and constraint functions respectively. While the real function might be expensive to evaluate the surrogate functions are often much faster. Recently, as an example for this approach, the solver COBRA was proposed and outperforms most other algorithms in terms of required function evaluations on a large number of benchmark functions. In this paper we propose a new implementation of COBRA and compare it with other constraint-based optimization algorithms. We discuss the internal components of the algorithm and find that by adding new strategies, the algorithm can be significantly improved. We also report on negative results where COBRA still shows a bad behaviour and gives indications for possible improvements.