A practical sequential lexicographic approach for derivative-free black-box constrained optimization

Many engineering optimization problems involve models that might not exhibit the necessary smoothness to warrant efficient use of gradient algorithms. Many of these problems are also subject to constraints that might be simulation-based and as costly to compute as the objective function. Traditionally, such problems are solved using either penalty methods or lexicographic ordering that evaluates aggregate constraints prior to computing objective values. This study describes a cost-effective approach to performing such optimizations. After classifying all constraints depending on their computational cost, points not satisfying linear constraints are feasibilized, and a suitable penalty term constructed. A sequential lexicographic ordering is then applied in which inexpensive nonlinear constraints take precedence over expensive ones, which in turn take precedence over objective function values. The performance advantage of the proposed method over traditional ones is demonstrated with a set of analytical test problems, and with oilfield-production optimization examples that use 'black-box' simulators.