GDS: Gradient Based Density Spline Surfaces For Multiobjective Optimization In Arbitrary Simulations

We present a novel approach for approximating objective functions in arbitrary deterministic and stochastic multi-objective blackbox simulations. Usually, simulated-based optimization approaches require pre-defined objective functions for optimization techniques in order to find a local or global minimum of the specified simulation objectives and multi-objective constraints. Due to the increasing complexity of state-of-the-art simulations, such objective functions are not always available, leading to so-called blackbox simulations. In contrast to existing approaches, we approximate the objective functions and design space for deterministic and stochastic blackbox simulations, even for convex and concave Pareto fronts, thus enabling optimization for arbitrary simulations. Additionally, Pareto gradient information can be obtained from our design space approximation. Our approach gains its efficiency from a novel gradient-based sampling of the parameter space in combination with a density-based clustering of sampled objective function values, resulting in a B-spline surface approximation of the feasible design space. We have applied our new method to several benchmarks and the results show that our approach is able to efficiently approximate arbitrary objective functions. Additionally, the computed multi-objective solutions in our evaluation studies are close to the Pareto front.