Expensive Multiobjective Optimization Research Articles

Statistical Improvement Criteria for Use in Multiobjective Design Optimization

Design of experiment and response surface modeling methods are applied to the problem of constructing Pareto fronts for computationally expensive multiobjective design optimization problems. The work presented combines design of experiment methods with kriging (Gaussian process) models to enable the parallel evolution of multiobjective Pareto sets. This is achieved via the use of updating schemes based on new extensions of the expected improvement criterion commonly applied in single-objective searches. The approaches described provide a statistically coherent means of solving expensive multiobjective design problems using single-objective search tools. They are compared to the use of nondominated sorting genetic algorithm (NSGA-ii) based multiobjective searches, both with and without response surface support. The new approaches are shown to give more exact, wider ranging, and more evenly populated Pareto fronts than the genetic algorithm based searches at reduced or similar cost.

ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems

This paper concerns multiobjective optimization in scenarios where each solution evaluation is financially and/or temporally expensive. We make use of nine relatively low-dimensional, nonpathological, real-valued functions, such as arise in many applications, and assess the performance of two algorithms after just 100 and 250 (or 260) function evaluations. The results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used. A significantly better performance (particularly, in the worst case) is, however, achieved on our test set by an algorithm proposed herein-ParEGO-which is an extension of the single-objective efficient global optimization (EGO) algorithm of Jones et al. ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation. Overall, ParEGO exhibits a promising performance for multiobjective optimization problems where evaluations are expensive or otherwise restricted in number.

Multiobjective Optimization Using Coupled Response Surface Model and Evolutionary Algorithm.

In this work we develop an efficient approach for computationally expensive multiobjective design optimization problems. In this approach we bring together design of experiment, a response surface model, a genetic algorithm, and computational-fluid-dynamics analysis tools to provide an integrated optimization system. We use an improved hypercube sampling to preselect an array of design points on which the computational-fluid-dynamics code will run. Then a computationally cheap surrogate model is constructed based on response surface approximation. A real-coded genetic algorithm is then applied on the surrogate model to perform multiobjective optimization. Representative solutions are chosen from the Pareto-optimal front to verify against the computational-fluid-dynamics code. This proposed method is used in the redesign of a single-stage turbopump, a two-stage turbopump, and the NASA rotor67 transonic compressor blade