Online and Offline Approximations for Population based Multi-objective Optimization

The high computational cost of population based optimization methods has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise approaches that can significantly reduce the number of function (or simulation) calls required in such optimization methods. This dissertation presents some new online and offline approximation approaches for design optimization. In particular, it presents new DOE and metamodeling techniques for Genetic Algorithm (GA) based multi-objective optimization methods along four research thrusts. The first research thrust is called: Online Metamodeling Assisted Fitness Evaluation. In this thrust, a new online metamodeling assisted fitness evaluation approach is developed that aims at significantly reducing the number of function calls in each generation of a Multi-Objective Genetic Algorithm (MOGA) for design optimization. The second research thrust is called: DOE in Online Metamodeling. This research thrust introduces a new DOE method that aims at reducing the number of generations in a MOGA. It is shown that the method developed under the second research thrust can, compared to the method in the first thrust, further reduce the number of function calls in the MOGA. The third research thrust is called: DOE in Offline Metamodeling. In this thrust, a new DOE method is presented for sampling points in the non-smooth regions of a design space in order to improve the accuracy of a metamodel. The method under the third thrust is useful in approximation assisted optimization when the number of available function calls is limited. Finally, the fourth research thrust is called: Dependent Metamodeling for Multi-Response Simulations. This research thrust presents a new metamodeling technique for an engineering simulation that has multiple responses. Numerous numerical and engineering examples are used to demonstrate the applicability and performance of the proposed online and offline approximation techniques

A kriging metamodel assisted multi-objective genetic algorithm for design optimization

ABSTRACT The high computational cost of population based optimization methods, such as multi-objective genetic algorithms, has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise methods that can significantly reduce the number of computationally intensive simulation (objective/constraint functions) calls. We present a new multi-objective design optimization approach in that kriging-based metamodeling is embedded within a multi-objective genetic algorithm. The approach is called Kriging assisted Multi-Objective Genetic Algorithm, or K-MOGA. The key difference between K-MOGA and a conventional MOGA is that in K-MOGA some of the design points or individuals are evaluated by kriging metamodels, which are computationally inexpensive, instead of the simulation. The decision as to whether the simulation or their kriging metamodels to be used for evaluating an individual is based on checking a simple condition. That is, it is determined whether by using the kriging metamodels for an individual the non-dominated set in the current generation is changed. If this set is changed, then the simulation is used for evaluating the individual; otherwise, the corresponding kriging metamodels are used. Seven numerical and engineering examples with different degrees of difficulty are used to illustrate applicability of the proposed K-MOGA. The results show that on the average, K-MOGA converges to the Pareto frontier with about 50% fewer number of simulation calls compared to a conventional MOGA. KEYWORDS: Multi-objective genetic algorithm, kriging metamodeling, multi-objective design optimization INTRODUCTION An important challenge faced by researchers in the area of Genetic Algorithm (GA) [1] based optimization has been the high computational cost of these population-based methods to obtain the solution for real-world engineering design problems. Researchers have been quite active in developing models and methods that improve the efficiency of GAs in terms of the number of simulation calls The fitness approximation methods are of two types: nonadaptive and adaptive. The non-adaptive methods are those in which metamodels are developed off-line, i.e., separately and prior to the start of an optimization algorithm [4, 6-8, 19, 20]. The shortcoming of non-adaptive methods is that it is difficult to obtain both a good fidelity metamodel over the entire design space and at the same time maintain low number of simulation calls or low computational cost In the adaptive approache