Efficient solution of optimization problems with constraints and/or cost functions expensive to evaluate

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Elektrik ve Elektronik Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2009

Öğrenci: AHMET GÖKHAN KURTDERE

Danışman: MEHMET KEMAL LEBLEBİCİOĞLU

Özet:

There are many optimization problems motivated by engineering applications, whose constraints and/or cost functions are computationally expensive to evaluate. What is more derivative information is usually not available or available at a considerable cost. For that reason, classical optimization methods, based on derivatives, are not applicable. This study presents a framework based on available methods in literature to overcome this important problem. First, a penalized model is constructed where the violation of the constraints are added to the cost function. The model is optimized with help of stochastic approximation algorithms until a point satisfying the constraints is obtained. Then, a sample point set satisfying the constraints is obtained by taking advantage of direct search algorithms based sampling strategies. In this context, two search direction estimation methods, convex hull based and estimated radius of curvature of the sample point set based methods can be applicable. Point set is used to create a barrier which imposes a large cost for points near to the boundary. The aim is to obtain convergence to local optima using the most promising direction with help of direct search methods. As regards to the evaluation of the cost function there are two directions to follow: a-) Gradient-based methods, b-) Non-gradient methods. In gradient-based methods, the gradient is approximated using the so-called stochastic approximation algorithms. In the latter case, direct search algorithms based sampling strategy is realized. This study is concluded by using all these ideas in the solution of complicated test problems where the cost and the constraint functions are costly to evaluate.