Engineering design optimization by dynamic cluster based framework using mixture surrogates

Abstract

The real-world engineering optimization problems utilize complex computational methods like finite element frameworks. These approaches are computationally costly and need high solution time. The work pays attention on finding the optimal solution to these complex engineering problems by using Surrogate Models (SM). SMs are mathematical models, which are utilized to minimize the required number of such costly function evaluations at the time of the optimization cycles. Instead of optimizing the Design Space (DS) as a whole, sub-region based strategies are found to be effectual, especially in the cases where prior knowledge of optimal solution is unavailable. In the present work, a surrogate centered optimization scheme is presented for local search, which dynamically sub-divides the DS into an optimum number of sub-regions by choosing the best cluster evaluation techniques as followed by the selection of best mixture SMs for each optimization cycle. For all objective functions and constraint functions in every sub-region, the mixture SMs are created by a combination of two or more single SMs. The MATSuMoTo, the Matlab based SM Toolbox by Juliane Muller and Robert Piché has been adapted for the creation and selection of best mixture SM. In this method, an individual surrogate is combined by utilizing the Dempster-Shafer theory (DST). Besides the above local search, a global search module is also introduced for ensuring faster convergence. This approach is tested on a constrained optimization benchmark test problem with smaller, disconnected feasible regions. It is perceived that the proposed algorithm accurately located all the local and global optima points with minimum function evaluations. The approach is applied to engineering problems like optimization of Machine Tool Spindle (MTS) design and frontal crash simulation on a full car body. For these engineering application problems also, mixture SM-based sub-region based search strategy is utilized to attain most accurate global optimum solution with a minimal number of costly function evaluations.