#CONSTRAINED LATIN HYPERCUBE SAMPLING FULL#
Keywords: Teaching-Learning-Based Optimization, Design Sampling, Computer-Aided Design, Generative DesignĪdaptive rejection sampling method to sample from a complicated full conditional density which satisfies the log-concavity condition. According to the experiments in this study, S-TLBO outperforms state-of-the-art techniques particularly when a high number of samples are generated. Samples in constrained design spaces are then generated. Sampling is first done for unconstrained design spaces, whereby the models obtained are shown to users in order to learn their preferences which are represented in the form of geometric constraints. Four CAD models, a yacht hull, a wheel rim and two different wine glasses, are employed to validate the performance of the S-TLBO approach. For constrained design sampling, a static constraint handling mechanism is utilized to penalize designs that do not satisfy the predefined design constraints. Space-filling is achieved using the Audze and Eglais’ technique. For unconstrained design sampling, the cost function favors the generation of space-filling and Latin Hypercube designs. Teachers of each sub-population are regarded as sampled designs after the application of S-TLBO. Iterations are performed until change in the cost values becomes negligibly small.
Teaching and learning phases are applied for each sub-population one by one which are based on a cost (fitness) function. To sample N designs in a predefined design space, N sub-populations are first generated each of which consists of separate learners. A good sampling technique should generate CAD models uniformly distributed in the entire design space so that designers or customers can well understand possible design options. Sampling CAD models in the design space can be useful for both designers and customers during the design stage. In this study, TLBO is extended for constrained and unconstrained CAD model sampling which is called Sampling-TLBO (S-TLBO). This algorithm is based on the influence of a teacher on the quality of learners in a population. has been presented in recent years, which is a population-based algorithm and operates on the principle of teaching and learning. The Teaching-Learning-Based Optimization (TLBO) algorithm of Rao et al. Furthermore, it does not produce good results for the designs space where infeasible designs are spread irregularly. Fuerle and Sienz method has some draw backs such that it cannot be implemented for the high dimensional sampling problems more than 3D. The coordinates of samples that are in infeasible region are modified using the mutation operator that is used for the genetic algorithms.
Desired number of designs to be sampled are defined first and these points are then randomly sampled using LHS in two dimensional space. Fuerle and Sienz proposed a method based on LHS for design selections for constrained spaces.
Although this technique has good space filling property but it is just applicable to only two dimensional constraint problems. To produce uniform sampling in the design space, a heuristic method based on the uniform finite element meshes was proposed. This technique is based on the triangulation of admissible space by Delaunay Triangulation method. and Mysakova and Leps proposed a technique to perform sampling for constrained spaces. The research problem becomes very complicated when selection of designs has to be performed in a constrained and high dimensional design space, as that of the current research. However, most works done by researchers are proposed for the unconstrained design spaces. There is considerable amount of research has been done on optimal selection of designs in the design space in order to improve the space-filling property of LHS.
0 kommentar(er)
