Diverse Competitive Design In Structural Optimization Based On Surrogate Model

Nowdays structural optimization is applied in industry in many fields. The optimization problems are becoming more and more complex, hence the designers need to consider many different factors. The most critical structural performance metrics are included in the objective function and constraints when the mathematical model is formulated at the preliminary design stage. However, some other structural performance metrics, called latent performance metrics, may not be included in the model due to different reasons. The optimum design obtained by the traditional optimization formulation has the optimal behavior in modeled structural performance without consideration of the latent performance. Here, modeled performance refers to those objectives that are already included in optimization formulation; latent performance refers to those objectives that are not included in optimization formulation, yet maybe turn out to be very important in the later detailing design stage. Besides, one single global optimum is often invalidated in detailed design stage since the analysis method used is not accurate enough. Therefore, we want to obtain several different designs at the initial design stage that meet the modeled performance in the optimization formulation. These designs have diversity in configuration and competitiveness in performance, which may satisfy those latent performance during the later detailed design stage.This dissertation studies diverse competitive design in structural optimization based on surrogate model. Here, diversity means that the two designs have adequate separation in design variable space to increase the chance of different latent performance; competitiveness means the objective function values of the two designs are close enough to the global optimum. This paper reveals the significance of DCD (Diverse Competitive Design) optimization, presents the optimization formulation of DCD and its dual form, studies the KKT (Karush-Kuhn-Tucker) conditions of DCD and the characteristics of KKT points, presents the algorithms and strategies based on surrogates, and applies DCD optimization in pre-fold energy absorption tubes.This dissertation studies the following aspects:1) This dissertation takes two typical topology and size optimization problems as examples, reveals the weakness of traditional optimization formulation, presents the DCD optimization formulation and illustrates the necessity of DCD design. For a bridge design optimization example, two DCD solutions are compared with the optimum obtained by the traditional topology and size optimization. The results show that the DCD designs could meet the requirements of construction, beauty, terrain, as well as other latent performance. For the 10-bar truss design optimization example DCD formulation provides one statically determinate structure and one statically indeterminate structure under single load case. Their different latent performance illustrate the demands of DCD design.2) This dissertation presents the DCD formulation to search for k solutions that all have n variables, discusses the related objective function and distance constraint. This paper studies the relationship between the number of designs, the distances between designs and the probability that all the designs will prove deficient, which may provide proofs for adopting the Euclidean distance as the diversity measurement.3) Surrogate based algorithms have been applied increasingly in the field of structural optimization. Compared with traditional optimization algorithms, surrogate based algorithms have advantages in dealing with problems which have noise or are very time-consuming in simulation. To avoid falling into local optima, surrogate based algorithms use infill criteria to balance exploitation and exploration. This paper presents a new global optimization algorithm based on multi-start local search with geometrical exploration (MSG), and compares it with the efficient global optimization (EGO) by using several test functions. This paper discusses the distance limit d in MSG and makes suggestion for selecting d. This paper presents and compares four algorithms that fit surrogates in n or kn dimensional design space with different infill criteria, and concludes the optimal strategy.4) This dissertation presents the dual form of DCD optimization——DDCD (Dual Diverse Competitive Design), studies the KKT conditions of DCD and DDCD formulations and characteristics of KKT solutions. To avoid missing the global optimum, a greedy approach is presented. The characteristics of DCD algorithms and greedy approach are discussed. This paper also improves the surrogate based algorithms that can obtain the global optimum simultaneously during the process of searching for DCD and DDCD solutions. Three test functions are used to compare the trade-off curves of diversity vs. performance penalty obtained from the two formulations. The convergence speed and feasible domians of DCD and DDCD formulations are discussed.5) This dissertation applies the DCD optimization in pre-fold energy absorption tubes, considers the specific energy absorption and peak force as the objective function, searches for two, three and four DCD designs. This paper illustrates the necessity of DCD design based on surrogate in structural optimization by studying the relationship between DCD designs' design space & solution space and latent performance when the tubes are impacted with 30° angle.