An Improved Genetic Algorithm for the Optimization of Composite Structures

최근에는 고층구조물이나 해양구조물(플랜트)의 경우 대부분 대형화로 설계 및 시공되고 있다. 대형구조물의 경우 주로 강재(steel)를 사용하여 설계하고 있다. 구조물 설계는 설계단계에서 최상의 부재를 선택하는 최적화를 적용함으로서 비용을 줄이는 경제적인 효과를 얻을 수 있다. 본 연구에서는 트러스와 프래임 구조물의 최적설계에 연속변수와 이산변수를 사용하여 최적화 하였고, 설계에서 사용된 이산자료는 규격화된 강재에 대한 자료와 데이터화된 이산자료를 사용하였다. 최적화는 이 모두에 적합한 이산최적화를 적용하였다. 최적화 기법으로는 유전자 알고리즘을 사용하였으며, 사용된 구조물은 10-Bar, 25-Bar 트러스와 1경간 2층, 1경간 7층 프레임 구조물이다. 설계시 제약조건은 고유진동수와 부재응력, 변위제약조건들이 적용되었다. 유전자 알고리즘에는 번식과장에서 엘리트 개체가 2번 사용되도록 하였으며, 제약조건 위반시 패널티를 사용하는 방법을 사용하였다. We present optimum design for truss and frame structures subject to constraints on stresses, displacement, and natural frequency. The optimum design procedure is used discrete and continuous design variables and Genetic Algorithms. Genetic Algorithms is used the method of Elitism and penalty parameters in order to improved fitness in the reproduction process, and optimum design is used steel(W-section) and pre-made discrete cross-section. Truss and frame structures optimization examples are used for 10-Bar truss, 25-Bar truss, 1-bay 2-story frame, 1-bay 7-story frame, and these examples are employed to demonstrate the availability and serviceability of Genetic Algorithms for solving optimum design of truss and frame.

This paper discusses the integrated topology and sizing optimization of frame structures where beam elements are used in the structural analysis model. Based on the ground structure approach, discrete variables (0, 1) representing the absence or presence of beam members and continuous sizing variables for beam cross sections are involved in the problem. A two-level multipoint approximation strategy is introduced to address this mixed-variable problem. A first-level approximate problem is first constructed using the branched multipoint approximate function involving both discrete and continuous variables. For solving this problem, discrete variables are optimized through a genetic algorithm, and when calculating the fitness in the genetic algorithm, a second-level approximate problem solved by the dual method is established to optimize the cross sections for the retained beam members. Temporal deletion techniques are used for displacement and stress constraints. Meanwhile, by considering local vibration modes in frequency-constrained problems, material density is assigned with an extremely small value for the removed beams to avoid these local modes. Thence, the singularities encountered in stress, displacement, and frequency constraints are overcome. Typical examples and a satellite application are given to verify the feasibility and efficiency of this method in handling the integrated topology and sizing optimization for frame structures.

The integrated optimization of structure and control systems is investigated for 2-D single structure using a typical planar frame taken from a building. The vibration control model is established for the plane frame, and the LQR algorithm is used to obtain equivalent stiffness and damping parameters of assigned passive controllers. The integrated optimization model, including design variables, the objective function and constraint function, is built. The design variables are the size parameters of structural elements, the parameters of the weighted matrix, the number and locations of the controllers. The maximal displacement of the controlled system in time domain is introduced as the objective function. Genetic algorithm is adopted to solve such a kind of optimization problem with discrete and continuous design variables. The results of a numerical example show that the proposed method is reasonable and effective for the integrated design of control/structural systems subjected to seismic load.

Mechanical sizing of a composite launcher structure by hybridizing a genetic algorithm with a local search method

This paper proposes a Sequential Approximate Optimization (SAO) for the discrete design variable problems using Radial Basis Function (RBF) Network. We consider that there are two important keys for SAO: One is the parameter adjustment for good approximation, and the other is to explore the sparse region for global approximation. The authors have proposed the simple estimate of the width in the Gaussian Kernel for good approximation. In addition, in order to explore the sparse region, we have developed the density function. The density function with the simple estimate of the width works well in the case of the continuous design variables. However, a simple application of the density function to the discrete design variable problems will cause some difficulties. In order to overcome these difficulties and find the sparse region of the discrete design variables with the density function, the new variables for the discrete design variables are introduced. By using the new variables, it is possible to find the sparse region of the discrete design variables. A simple sampling algorithm is shown, in which the Discrete Differential Evolution (DDE) for the discrete design variables is employed. Through typical numerical examples, the validity of proposed approach is examined.

A modification to the genetic algorithm (GA) based search procedure, based on the modeling of a biological immune system, is proposed as an approach to solving the multicriterion design problem. Such problems have received considerable attention, given that decisions in engineering design practice typically require allocation of resources to satisfy multiple, and frequently conflicting requirements. The approach is particularly amenable to problems with a mix of continuous, discrete, and integer design variables, where the GA has been shown to perform in an effective manner. The approach considered in the present work is based on the concept of converting the multicriterion problem into one with a scalar objective through the use of the utility function. The strength of the approach is in its ability to generate the Pareto-Edgeworth front of compromise solutions in a single execution of the GA. A characteristic feature of biological immune systems which allows for the generation of multiple specialist antibodies, is shown to be an effective approach to facilitate the generation of the Pareto-Edgeworth front. Solutions to problems in structural design are presented in support of the proposed approach.

Space satellite design generally involves multidisciplinary collaboration processes, such as structural, heat transfer and electrical design processes, aimed at fulfilling various functional requirements that are subject to stringent weight and spatial limitations. This paper discusses a practical application of a systematic design optimization approach to the design of a small satellite called “Micro-LabSat,” in order to obtain optimal solutions that take into account such multidisciplinary design factors. The satellite design problem has two sub design problems, a component arrangement problem and a structural design problem, and the features of these two problems are entirely different since the component arrangement problem involves discrete design variables such as the positions of the components, while the structural design problem has continuous design variables such as the dimensions of the parts. Therefore, a bi-level optimization procedure is applied. First, two sublevel optimization problems for the sub design problems are solved. A two-phase optimization procedure that uses genetic algorithms and SQP (Sequential Quadratic Programming) is applied to the component arrangement problem, and SQP is applied to the structural optimization. Then, the satellite-level optimization problem that considers all factors, including both the component arrangement and structural problems, is solved using the sublevel optimal solutions as initial points for optimization. The bi-level optimization scheme presented here provides an efficient search procedure, and offers optimal solutions in short calculation times.

A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.

This paper describes the numerical optimisation procedure developed for the design of structural components of Formula One racing cars made of composite materials. The numerical procedure, developed using Matlab, is based on coupling a commercial finite element code for structural analysis (MSC/NASTRAN), with a genetic algorithm optimisation tool. It takes into account both continuous and discrete design variables, and the application of continuity technological constraints. Two different application examples related to a Formula One car are reported: the first one concerns a turning vane subject to static requirements, while the second one concerns a rear wing, subject to static, dynamic and buckling requirements.

Optimization problems concerning complex structures with many design variables may entail an unacceptable computational cost. This problem can be reduced considerably with a multilevel approach: A structure consisting of several components is optimized as a whole (global) as well as on the component level. In this paper, an optimization method is discussed with applications in the assessment of the impact of new design considerations in the development of a structure. A strategy based on fully stressed design is applied for optimization problems in linear statics. A global model is used to calculate the interactions (e.g., loads) for each of the components. These components are then optimized using the prescribed interactions, followed by a new global calculation to update the interactions. Mixed discrete and continuous design variables as well as different design configurations are possible. An application of this strategy is presented in the form of the full optimization of a vertical tail plane center box of a generic large passenger aircraft. In linear dynamics, the parametrization of the component interactions is problematic due to the frequency dependence. Hence, a modified method is presented in which the speed of component mode synthesis is used to avoid this parametrization. This method is applied to a simple test case that originates from noise control.

Recent advances in non-gradient based optimization methods (e.g., Genetic Algorithms, Particle Swarm Optimization) enhanced the abilities of discrete, integer, and mixed optimization problems. However, the very nature of non-gradient based algorithms is that the number of analyses required to get to an optimal solution is several orders of magnitude higher than for traditional gradient based optimization methods or response surface optimization methods, when considering continuous problems. Instead of these approaches we propose to use a response surface approximate optimization method modified to work with discrete design variables. In this case whenever it is required to perform the actual analysis of responses for the purpose of fitting a response surface approximation, the design variables will be converted to corresponding discrete values. Two discretization techniques are proposed. We demonstrate that although lacking global search properties like Genetic Algorithms and Particle Swarm Optimization, the discrete response surface optimization provides a computationally efficient way of improving an initial design and getting into a region of an optimum using only discrete points for analysis.

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

A novel optimization method based on a differential evolution (DE) strategy for designing low-weight truss structures is presented for both continuous and discrete variables. Applications of this technique on the optimization of a benchmark-type truss structure with continuous and discrete variables are given to evaluate its effectiveness. Results are compared with various classical and evolutionary optimization methods which show that the proposed procedure based on DE outperforms other methods and can effectively be applied to the optimization problems of truss structures with both continuous and discrete design variables.

In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems.

This paper describes an optimal design method for high-field and highly homogeneous superconducting magnet systems with hybrid iron and active shielding. The presented design technique is a combination of the equivalent magnetization current method for the computation of the magnetic field problem, which includes nonlinear and saturated iron, and the simulated annealing for solving the corresponding optimization problem. The equivalent magnetization current method is superior in estimating the field homogeneity at the center of the magnet systems. By using the simulated annealing, the positions of each coil are optimized as continuous design variables, while the number of turns and layers of the coil windings are treated as discrete design variables. In this paper, the detail of the algorithm and the example of its application to 9 T magnet system with hybrid iron and active shielding are shown.