Integrated Design of Control/Structural Systems Based on Genetic Algorithm

Integrated optimization of structural topology and control for piezoelectric smart trusses using genetic algorithm

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

There are more than 100 design variables and 2000 constraint conditions in designing mid-ship section of ship structure, and hence, it is very difficult to determine all design variables with satisfying all constraint conditions and having a reasonable value of objective function, or construction cost. Since this kind of optimization problem has so many design variables and a huge number of constraint conditions, it takes unbelievably large computational effort for obtaining an optimal solution when all design variables are solved simultaneously. A multi-step optimization method is introduced here with the aim of reducing the computational time. Since the design process of a mid-ship section is divided into three stages, double bottom, bilge hopper tank and topside tank stages, traditionally, three-step optimization may be rational and is introduced. But, when design variables in each step are determined separately, the solution obtained after the final step is far form the optimal solution obtained by solving all design the variables at once. In order to resolve this problem, characteristic design variable method is introduced and investigated here. The proposed method gives good solutions with satisfying all constraint conditions and having reasonable value of the objective function instead of solving all design variables at once. Genetic algorithm is used for optimization procedure in this study.

This paper presents the population-based sampling genetic algorithm, which allows for discrete design optimization under uncertainty. The population-based sampling approach uses the genetic algorithm population to provide samples for the probabilistic evaluation of aggregate uncertain constraint or objective functions. In population-based sampling, large numbers of samples are accumulated to evaluate the fitness values of good designs during the genetic algorithm run, whereas the computational cost spent on designs with poor fitness is minimal. Using Monte Carlo sampling with a genetic algorithm for optimization under uncertainty is a currently accepted approach; however, this approach incurs a large computational cost. In this paper, the genetic algorithm with population-based sampling generates solutions to a discrete optimization problem under uncertainty associated with a commercial satellite design that was solved in previous work via a genetic algorithm with Monte Carlo sampling. The genetic algorithm with population-based sampling and genetic algorithm with Monte Carlo sampling approaches are compared in terms of efficiency (computational cost) and effectiveness (solution quality). The comparison also examines the scalability of the algorithms' performance when solving three additional problem sizes. Furthermore, two population-based sampling variants are introduced, namely, the variable population-based sampling approach, which combines the concepts of population-based sampling and Monte Carlo sampling, and the generalized population-based sampling approach, which removes the restriction in population-based sampling that the uncertain parameters associated with the design variables all have Gaussian probability distributions.

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 describes a new approach for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed modification improves the efficiency of the memory constructed in terms of the continuous variables. The work presents the algorithmic implementation of the proposed memory scheme and demonstrates the efficiency of the proposed multivariate approximation procedure for the weight optimization of a segmented open cross section composite beam subjected to axial tension load. Results are generated to demonstrate the advantages of the proposed improvements to a standard genetic algorithm.

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.

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.

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.

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.

Refined models for the optimal design of adaptive structures using simulated annealing

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.

<div class="htmlview paragraph">Many design processes could be made faster and cheaper by use of shape optimization techniques. However, the computational cost of evaluating the necessary derivatives often limits the application of optimization methods to simple engineering problems. Nevertheless, techniques based on the control theory have been shown to decrease dramatically this cost when compared with Finite Difference methods.</div> <div class="htmlview paragraph">In this paper we describe how an optimization algorithm can be used, along with adjoint based methods, in the stamping process design. We first show how the stamping process can be stated in mathematical terms and expressed as a classical optimization problem. In this formulation, the objective and constraint functions are expressed in terms of the strain distribution in the part. This strain distribution is evaluated by a simplified finite element procedure. We then show how the gradients and Hessians can be computed with adjoint based methods. In our approach we use the shape of the entire addendum surface as the design variable. This surface is approximated by the finite element mesh and the discrete design variables are the vertical coordinates of the nodes. Finally, plane strain examples illustrate the model described.</div>

Optimal design considering buckling of compressive members is an important subject in structural engineering. The strength of compressive members can be compensated by initial geometrical imperfection due to the manufacturing process; therefore, geometrical imperfection can affect the optimal design of structures. In this study, the metaheuristic teaching-learning-based-optimization (TLBO) algorithm is applied to study the geometrical imperfection-sensitivity of members' buckling in the optimal design of space trusses. Three benchmark trusses and a real-life bridge with continuous and discrete design variables are considered, and the results of optimization are compared for different degrees of imperfection, namely 0.001, 0.002, and 0.003. The design variables are the cross-sectional areas, and the objective is to minimize the total weight of the structures under the following constraints: tensile and compressive yielding stress, Euler buckling stress considering imperfection, nodal displacement, and available cross-sectional areas. The results reveal that higher geometrical imperfection degrees significantly change the critical buckling load of compressive members, and consequently, increase the weight of the optimal design. This increase varies from 0.4 to 119% for different degrees of imperfection in the studied trusses.

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.