• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.359-372
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• 1995

This study presents an efficient method for optimum design of plate and shell structures, when the design variables are continuous or discrete. Both sizing and shape design variables are considered. First the structural responses such as element forces are approximated in terms of some intermediate variables. By substituting these approximate relations into the original design problem, an explicit nonlinear approximate design task with high quality approximation is achieved. This problem with continuous variables, can be solved by means of numerical optimization techniques very efficiently, the results of which are then used for discrete variable optimization. Now, the approximate problem is converted into a sequence of second level approximation problems of separable form and each of which is solved by a dual strategy with discrete design variables. The approach is efficient in terms of the number of required structural analyses, as well as the overall computational cost of optimization. Examples are offered and compared with other methods to demonstrate the features of the proposed method.

• Proceedings of the KIEE Conference
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• 2007.11b
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• pp.226-228
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• 2007

This paper proposes Nonlinear Interior Point Method (NIPM) including discrete control variables optimal power flow formulations. The algorithm utilizes the robustness in terms of starting point and fast convergence for large scale power system of NIPM and an introduction of rounding penalty function which is augmented in the Lagrangian function to handle discrete control variables. The derived formulation shows a simplified approach to deal with discrete control problems which is implementable in real large scale systems.

• Journal of Ocean Engineering and Technology
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• v.21 no.2 s.75
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• pp.75-80
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• 2007

The design variables for structural systems, in most practical designs, are chosen from a list of discrete values, which are commercially available sizing. This paper presents the application of Genetic Algorithms for determining the optimum design for two-dimensional structures with discrete and pseudocontinuous design variables. Genetic Algorithms are heuristic search algorithms and are effective tools for finding global solutions for discrete optimization. In this paper, Genetic Algorithms are used as the method of Elitism and penalty parameters, in order to improve fitness in the reproduction process. Examples in this paper include: 10 bar planar truss and 1 bay 8-story frame. Truss with discrete and pseudoucontinuous design variables and steel frame with W-sections are used for the design of discrete optimization.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.285-299
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• 2020

In many cases, we are interested in identifying independence between variables. For continuous random variables, correlation coefficients are often used to describe the relationship between variables; however, correlation does not imply independence. For finite discrete random variables, we can use the Pearson chi-square test to find independency. For the mixed type of continuous and discrete random variables, we do not have a general type of independent test. In this study, we develop a independence test of a continuous random variable and a discrete random variable without assuming a specific distribution using kernel density estimation. We provide some statistical criteria to test independence under some special settings and apply the proposed independence test to Pima Indian diabetes data. Through simulations, we calculate false positive rates and true positive rates to compare the proposed test and Kolmogorov-Smirnov test.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.9-16
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• 1995

This study presents the applicable possibility of numerical optimization and Genetic Algorithm in the design of truss structures using discrete variables and real constraints. The introduction of Genetic Algorithm in the design of truss structures enables us to do easier formulation and handle discrete variables. To investigate these applicable possibility, the design of 15 - bar truss structures has been studied using GT/STRUDL and Genetic Algorithm and the results of Genetic Algorithm are compared with GT/STRUDL's.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.53-57
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• 2003

Optimum design of most structural system requires that design variables are regarded as discrete quantities. This paper presents the use of Genetic Algorithm for determining the optimum design for truss with discrete variables. Genetic Algorithm are know as heuristic search algorithms, and are effective global search methods for discrete optimization. In this paper, Elitism and the method of conferring penalty parameters in the design variables, in order to achieve improved fitness in the reproduction process, is used in the Genetic Algorithm. A 10-Bar plane truss and a 25-Bar space truss are used for discrete optimization. These structures are designed for stress and displacement constraints, but buckling is not considered. In particular, we obtain continuous solution using Genetic Algorithms for a 10-bar truss, compared with other results. The effectiveness of Genetic Algorithms for global optimization is demonstrated through two truss examples.

• The Mathematical Education
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• v.59 no.1
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• pp.47-62
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• 2020

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.195-202
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• 1995

In this study, the optimization program is developed to provide preliminary designs of steel-box girder bridges with minimum cost. The advantages of steel-box girder deck, when comparing with other girder types, are higher torsional rigidity and better resistance against corrosion. To achieve more rational design, systematic design procedure is required, by which the design constraints on steel-box girder are satisfied and the design variables with minimum cost are obtained. In the Proposed optmum design Process, the design variables are forced to be selected from the available discrete value set. The efficiency of the developed program has been verified by companing with previous designed sections and the resulting optimum cost with discrete variables has been compared with those of continuous variables.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.351-358
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• 2005

Many methods have been developed and are in use for structural size optimization problems, In which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) meta-heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary In this paper, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through a standard truss example. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current method.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.33 no.12
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• pp.53-62
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• 2017

Many gradient-based mathematical methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. The main objective of this paper is to propose an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) meta-heuristic algorithm that is derived using penalty function. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this paper, a discrete search strategy using the HS algorithm with a static penalty function is presented in detail and its applicability using several standard truss examples is discussed. The numerical results reveal that the HS algorithm with the static penalty function proposed in this study is a powerful search and design optimization technique for structures with discrete-sized members.