• Title, Summary, Keyword: discrete optimization

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Optimization of Frame Structures with Natural Frequency Constraints (고유진동수 제약조건을 고려한 프레임 구조물의 최적화)

  • Kim, Bong-Ik;Lee, Seong-Dae
    • Journal of Ocean Engineering and Technology
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    • v.24 no.6
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    • pp.109-113
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    • 2010
  • We present the minimum weight optimum design of cross sectional for frame structures subject to natural frequency. The optimum design in this paper employ discrete and continuous design variables and Genetic Algorithms. In this paper, Genetic Algorithms is used in optimization process, and be used the method of Elitism and penalty parameters in order to improved fitness in the reproduction process. For 1-Bay 2-Story frame structure, in examples, continuous and discrete design variables are used, and W-section (No.1~No.64), from AISC, discrete data are used in discrete optimization. In this case, Exhaustive search are used for finding global optimum. Continuous variables are used for 1-Bay 7-Story frame structure. Two typical frame structure optimization examples are employed to demonstrate the availability of Genetic Algorithms for solving minimum weight optimum of frame structures with fundamental and multi frequency.

Performance Comparison of Discrete Particle Swarm Optimizations in Sequencing Problems (순서화 문제에서 01산적 Particle Swarm Optimization들의 성능 비교)

  • Yim, D.S.
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.33 no.4
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    • pp.58-68
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    • 2010
  • Particle Swarm Optimization (PSO) which has been well known to solve continuous problems can be applied to discrete combinatorial problems. Several DPSO (Discrete Particle Swarm Optimization) algorithms have been proposed to solve discrete problems such as traveling salesman, vehicle routing, and flow shop scheduling problems. They are different in representation of position and velocity vectors, operation mechanisms for updating vectors. In this paper, the performance of 5 DPSOs is analyzed by applying to traditional Traveling Salesman Problems. The experiment shows that DPSOs are comparable or superior to a genetic algorithm (GA). Also, hybrid PSO combined with local optimization (i.e., 2-OPT) provides much improved solutions. Since DPSO requires more computation time compared with GA, however, the performance of hybrid DPSO is not better than hybrid GA.

Local Solution of Sequential Algorithm Using Orthogonal Arrays in Discrete Design Space (이산설계공간에서 직교배열표를 이용한 순차적 알고리듬의 국부해)

  • Yi, Jeong-Wook;Park, Gyung-Jin
    • Proceedings of the KSME Conference
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    • pp.1005-1010
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    • 2004
  • The structural optimization has been carried out in the continuous design space or in the discrete design space. Generally, available designs are discrete in design practice. But methods for discrete variables are extremely expensive in computational cost. In order to overcome this weakness, an iterative optimization algorithm was proposed for design in the discrete space, which is called as a sequential algorithm using orthogonal arrays (SOA). We focus to verify the fact that the local solution can be obtained throughout the optimization with this algorithm. The local solution is defined in discrete design space. Then the search space, which is the set of candidate values of each design variables formed by the neighborhood of current design point, is defined. It is verified that a local solution can be founded by moving sequentially the search space. The SOA algorithm has been applied to problems such as truss type structures. Then it is confirmed that a local solution can be obtained using the SOA algorithm

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Discrete Optimization of Unsymmetric Composite Laminates Using Linear Aproximation Method (선형 근사화방법을 이용한 비대칭 복합 적층평판의 이산최적화)

  • 이상근;구봉근;한상훈
    • Computational Structural Engineering
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    • v.10 no.2
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    • pp.255-263
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    • 1997
  • The optimum design of most structural systems used in practice requires considering design variables as discrete quantities. The present paper shows that the linear approximation method is very effective as a tool for the discrete optimum designs of unsymmetric composite laminates. The formulated design problem is subjected to a multiple in-plane loading condition due to shear and axial forces, bending and twisting moments, which is controlled by maximum strain criterion for each of the plys of a composite laminate. As an initial approach, the process of continuous variable optimization by FDM is required only once in operating discrete optimization. The nonlinear discrete optimization problem that has the discrete and continuous variables is transformed into the mixed integer programming problem by SLDP. In numerical examples, the discrete optimum solutions for the unsymmetric composite laminates consisted of six plys according to rotated stacking sequence were found, and then compared the results with the nonlinear branch and bound method to verify the efficiency of present method.

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Genetic-Based Combinatorial Optimization Method for Design of Rolling Element Bearing (구름 베어링 설계를 위한 유전 알고리듬 기반 조합형 최적설계 방법)

  • 윤기찬;최동훈;박창남
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • pp.166-171
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    • 2001
  • In order to improve the efficiency of the design process and the quality of the resulting design for the application-based exclusive rolling element bearings, this study propose design methodologies by using a genetic-based combinatorial optimization. By the presence of discrete variables such as the number of rolling element (standard component) and by the engineering point of views, the design problem of the rolling element bearing can be characterized by the combinatorial optimization problem as a fully discrete optimization. A genetic algorithm is used to efficiently find a set of the optimum discrete design values from the pre-defined variable sets. To effectively deal with the design constraints and the multi-objective problem, a ranking penalty method is suggested for constructing a fitness function in the genetic-based combinatorial optimization. To evaluate the proposed design method, a robust performance analyzer of ball bearing based on quasi-static analysis is developed and the computer program is applied to some design problems, 1) maximize fatigue life, 2) maximize stiffness, 3) maximize fatigue life and stiffness, of a angular contact ball bearing. Optimum design results are demonstrate the effectiveness of the design method suggested in this study. It believed that the proposed methodologies can be effectively applied to other multi-objective discrete optimization problems.

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Optimum Design of Two-Dimensional Steel Structures Using Genetic Algorithms (유전자 알고리즘을 이용한 2차원 강구조물의 최적설계)

  • Kim, Bong-Ik;Kwon, Jung-Hyun
    • Journal of Ocean Engineering and Technology
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    • v.21 no.2
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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.

Discrete Sizing Design of Truss Structure Using an Approximate Model and Post-Processing (근사모델과 후처리를 이용한 트러스 구조물의 이산 치수설계)

  • Lee, Kwon-Hee
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.19 no.5
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    • pp.27-37
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    • 2020
  • Structural optimization problems with discrete design variables require more function calculations (or finite element analyses) than those in the continuous design space. In this study, a method to find an optimal solution in the discrete design of the truss structure is presented, reducing the number of function calculations. Because a continuous optimal solution is the Karush-Kuhn-Tucker point that satisfies the optimality condition, it is assumed that the discrete optimal solution is around the continuous optimum. Then, response values such as weight, displacement, and stress are predicted using approximate models-referred to as hybrid metamodels-within specified design ranges. The discrete design method using the hybrid metamodels is used as a post-process of the continuous optimization process. Standard truss design problems of 10-bar, 25-bar, 15-bar, and 52-bar are solved to show the usefulness of this method. The results are compared with those of existing methods.

Generalized evolutionary optimum design of fiber-reinforced tire belt structure

  • Cho, J.R.;Lee, J.H.;Kim, K.W.;Lee, S.B.
    • Steel and Composite Structures
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    • v.15 no.4
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    • pp.451-466
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    • 2013
  • This paper deals with the multi-objective optimization of tire reinforcement structures such as the tread belt and the carcass path. The multi-objective functions are defined in terms of the discrete-type design variables and approximated by artificial neutral network, and the sensitivity analyses of these functions are replaced with the iterative genetic evolution. The multi-objective optimization algorithm introduced in this paper is not only highly CPU-time-efficient but it can also be applicable to other multi-objective optimization problems in which the objective function, the design variables and the constraints are not continuous but discrete. Through the illustrative numerical experiments, the fiber-reinforced tire belt structure is optimally tailored. The proposed multi-objective optimization algorithm is not limited to the tire reinforcement structure, but it can be applicable to the generalized multi-objective structural optimization problems in various engineering applications.

Phasor Discrete Particle Swarm Optimization Algorithm to Configure Community Energy Systems (구역전기사업자 구성을 위한 Phasor Discrete Particle Swarm Optimization 알고리즘)

  • Bae, In-Su;Kim, Jin-O
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.23 no.9
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    • pp.55-61
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    • 2009
  • This paper presents a modified Phasor Discrete Particle Swarm Optimization (PDPSO) algorithm to configure Community Energy Systems(CESs) in the distribution system. The CES obtains electric power from its own Distributed Generations(DGs) and purchases insufficient power from the competitive power market, to supply power for customers contracted with the CES. When there are two or more CESs in a network, the CESs will continue the competitive expansion to reduce the total operation cost. The particles of the proposed PDPSO algorithm have magnitude and phase angle values, and move within a circle area. In the case study, the results by PDPSO algorithm was compared with that by the conventional DPSO algorithm.

Development of an Optimization Algorithm Using Orthogonal Arrays in Discrete Design Space (직교배열표를 이용한 이산공간에서의 최적화 알고리듬 개발)

  • Lee, Jeong-Uk;Park, Jun-Seong;Lee, Gwon-Hui;Park, Gyeong-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.10
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    • pp.1621-1626
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    • 2001
  • The structural optimization have been carried out in the continuous design space or in the discrete design space. Methods fur discrete variables such as genetic algorithms , are extremely expensive in computational cost. In this research, an iterative optimization algorithm using orthogonal arrays is developed for design in discrete space. An orthogonal array is selected on a discrete des inn space and levels are selected from candidate values. Matrix experiments with the orthogonal array are conducted. New results of matrix experiments are obtained with penalty functions leer constraints. A new design is determined from analysis of means(ANOM). An orthogonal array is defined around the new values and matrix experiments are conducted. The final optimum design is found from iterative process. The suggested algorithm has been applied to various problems such as truss and frame type structures. The results are compared with those from a genetic algorithm and discussed.