• Title/Summary/Keyword: Mathematical Programming

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Mathematical Optimization Models for Determination of Optimal Vertical Alignment (종단선형설계 최적화 기법에 관한 연구)

  • 강성철;전경수;박영부
    • Journal of Korean Society of Transportation
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    • v.12 no.3
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    • pp.5-13
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    • 1994
  • In the fields of rail and road design, most vertical alignment design have been thus far heavily dependent upon trial-and-errors of experienced engineers. However, it has long been inefficient in productivity of designing process. In order to overcome this inefficiency, this paper presents the optimal vertical alignment design method using mathematical optimization techniques. For optimization, mathematical model to minimize the construction cost is formulated and the separable programming technique and the Zoutendijk method are introduced to solve it. As result, it is shown that this optimization technique can give efficient solutions to all vertical alignment design fields with properly-estimated cost function.

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Parameter Optimization for Runoff Calibration of SWMM (SWMM의 유출량 보정을 위한 매개변수 최적화)

  • Cho, Jae-Heon;Lee, Jong-Ho
    • Journal of Environmental Impact Assessment
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    • v.15 no.6
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    • pp.435-441
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    • 2006
  • For the calibration of rainfall-runoff model, automatic calibration methods are used instead of manual calibration to obtain the reliable modeling results. When mathematical programming techniques such as linear programming and nonlinear programming are applied, there is a possibility to arrive at the local optimum. To solve this problem, genetic algorithm is introduced in this study. It is very simple and easy to understand but also applicable to any complicated mathematical problem, and it can find out the global optimum solution effectively. The objective of this study is to develope a parameter optimization program that integrate a genetic algorithm and a rainfall-runoff model. The program can calibrate the various parameters related to the runoff process automatically. As a rainfall-runoff model, SWMM is applied. The automatic calibration program developed in this study is applied to the Jangcheon watershed flowing into the Youngrang Lake that is in the eutrophic state. Runoff surveys were carried out for two storm events on the Jangcheon watershed. The peak flow and runoff volume estimated by the calibrated model with the survey data shows good agreement with the observed values.

Optimum design of shape and size of truss structures via a new approximation method

  • Ahmadvand, Hosein;Habibi, Alireza
    • Structural Engineering and Mechanics
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    • v.76 no.6
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    • pp.799-821
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    • 2020
  • The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

An Efficient Mixed-Integer Programming Model for Berth Allocation in Bulk Port (벌크항만의 하역 최적화를 위한 정수계획모형)

  • Tae-Sun, Yu;Yushin, Lee;Hyeongon, Park;Do-Hee, Kim;Hye-Rim, Bae
    • Journal of Korea Society of Industrial Information Systems
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    • v.27 no.6
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    • pp.105-114
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    • 2022
  • We examine berth allocation problems in tidal bulk ports with an objective of minimizing the demurrage and dispatch associated berthing cost. In the proposed optimization model inventory (or stock) level constraints are considered so as to satisfy the service level requirements in bulk terminals. It is shown that the mathematical programming formulation of this research provides improved schedule resolution and solution accuracy. We also show that the conventional big-M method of standard resource allocation models can be exempted in tidal bulk ports, and thus the computational efficiency can be significantly improved.

Locomotive Scheduling Using Constraint Satisfaction Problems Programming Technique

  • Hwang, Jong-Gyu;Lee, Jong-Woo;Park, Yong-Jin
    • KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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    • v.4B no.1
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    • pp.29-35
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    • 2004
  • Locomotive scheduling in railway systems experiences many difficulties because of the complex interrelations among resources, knowledge and various constraints. Artificial intelligence technology has been applied to solve these scheduling problems. These technologies have proved to be efficient in representing knowledge and rules for complex scheduling problems. In this paper, we have applied the CSP (Constraints Satisfaction Problems) programming technique, one of the AI techniques, to solve the problems associated with locomotive scheduling. This method is more effective at solving complex scheduling problems than available mathematical programming techniques. The advanced locomotive scheduling system using the CSP programming technique is realized based on the actual timetable of the Saemaul type train on the Kyong-bu line. In this paper, an overview of the CSP programming technique is described, the modeling of domain and constraints is represented and the experimental results are compared with the real-world existing schedule. It is verified that the scheduling results by CSP programming are superior to existing scheduling performed by human experts. The executing time for locomotive scheduling is remarkably reduced to within several decade seconds, something requiring several days in the case of locomotive scheduling by human experts.

Optimal Cognitive System Modeling Using the Stimulus-Response Matrix (자극-반응 행렬을 이용한 인지 시스템 최적화 모델)

  • Choe, Gyeong-Hyeon;Park, Min-Yong;Im, Eun-Yeong
    • Journal of the Ergonomics Society of Korea
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    • v.19 no.1
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    • pp.11-22
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    • 2000
  • In this research report, we are presenting several optimization models for cognitive systems by using stimulus-response matrix (S-R Matrix). Stimulus-response matrices are widely used for tabulating results from various experiments and cognition systems design in which the recognition and confusability of stimuli. This paper is relevant to analyze the optimization/mathematical programming models. The weakness and restrictions of the existing models are resolved by generalization considering average confusion of each subset of stimuli. Also, clustering strategies are used in the extended model to obtain centers of cluster in terms of minimal confusion as well as the character of each cluster.

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Automatic Synthesis of Chemical Processes by a State Space Approach (상태공간 접근법에 의한 화학공정의 자동합성)

  • 최수형
    • Journal of Institute of Control, Robotics and Systems
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    • v.9 no.10
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    • pp.832-835
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    • 2003
  • The objective of this study is to investigate the possibility of chemical process synthesis purely based on mathematical programming when given an objective, feed conditions, product specifications, and model equations for available process units. A method based on a state space approach is proposed, and applied to an example problem with a reactor, a heat exchanger, and a separator. The results indicate that a computer can automatically synthesize an optimal process without any heuristics or expertise in process design provided that global optimization techniques are improved to be suitable for large problems.

Mathematical Programming Approaches to GT Cell Formation: A Comparative Study

  • 원유경
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.2
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    • pp.137-137
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    • 1991
  • This paper compares and evaluates the performances of the two types of mathematical programming models for solving the machine-part cell formation problem in group technology manufacturing : indirect formulation relying on surrogate measure such as similarity coefficient and direct formulation seeking to minimize the number of exceptional elements. New indirect formulation, called the generalized p-median model. is proposed. Unlike existing p-median formulations, proposed formulation includes the classical cell formation problem in which only one process plan exsits for each part as a special case. The proposed new formulation can also deal with the cell formation problem in which alternative process plans exist for a part. The indirect formulation is compared with a new direct formulation which needs much fewer extra variables and constraints than existing direct formulations. Some significant findings from comparative experiment are discussed.

Reverse-Simulation Method for Single Run Simulation Optimization (단일 실행 시뮬레이션 최적화를 위한 Reverse-Simulation 기법)

  • 이영해
    • Journal of the Korea Society for Simulation
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    • v.5 no.2
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    • pp.85-93
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    • 1996
  • Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. This objective is similar to that of optimization problems and thus, mathematical programming techniques may be applied to simulation. However, the application of mathematical programming techniques, e.g., the gradient methods, to simulation is compounded by the random nature of simulation responses and by the complexity of the statistical issues involved. In this paper, therefore, we explain the Reverse-Simulation method to optimize a simulation model in a single simulation run. First, we point the problem of the previous Reverse-Simulation method. Secondly, we propose the new algorithm to solve the previous method and show the efficiency of the proposed algorithm.

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Mathematical Programming Approaches to GT Cell Formation: A Comparative Study

  • 원유경
    • Korean Management Science Review
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    • v.16 no.2
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    • pp.137-147
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    • 1999
  • This paper compares and evaluates the performances of the two types of mathematical programming models for solving the machine-part cell formation problem in group technology manufacturing : indirect formulation relying on surrogate measure such as similarity coefficient and direct formulation seeking to minimize the number of exceptional elements. New indirect formulation, called the generalized {{{{ { p}_{ } }}-median model. is proposed. Unlike existing {{{{ { p}_{ } }}-median formulations, proposed formulation includes the classical cell formation problem in which only one process plan exsits for each part as a special case. The proposed new formulation can also deal with the cell formation problem in which alternative process plans exist for a part. The indirect formulation is compared with a new direct formulation which needs much fewer extra variables and constraints than existing direct formulations. Some significant findings from comparative experiment are discussed.

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