• Title/Summary/Keyword: Constraint Optimization Problem

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Constraint Programming Approach for a Course Timetabling Problem

  • Kim, Chun-Sik;Hwang, Junha
    • Journal of the Korea Society of Computer and Information
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    • v.22 no.9
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    • pp.9-16
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    • 2017
  • The course timetabling problem is a problem assigning a set of subjects to the given classrooms and different timeslots, while satisfying various hard constraints and soft constraints. This problem is defined as a constraint satisfaction optimization problem and is known as an NP-complete problem. Various methods has been proposed such as integer programming, constraint programming and local search methods to solve a variety of course timetabling problems. In this paper, we propose an iterative improvement search method to solve the problem based on constraint programming. First, an initial solution satisfying all the hard constraints is obtained by constraint programming, and then the solution is repeatedly improved using constraint programming again by adding new constraints to improve the quality of the soft constraints. Through experimental results, we confirmed that the proposed method can find far better solutions in a shorter time than the manual method.

Analysis on a Power Transaction with Fuel-Constrained Generations in an Electricity Market (연료제약 발전기를 고려한 전력거래 해석기법 연구)

  • 이광호
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.53 no.8
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    • pp.484-489
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    • 2004
  • When the energy resource available to a particular plant (be it coal, oil, gas, water, or nuclear fuel) is a limiting factor in the operation of the plant, the entire economic dispatch calculation must be done differently. Each economic dispatch calculation must account for what happened before and what will happen in the future. This paper presents a formulation and a solution method for the optimization problem with a fuel constraint in a competitive electricity market. Take-or- Pay (TOP) contract for an energy resource is the typical constraint as a limiting factor. Two approaches are proposed in this paper for modeling the dispatch calculation in a market mechanism. The approaches differ in the subject who considers and inserts the fuel-constraint into its optimization problem. Market operator and each power producer having a TOP contract are assumed as such subjects. The two approaches are compared from the viewpoint of profits. surplus. and social welfare on the basis of Nash Equilibrium.

Efficiency Evaluation of Harmony Search Algorithm according to Constraint Handling Techniques : Application to Optimal Pipe Size Design Problem (제약조건 처리기법에 따른 하모니써치 알고리즘의 효율성 평가 : 관로 최소비용설계 문제의 적용)

  • Yoo, Do Guen;Lee, Ho Min;Lee, Eui Hoon;Kim, Joong Hoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.7
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    • pp.4999-5008
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    • 2015
  • The application of efficient constraint handling technique is fundamental method to find better solutions in engineering optimization problems with constraints. In this research four of constraint handling techniques are used with a meta-heuristic optimization method, harmony search algorithm, and the efficiency of algorithm is evaluated. The sample problem for evaluation of effectiveness is one of the typical discrete problems, optimal pipe size design problem of water distribution system. The result shows the suggested constraint handling technique derives better solutions than classical constraint handling technique with penalty function. Especially, the case of ${\varepsilon}$-constrained method derives solutions with efficiency and stability. This technique is meaningful method for improvement of harmony search algorithm without the need for development of new algorithm. In addition, the applicability of suggested method for large scale engineering optimization problems is verified with application of constraint handling technique to big size problem has over 400 of decision variables.

Optimum Sensitivity of Objective Function Using Equality Constraint (등제한조건을 이용한 목적함수에 대한 최적민감도)

  • Shin Jung-Kyu;Lee Sang-Il;Park Gyung-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.12 s.243
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    • pp.1629-1637
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    • 2005
  • Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

Optimum Sensitivity of Objective Function using Equality Constraint (등제한조건을 이용한 목적함수에 대한 최적민감도)

  • Yi S.I.;Shin J.K.;Park G.J.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2005.10a
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    • pp.464-469
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    • 2005
  • Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

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A Geometry Constraint Handling Technique in Beam Stiffener Layout Optimization Problem (보 보강재 배치 최적화 문제에서의 기하구속조건 처리기법)

  • 이준호;박영진;박윤식
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.05a
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    • pp.870-875
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    • 2004
  • Beam stiffeners have frequently been used for raising natural frequencies of base structures. In stiffener layout optimization problems, most of the previous researches considering the position and/or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle. The reason is concave shape structures have difficulties ill formulating geometry constraints. In this paper, a new geometry constraint handling technique, which can define both convex and concave feasible lesions and measure a degree of geometry constraint violation, is proposed. Evolution strategies (ESs) is utilized as an optimization tool. In addition, the constraint-handling technique of EVOSLINOC (EVOlution Strategy for scalar optimization with Lineal and Nonlinear Constraints) is utilized to solve constrained optimization problems. From a numerical example, the proposed geometry constraint handling technique is verified and proves that the technique can easily be applied to structures in net only convex but also concave shapes, even with a protrusion or interior holes.

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Integer Programming-based Local Search Technique for Linear Constraint Satisfaction Optimization Problem (선형 제약 만족 최적화 문제를 위한 정수계획법 기반 지역 탐색 기법)

  • Hwang, Jun-Ha;Kim, Sung-Young
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.9
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    • pp.47-55
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    • 2010
  • Linear constraint satisfaction optimization problem is a kind of combinatorial optimization problem involving linearly expressed objective function and complex constraints. Integer programming is known as a very effective technique for such problem but require very much time and memory until finding a suboptimal solution. In this paper, we propose a method to improve the search performance by integrating local search and integer programming. Basically, simple hill-climbing search, which is the simplest form of local search, is used to solve the given problem and integer programming is applied to generate a neighbor solution. In addition, constraint programming is used to generate an initial solution. Through the experimental results using N-Queens maximization problems, we confirmed that the proposed method can produce far better solutions than any other search methods.

A Constraint Programming-based Automated Course Timetabling System

  • Hwang, Junha
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.4
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    • pp.27-34
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    • 2019
  • The course timetabling problem is a kind of very complex combinatorial optimization problems, which is known as an NP-complete problem. Sometimes a given course timetabling problem can be accompanied by many constraints. At this time, even if only one constraint is violated, it can be an infeasible timetable. Therefore, it is very difficult to make an automated course timetabling system for a complex real-world course timetabling problem. This paper introduces an automated course timetabling system using constraint programming. The target problem has 26 constraints in total, and they are expressed as 24 constraints and an objective function in constraint programming. Currently, we are making a timetable through this system and applying the result to the actual class. Members' satisfaction is also much higher than manual results. We expect this paper can be a guide for making an automated course timetabling system.

Group Power Constraint Based Wi-Fi Access Point Optimization for Indoor Positioning

  • Pu, Qiaolin;Zhou, Mu;Zhang, Fawen;Tian, Zengshan
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.5
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    • pp.1951-1972
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    • 2018
  • Wi-Fi Access Point (AP) optimization approaches are used in indoor positioning systems for signal coverage enhancement, as well as positioning precision improvement. Although the huge power consumption of the AP optimization forms a serious problem due to the signal coverage requirement for large-scale indoor environment, the conventional approaches treat the problem of power consumption independent from the design of indoor positioning systems. This paper proposes a new Fast Water-filling algorithm Group Power Constraint (FWA-GPC) based Wi-Fi AP optimization approach for indoor positioning in which the power consumed by the AP optimization is significantly considered. This paper has three contributions. First, it is not restricted to conventional concept of one AP for one candidate AP location, but considered spare APs once the active APs break off. Second, it utilizes the concept of water-filling model from adaptive channel power allocation to calculate the number of APs for each candidate AP location by maximizing the location fingerprint discrimination. Third, it uses a fast version, namely Fast Water-filling algorithm, to search for the optimal solution efficiently. The experimental results conducted in two typical indoor Wi-Fi environments prove that the proposed FWA-GPC performs better than the conventional AP optimization approaches.

Optimization of Computer Network with a Cost Constraint (비용 제약을 갖는 컴퓨터 네트워크의 최적화)

  • Lee, Han-Jin;Yum, Chang-Sun
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.30 no.1
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    • pp.82-88
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    • 2007
  • This paper considers a topological optimization of a computer network design with a cost constraint. The objective is to find the topological layout of links, at maximal reliability, under the constraint that the network cost is less or equal than a given level of budget. This problem is known to be NP-hard. To efficiently solve the problem, a genetic approach is proposed. Two illustrative examples are used to explain and test the proposed approach. Experimental results show evidence that the proposed approach performs more efficiently for finding a good solution or near optimal solution in comparison with a simulated annealing method.