• Title/Summary/Keyword: Problem Solution

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Tikhonov's Solution of Unstable Axisymmetric Initial Value Problem of Wave Propagation: Deteriorated Noisy Measurement Data

  • Jang, Taek-Soo;Han, So-Lyoung
    • Journal of Ocean Engineering and Technology
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    • v.22 no.4
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    • pp.1-7
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    • 2008
  • The primary aim of the paper is to solve an unstable axisymmetric initial value problem of wave propagation when given initial data that is deteriorated by noise such as measurement error. To overcome the instability of the problem, Tikhonov's regularization, known as a non-iterative numerical regularization method, is introduced to solve the problem. The L-curvecriterion is introduced to find the optimal regularization parameter for the solution. It is confirmed that fairly stable solutions are realized and that they are accurate when compared to the exact solution.

A Study on the Job Shop Scheduling Using CSP and SA (CSP와 SA를 이용한 Job Shop 일정계획에 관한 연구)

  • 윤종준;손정수;이화기
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.23 no.61
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    • pp.105-114
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    • 2000
  • Job Shop Problem which consists of the m different machines and n jobs is a NP-hard problem of the combinatorial optimization. Each job consists of a chain of operations, each of which needs to be processed during an uninterrupted time period of a given length on a given machine. Each machine can process at most one operation at a time. The purpose of this paper is to develop the heuristic method to solve large scale scheduling problem using Constraint Satisfaction Problem method and Simulated Annealing. The proposed heuristic method consists of the search algorithm and optimization algorithm. The search algorithm is to find the solution in the solution space using CSP concept such as backtracking and domain reduction. The optimization algorithm is to search the optimal solution using SA. This method is applied to MT06, MT10 and MT20 Job Shop Problem, and compared with other heuristic method.

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APPLICATION OF THE CONSTRAINT SATISFACTION APPROACH TO GENERAL LAYOUT PROBLEMS (일반 배치문제 해결을 위한 제약만족기법의 적용)

  • Park, Sung-Joon;Jung, Eui-S.
    • Journal of Korean Institute of Industrial Engineers
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    • v.24 no.4
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    • pp.539-550
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    • 1998
  • A computerized layout system based on a constraint satisfaction problem (CSP) technique was developed to treat both facility layout and instrument panel layout problems. This layout system attempts to allocate various facilities under multiple layout criteria including qualitative design objectives. Since most of the design objectives can be understood as constraints which the layout solution must satisfy to improve the goodness of the solution, a CSP technique was employed to solve the multi-constraints layout problem. The effectiveness of the system was evaluated by the comparison with the well-known facility layout program, CORELAP. Furthermore, the proposed system can also be applied to the instrument panel layout problem successfully. Several user-centered guidelines were well reflected on the solution obtained. CONSLAY, the prototype layout system being developed in the research, greatly enhanced the interactions with the designer so as to deal with the problem-dependent nature of the layout problem and to properly reflect the domain-specific knowledge of the designer.

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APPLYING ELITIST GENETIC ALGORITHM TO RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM

  • Jin-Lee Kim;Ok-Kyue Kim
    • International conference on construction engineering and project management
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    • 2007.03a
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    • pp.739-748
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    • 2007
  • The objective of this research study is to develop the permutation-based genetic algorithm for solving the resource-constrained project scheduling problem in construction engineering by incorporating elitism into genetic algorithm. A key aspect of the algorithm was the development of the elitist roulette selection operator to preserve the best individual solution for the next generation so the improved solution can be obtained. Another notable characteristic is the application of the parallel schedule generation scheme to generate a feasible solution to the problem. Case studies with a standard test problem were presented to demonstrate the performance and accuracy of the algorithm. The computational results indicate that the proposed algorithm produces reasonably good solutions for the resource-constrained project scheduling problem.

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ITERATIVE ALGORITHMS FOR THE LEAST-SQUARES SYMMETRIC SOLUTION OF AXB = C WITH A SUBMATRIX CONSTRAINT

  • Wang, Minghui;Feng, Yan
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.1-12
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    • 2009
  • Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.

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A Study on the Generation of Capillary Waves on Steep Gravity Waves

  • Lee, Seung-Joon
    • Journal of Ship and Ocean Technology
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    • v.4 no.4
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    • pp.45-55
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    • 2000
  • A formal solution method using the complex analysis is given for the problems derived by Longuet-Higgins(1963). The same method is applied to a new perturbation problem of higher approximation. Interpretation of its solution made it possible to confirm that the rough agree-ment of Longuet-Higgins\`s prediction with experimental data of Cox(1958) was mainly due to the fact that the gravity effect in the perturbation problem was neglected for the case when the basic gravity wave not sufficiently steep.

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Eigenfunction expansion solution and finite element solution for orthotropic hollow cylinder under sinusoidal impact load

  • Wang, X.;Dai, H.L.
    • Structural Engineering and Mechanics
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    • v.16 no.1
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    • pp.35-46
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    • 2003
  • The histories and distributions of dynamic stresses in an orthotropic hollow cylinder under sinusoidal impact load are obtained by making use of eigenfunction expansion method in this paper. Dynamic equations for axially symmetric orthotropic problem are founded and results are carried out for a practical example in which an orthotropic hollow cylinder is in initially at rest and subjected to a dynamic interior pressure $p(t)=-{\sigma}_0(sin{\alpha}t+1)$. The features of the solution appear the propagation of the cylindrical waves. The other hand, a dynamic finite element solution for the same problem is also got by making use of structural software (ABAQUS) program. Comparing theoretical solution with finite element solution, it can be found that two kinds of results obtained by two different solving methods are suitably approached. Thus, it is further concluded that the method and computing process of the theoretical solution are effective and accurate.

How Does Problem Epistasis Affect the performance of Genetic Algorithm? (문제 상위는 유전 알고리즘의 성능에 어떤 영향을 미치는가?)

  • Yu, Dong-Pil;Kim, Yong-Hyuk
    • Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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    • v.8 no.4
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    • pp.251-258
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    • 2018
  • In mathematics and computer science, an optimization problem is the problem of finding the best solution from feasible ones. In the context of genetic algorithm, the difficulty of an optimization problem can be explained in terms of problem epistasis. In biology, epistasis means that the phenotype of a gene is suppressed by one or more genes, but in an evolutionary algorithm it means the interaction between genes. In this paper, we experimentally show that problem epistasis and the performance of genetic algorithm are closely related. We compared problem epistasis (One-Max, Royal Road, and NK-Landscape) using a framework that quantifies problem epistasis based on Shannon's information theory, and could show that problem becomes more difficult as problem epistasis grows. In the case that a genetic algorithm finds the optimal solution, performance is compared through the number of generations, otherwise through the ratio of the fitness of the optimal solution to that of the best solution.

Solving the Travelling Salesman Problem Using an Ant Colony System Algorithm

  • Zakir Hussain Ahmed;Majid Yousefikhoshbakht;Abdul Khader Jilani Saudagar;Shakir Khan
    • International Journal of Computer Science & Network Security
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    • v.23 no.2
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    • pp.55-64
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    • 2023
  • The travelling salesman problem (TSP) is an important combinatorial optimization problem that is used in several engineering science branches and has drawn interest to several researchers and scientists. In this problem, a salesman from an arbitrary node, called the warehouse, starts moving and returns to the warehouse after visiting n clients, given that each client is visited only once. The objective in this problem is to find the route with the least cost to the salesman. In this study, a meta-based ant colony system algorithm (ACSA) is suggested to find solution to the TSP that does not use local pheromone update. This algorithm uses the global pheromone update and new heuristic information. Further, pheromone evaporation coefficients are used in search space of the problem as diversification. This modification allows the algorithm to escape local optimization points as much as possible. In addition, 3-opt local search is used as an intensification mechanism for more quality. The effectiveness of the suggested algorithm is assessed on a several standard problem instances. The results show the power of the suggested algorithm which could find quality solutions with a small gap, between obtained solution and optimal solution, of 1%. Additionally, the results in contrast with other algorithms show the appropriate quality of competitiveness of our proposed ACSA.

The Optimal Algorithm for Assignment Problem (할당 문제의 최적 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.17 no.9
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    • pp.139-147
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    • 2012
  • This paper suggests simple search algorithm for optimal solution in assignment problem. Generally, the optimal solution of assignment problem can be obtained by Hungarian algorithm. The proposed algorithm reduces the 4 steps of Hungarian algorithm to 1 step, and only selects the minimum cost of row and column then gets the optimal solution simply. For the 27 balanced and 7 unbalanced assignment problems, this algorithm finds the optimal solution but the genetic algorithm fails to find this values. This algorithm improves the time complexity O($n^3$) of Hungarian algorithm to O(n). Therefore, the proposed algorithm can be general algorithm for assignment problem replace Hungarian algorithm.