• Title/Summary/Keyword: global optimal solution

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A study on the structure evolution of neural networks using genetic algorithms (유전자 알고리즘을 이용한 신경회로망의 구조 진화에 관한 연구)

  • 김대준;이상환;심귀보
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.223-226
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    • 1997
  • Usually, the Evolutionary Algorithms(EAs) are considered more efficient for optimal, system design because EAs can provide higher opportunity for obtaining the global optimal solution. This paper presents a mechanism of co-evolution consists of the two genetic algorithms(GAs). This mechanism includes host populations and parasite populations. These two populations are closely related to each other, and the parasite populations plays an important role of searching for useful schema in host populations. Host population represented by feedforward neural network and the result of co-evolution we will find the optimal structure of the neural network. We used the genetic algorithm that search the structure of the feedforward neural network, and evolution strategies which train the weight of neuron, and optimize the net structure. The validity and effectiveness of the proposed method is exemplified on the stabilization and position control of the inverted-pendulum system.

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Optimal Control by the Gradient Method (경사법에의한 최적제어)

  • 양흥석;황희융
    • 전기의세계
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    • v.21 no.3
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    • pp.48-52
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    • 1972
  • The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

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Search Method for Optimal Valve Setting and Location to Reduce Leakage in Water Distribution Networks (배수관망시스템 누수저감을 위한 최적 밸브제어 및 위치탐색 모델 개발)

  • Choi, Jong Sub;Kala, Vairavamoorthy;Ahn, Hyo Won
    • Journal of Korean Society of Water and Wastewater
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    • v.22 no.1
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    • pp.149-157
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    • 2008
  • The reduction of leakage is a major issue of the South Korea water industry. The inclusion of pressure dependent leakage terms in network analysis allows the application of optimization techniques to identify the most effective means of reducing water leakage in distribution networks. This paper proposes a method to find optimal setting and location of control valve for reducing leakage efficiently. The proposed search method differs from previous methods for addressing optimal valve location problem and improves the GA simulation time with guaranteeing for getting the global optimal solution. The strength of this method has been demonstrated by means of case studies. This allows the procedure of optimization to be more robust and computational efficient.

A Validation Method for Solution of Nonlinear Differential Equations: Construction of Exact Solutions Neighboring Approximate Solutions

  • Lee, Sang-Chul
    • International Journal of Aeronautical and Space Sciences
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    • v.3 no.2
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    • pp.46-58
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    • 2002
  • An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

Stochastic Optimization Approach for Parallel Expansion of the Existing Water Distribution Systems (추계학적 최적화방법에 의한 기존관수로시스템의 병열관로 확장)

  • Ahn, Tae-Jin;Choi, Gye-Woon;Park, Jung-Eung
    • Water for future
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    • v.28 no.2
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    • pp.169-180
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    • 1995
  • The cost of a looped pipe network is affected by a set of loop flows. The mathematical model for optimizing the looped pipe network is expressed in the optimal set of loop flows to apply to a stochastic optimization method. Because the feasible region of the looped pipe network problem is nonconvex with multiple local optima, the Modified Stochastic Probing Method is suggested to efficiently search the feasible region. The method consists of two phase: i) a global search phase(the stochastic probing method) and ii) a local search phase(the nearest neighbor method). While the global search sequentially improves a local minimum, the local search escapes out of a local minimum trapped in the global search phase and also refines a final solution. In order to test the method, a standard test problem from the literature is considered for the optimal design of the paralled expansion of an existing network. The optimal solutions thus found have significantly smaller costs than the ones reported previously by other researchers.

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Improvement of Ant Colony Optimization Algorithm to Solve Traveling Salesman Problem (순회 판매원 문제 해결을 위한 개미집단 최적화 알고리즘 개선)

  • Jang, Juyoung;Kim, Minje;Lee, Jonghwan
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.42 no.3
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    • pp.1-7
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    • 2019
  • It is one of the known methods to obtain the optimal solution using the Ant Colony Optimization Algorithm for the Traveling Salesman Problem (TSP), which is a combination optimization problem. In this paper, we solve the TSP problem by proposing an improved new ant colony optimization algorithm that combines genetic algorithm mutations in existing ant colony optimization algorithms to solve TSP problems in many cities. The new ant colony optimization algorithm provides the opportunity to move easily fall on the issue of developing local optimum values of the existing ant colony optimization algorithm to global optimum value through a new path through mutation. The new path will update the pheromone through an ant colony optimization algorithm. The renewed new pheromone serves to derive the global optimal value from what could have fallen to the local optimal value. Experimental results show that the existing algorithms and the new algorithms are superior to those of existing algorithms in the search for optimum values of newly improved algorithms.

Hybrid Simulated Annealing for Data Clustering (데이터 클러스터링을 위한 혼합 시뮬레이티드 어닐링)

  • Kim, Sung-Soo;Baek, Jun-Young;Kang, Beom-Soo
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.40 no.2
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    • pp.92-98
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    • 2017
  • Data clustering determines a group of patterns using similarity measure in a dataset and is one of the most important and difficult technique in data mining. Clustering can be formally considered as a particular kind of NP-hard grouping problem. K-means algorithm which is popular and efficient, is sensitive for initialization and has the possibility to be stuck in local optimum because of hill climbing clustering method. This method is also not computationally feasible in practice, especially for large datasets and large number of clusters. Therefore, we need a robust and efficient clustering algorithm to find the global optimum (not local optimum) especially when much data is collected from many IoT (Internet of Things) devices in these days. The objective of this paper is to propose new Hybrid Simulated Annealing (HSA) which is combined simulated annealing with K-means for non-hierarchical clustering of big data. Simulated annealing (SA) is useful for diversified search in large search space and K-means is useful for converged search in predetermined search space. Our proposed method can balance the intensification and diversification to find the global optimal solution in big data clustering. The performance of HSA is validated using Iris, Wine, Glass, and Vowel UCI machine learning repository datasets comparing to previous studies by experiment and analysis. Our proposed KSAK (K-means+SA+K-means) and SAK (SA+K-means) are better than KSA(K-means+SA), SA, and K-means in our simulations. Our method has significantly improved accuracy and efficiency to find the global optimal data clustering solution for complex, real time, and costly data mining process.

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.

Reinforcement Learning using Propagation of Goal-State-Value (목표상태 값 전파를 이용한 강화 학습)

  • Kim, Byeong-Cheon;Yun, Byeong-Ju
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.5
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    • pp.1303-1311
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    • 1999
  • In order to learn in dynamic environments, reinforcement learning algorithms like Q-learning, TD(0)-learning, TD(λ)-learning have been proposed. however, most of them have a drawback of very slow learning because the reinforcement value is given when they reach their goal state. In this thesis, we have proposed a reinforcement learning method that can approximate fast to the goal state in maze environments. The proposed reinforcement learning method is separated into global learning and local learning, and then it executes learning. Global learning is a learning that uses the replacing eligibility trace method to search the goal state. In local learning, it propagates the goal state value that has been searched through global learning to neighboring sates, and then searches goal state in neighboring states. we can show through experiments that the reinforcement learning method proposed in this thesis can find out an optimal solution faster than other reinforcement learning methods like Q-learning, TD(o)learning and TD(λ)-learning.

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Design of Optimal Controller for TS Fuzzy Models and Its Application to Nonlinear Systems (TS 퍼지 모델을 이용한 최적 제어기 설계 및 비선형 시스템에서의 응용)

  • Chang, Wook;Joo, Young-Hoon;Park, Jin-Bae
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.49 no.2
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    • pp.68-73
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    • 2000
  • This paper addresses the analysis and design of fuzzy control systems for a class of complex nonlinear systems. Firstly, the nonlinear system is represented by Takagi-Sugeno(TS) fuzzy model and the global controller is constructed by compensating each linear model in the rule of TS fuzzy model. The design of conventional TS fuzzy-model-based controller is composed of two processes. One is to determine the static state feedback gain of each local model and the other is to validate the stability of the designed fuzzy controller. In this paper, we propose an alternative methods for the design of TS fuzzy-model-based controller. The design scheme is based on the extension of conventional optimal control theory to the design of TS fuzzy-model-based controller. By using the proposed method, the design and stability analysis of the TS fuzzy model-based controller is reduced to the problem of finding the solution of a set of algebraic Riccati equations. And we use the recently developed interior point method to find the solution of AREs, where AREs are recast as the LMI formulation. A numerical simulation example is given to show the effectiveness and feasibiltiy of the proposed fuzzy controller design method.

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