• Title/Summary/Keyword: local optimal solution

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Optimal Solution of a Large-scale Travelling Salesman Problem applying DNN and k-opt (DNN과 k-opt를 적용한 대규모 외판원 문제의 최적 해법)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.4
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    • pp.249-257
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    • 2015
  • This paper introduces a heuristic algorithm to NP-hard travelling salesman problem. The proposed algorithm, in its bid to determine initial path, applies SW-DNN, DW-DNN, and DC-DNN, which are modified forms of the prevalent Double-sided Nearest Neighbor Search and searches the minimum value. As a part of its optimization process on the initial solution, it employs 2, 2.5, 3-opt of a local search k-opt on candidate delete edges and 4-opt on undeleted ones among them. When tested on TSP-1 of 26 European cities and TSP-2 of 49 U.S. cities, the proposed algorithm has successfully obtained optimal results in both, disproving the prevalent disbelief in the attainability of the optimal solution and making itself available as a general algorithm for the travelling salesman problem.

A Genetic Algorithm Approach to the Continuous Network Design Problem with Variational Inequality Constraints (유전자 알고리즘을 이용한 변동부등식 제약하의 연속형 가로망 설계)

  • 김재영;임강원
    • Journal of Korean Society of Transportation
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    • v.18 no.1
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    • pp.61-73
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    • 2000
  • The equilibrium network design problem can be formulated as a mathematical Program with variational inequality constraints. We know this problem may have may multiple local solutions due to its inherent characteristics - Nonlinear Objective function and Nonlinear, Nonconvex constraints. Hence, it is difficult to solve for a globally optimal solution. In this paper, we propose a genetic algorithm to obtain a globa1 optimum among many local optima. A Proposed a1gorithm is compared with 4 different solution algorithms for 1 small test network and 1 real-size network. The results of some computational testing are reported.

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A Study on the Optimization Method using the Genetic Algorithm with Sensitivity Analysis (민감도가 고려된 알고리듬을 이용한 최적화 방법에 관한 연구)

  • Lee, Jae-Gwan;Sin, Hyo-Cheol
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.6 s.177
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    • pp.1529-1539
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    • 2000
  • A newly developed optimization method which uses the genetic algorithm combined with the sensitivity analysis is presented in this paper. The genetic algorithm is a probabilistic method, searching the optimum at several points simultaneously, requiring only the values of the object and constraint functions. It has therefore more chances to find global solution and can be applied various problems. Nevertheless, it has such shortcomings that even it approaches the optimum rapidly in the early stage, it slows down afterward and it can't consider the constraints explicitly. It is only because it can't search the local area near the current points. The traditional method, on the other hand, using sensitivity analysis is of great advantage in searching the near optimum. Thus the combination of the two techniques makes use of the individual advantages, that is, the superiority both in global searching by the genetic algorithm and in local searching by the sensitivity analysis. Application of the method to the several test functions verifies that the method suggested is very efficient and powerful to find the global solutions, and that the constraints can be considered properly.

A Study on the Support location Optimizations of the Beams using the Genetic Algorithm and the Sensitivity Analysis. (민감도가 고려된 유전 알고리듬을 이용한 보 구조물의 지지점 최적화에 관한 연구)

  • 이재관;신효철
    • Journal of KSNVE
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    • v.10 no.5
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    • pp.783-791
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    • 2000
  • This describes a study on the support location optimizations of the beams using the genetic algorithm and the sensitivity analysis. The genetic algorithm is a probabilistic method searching the optimum at several points simultaneously and requiring only the values of the object and constraint functions. It has therefore more chances to find the global solution and can be applied to the various problems. Nevertheless, it has such a shortcoming that it takes too many calculations, because it is ineffective in local search. While the traditional method using sensitivity analysis is of great advantage in searching the near optimum. thus the combination of the two techniques will make use of the individual advantages, that is, the superiority in global searching form the genetic algorithm and that in local searching form the sensitivity analysis. In this thesis, for the practical applications, the analysis is conducted by FEB ; and as the shapes of structures are taken as the design variation, it requires re-meshing for every analysis. So if it is not properly controlled, the result of the analysis is affected and the optimized solution amy not be the real one. the method is efficiently applied to the problems which the traditional methods are not working properly.

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Optimization of the Travelling Salesman Problem Using a New Hybrid Genetic Algorithm

  • Zakir Hussain Ahmed;Furat Fahad Altukhaim;Abdul Khader Jilani Saudagar;Shakir Khan
    • International Journal of Computer Science & Network Security
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    • v.24 no.3
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    • pp.12-22
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    • 2024
  • The travelling salesman problem is very famous and very difficult combinatorial optimization problem that has several applications in operations research, computer science and industrial engineering. As the problem is difficult, finding its optimal solution is computationally very difficult. Thus, several researchers have developed heuristic/metaheuristic algorithms for finding heuristic solutions to the problem instances. In this present study, a new hybrid genetic algorithm (HGA) is suggested to find heuristic solution to the problem. In our HGA we used comprehensive sequential constructive crossover, adaptive mutation, 2-opt search and a new local search algorithm along with a replacement method, then executed our HGA on some standard TSPLIB problem instances, and finally, we compared our HGA with simple genetic algorithm and an existing state-of-the-art method. The experimental studies show the effectiveness of our proposed HGA for the problem.

PC Cluster Based Parallel Genetic Algorithm-Tabu Search for Service Restoration of Distribution Systems (PC 클러스터 기반 병렬 유전 알고리즘-타부 탐색을 이용한 배전계통 고장 복구)

  • Mun Kyeong-Jun;Lee Hwa-Seok;Park June Ho
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.54 no.8
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    • pp.375-387
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    • 2005
  • This paper presents an application of parallel Genetic Algorithm-Tabu Search (GA-TS) algorithm to search an optimal solution of a service restoration in distribution systems. The main objective of service restoration of distribution systems is, when a fault or overload occurs, to restore as much load as possible by transferring the do-energized load in the out of service area via network reconfiguration to the appropriate adjacent feeders at minimum operational cost without violating operating constraints, which is a combinatorial optimization problem. This problem has many constraints with many local minima to solve the optimal switch position. This paper develops parallel GA-TS algorithm for service restoration of distribution systems. In parallel GA-TS, GA operators are executed for each processor. To prevent solutions of low fitness from appearing in the next generation, strings below the average fitness are saved in the tabu list. If best fitness of the GA is not changed for several generations, TS operators are executed for the upper $10\%$ of the population to enhance the local searching capabilities. With migration operation, best string of each node is transferred to the neighboring node after predetermined iterations are executed. For parallel computing, we developed a PC cluster system consists of 8 PCs. Each PC employs the 2 GHz Pentium IV CPU and is connected with others through ethernet switch based fast ethernet. To show the validity of the proposed method, proposed algorithm has been tested with a practical distribution system in Korea. From the simulation results, we can find that the proposed algorithm is efficient for the distribution system service restoration in terms of the solution quality, speedup, efficiency and computation time.

Performance Improvement of Network Based Parallel Genetic Algorithm by Exploiting Server's Computing Power (서버의 계산능력을 활용한 네트워크기반 병렬유전자알고리즘의 성능향상)

  • 송봉기;김용성;성길영;우종호
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.41 no.4
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    • pp.67-72
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    • 2004
  • This paper proposes a method improving the convergence speed of optimal solution for parallel genetic algorithm in the network based client-server model. Unlike the existing methods of obtaining global elite only by evaluating local elites in server, the proposed method obtains it by evaluating local elites and improving its fitness by applying genetic algorithm during idle time of the server. By using the improved chromosome in server for the client's genetic algorithm processing, the convergence speed of the optimal solution is increased. The improvement of fitness at the server during the interval of chromosome migration is (equation omitted)(F$_{max}$(g)-F$_{max}$(g-1)), whole F$_{max}$(g) is a max fitness of the g-th generation and G is the number of improved generation by the server. As the number of clients increases and G decreases, the improvement of fitness goes down. However the improvement of fitness is better than existing methods..

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.

Coalitonal Game Theoretic Power Control for Delay-Constrained Wireless Sensor Networks (지연제약 무선 센서 네트워크를 위한 협력게임 기법에 기반한 전송 파워 제어 기법)

  • Byun, Sang-Seon
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2015.10a
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    • pp.107-110
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    • 2015
  • In this paper, we propose a coalitonal game theoritic approach to the power control problem in resource-constrained wireless sensor networks, where the objective is to enhance power efficiency of individual sensors while providing the QoS requirements. We model this problem as two-sided one-to-one matching game and deploly deferred acceptance procedure that produces a single matching in the core. Furthermore, we show that, by applying the procedure repeatedly, a certain stable state is achieved where no sensor can anticipate improvements in their power efficiency as far as all of them are subject to their own QoS constraints. We evaluate our proposal by comparing them with cluster-based and the local optimal solution obtained by maximizing the total system energy efficiency, where the objective function is non-convex.

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Distribution System Reconfiguration Using the PC Cluster based Parallel Adaptive Evolutionary Algorithm

  • Mun Kyeong-Jun;Lee Hwa-Seok;Park June Ho;Hwang Gi-Hyun;Yoon Yoo-Soo
    • KIEE International Transactions on Power Engineering
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    • v.5A no.3
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    • pp.269-279
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    • 2005
  • This paper presents an application of the parallel Adaptive Evolutionary Algorithm (AEA) to search an optimal solution of a reconfiguration in distribution systems. The aim of the reconfiguration is to determine the appropriate switch position to be opened for loss minimization in radial distribution systems, which is a discrete optimization problem. This problem has many constraints and it is very difficult to find the optimal switch position because of its numerous local minima. In this investigation, a parallel AEA was developed for the reconfiguration of the distribution system. In parallel AEA, a genetic algorithm (GA) and an evolution strategy (ES) in an adaptive manner are used in order to combine the merits of two different evolutionary algorithms: the global search capability of GA and the local search capability of ES. In the reproduction procedure, proportions of the population by GA and ES are adaptively modulated according to the fitness. After AEA operations, the best solutions of AEA processors are transferred to the neighboring processors. For parallel computing, a PC-cluster system consisting of 8 PCs·was developed. Each PC employs the 2 GHz Pentium IV CPU, and is connected with others through switch based fast Ethernet. The new developed algorithm has been tested and is compared to distribution systems in the reference paper to verify the usefulness of the proposed method. From the simulation results, it is found that the proposed algorithm is efficient and robust for distribution system reconfiguration in terms of the solution quality, speedup, efficiency, and computation time.