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A Linear Time Solution for N-Queens Problem Using Generalized Networks of Evolutionary Polarized Processors

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2020年第1期31卷 7-21页

作者： Arroyo Montoro, Fernando Gomez-Canaval, Sandra Jimenez Vega, Karina Ortega de la Puente, Alfonso Univ Politecn Madrid ETS Ingn Sistemas Informat Calle Alan Turing S-N Madrid 28031 Spain Univ Autonoma Madrid Escuela Politecn Super Calle Francisco Tomas y Valiente 11 E-28049 Madrid Spain

In this paper we consider a new variant of Networks of Polarized Evolutionary Processors (NPEP) named Generalized Networks of Evolutionary Polarized Processors (GNPEP) and propose them as solvers of combinatorial optimization problems. Unlike the NPEP model, GNPEP uses its numerical evaluation over the processed data from a quantitative perspective, hence this model might be more suitable to solve specific hard problems in a more efficient and economic way. In particular, we propose a GNPEP network to solve a well-known NP-hard problem, namely the N-queens. We prove that this GNPEP algorithm requires a linear time in the size of a given instance. This result suggests that the GNPEP model is more suitable to address problems related to combinatorial optimization in which integer restrictions have a relevant role.

关键词： Bio-inspired computational model networks of polarized evolutionary processors generalized networks of polarized evolutionary processors combinatorial optimization problems N-queens problem massively parallel and distributed algorithms

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ANT COLONY optimization FOR VLSI FLOORPLANNING WITH CLUSTERING CONSTRAINTS

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2009年第6期26卷 440-448页

作者： Chiang, Chuan-Wen Natl Kaohsiung First Univ Sci & Technol Dept Comp & Commun Engn 2 Jhuoyue Rd Kaohsiung 811 Taiwan

In this study the very large scale integration (VLSI) floorplanning problem with clustering constraints and the layout area as the minimization criterion is considered. An algorithm, which is based on the primary principles of ant colony optimization (ACO), to solve this problem is presented. This ACO-based algorithm employs two different types of pheromone trails as the communication media among artificial ants to effectively guide them to cooperatively construct a high quality floorplan. On the basis of the characteristics of ACO, moreover, an encoding scheme, which is referred to as dynamic junction list (DJL), is proposed to represent the geometric relationships between circuit modules for a floorplan. Experimental results using the Microelectronics Center of North Carolina (MCNC) benchmarks demonstrate the effectiveness of the proposed algorithm.

关键词： very large scale integration floorplanning clustering constraints combinatorial optimization problems ant colony optimization

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Optimal Power Network Decomposition for Voltage and Reactive Power Control with Predator-Prey Brain Storm optimization

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IFAC-PapersOnLine 2018年第28期51卷 227-232页

作者： Mori, H. Ogawa, S. Chiang, H.D. Dept. of Network-Design Meiji University Tokyo Japan School of Electrical & Computer Eng. Cornell University IthacaNY14850 United States

This paper proposes an efficient method for optimizing transmission power network decomposition for voltage and reactive power control (VQC). To realize the distributed control, the idea of power network decomposition becomes much more important. It may be expressed as a combinatorial optimization problem of the NP-hard. As a result, more sophisticated methods are required to solve it in the Smart Grid environment. In this paper, an efficient metaheuristic method is proposed for optimal network decomposition for VQC. As the optimizer, the proposed method makes use of Predator-Prey Brain Storm optimization (PPBSO) that is an extension of Brain Storm optimization (BSO) stemmed from the process of human's brain storming. PPBSO applies the Predator-Prey strategy to BSO so that the global swarm information is improved during the search process. The effectiveness of the proposed method is demonstrated in the IEEE sample power systems. © 2018

关键词： Power control Artificial intelligence combinatorial mathematics combinatorial optimization Distributed parameter control systems Electric network analysis Electric power transmission networks Global optimization Reactive power Storms Voltage control Brain storm optimizations combinatorial optimization problems Decomposition methods Distributed control Meta heuristic methods Power network decomposition Voltage and reactive power control Voltage and reactive power control (VQC)

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Choosing the Capacity of Arcs with Constraint on Flow Delay Time

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CYBERNETICS AND SYSTEMS ANALYSIS 2019年第4期55卷 561-569页

作者： Trofymchuk, O. M. Vasyanin, V. A. Natl Acad Sci Ukraine Inst Telecommun & Global Informat Space Kiev Ukraine

The authors consider the problem of choosing the capacity of arcs from a given set, which is important in flow distribution in multicommodity communication networks with constraint on flow delay time. Such problem is proved to be NP-hard. The algorithms for the approximate solution of the problem and results of their experimental comparison with exact algorithm based on generating a sequence of binary reflected Gray codes are given. It is noted that obtaining an exact solution is possible with the use of pseudopolynomial algorithms for the 0-1 multiple-choice knapsack problem.

关键词： flows in networks flow delay time combinatorial optimization problems

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Linear time algorithm for Precedence Constrained Asymmetric Generalized Traveling Salesman Problem

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IFAC-PapersOnLine 2016年第12期49卷 651-655页

作者： Chentsov, Alexander Khachay, Michael Khachay, Daniel Krasovsky Institute of Mathematics and Mechanics Ural Federal University 16 S.Kovalevskoy str. 19 Mira str Ekaterinburg620990 Russia

We consider the combinatorial optimization problem of visiting clusters of a fixed number of nodes (cities), where, on the set of clusters should be visited according to some kind of partial order defined by additional precedence constraints. This problem is a kind of the Asymmetric Generalized Traveling Salesman Problem (AGTSP). To find an optimal solution of the problem, we propose a dynamic programming based on algorithm extending the well known Held and Karp technique. In terms of special type of precedence constraints, we describe subclasses of the problem, with polynomial (or even linear) in n upper bounds of time complexity. © 2016

关键词： Traveling salesman problem Clustering algorithms combinatorial optimization Computational complexity Dynamic programming combinatorial optimization problems Fixed numbers Generalized traveling salesman problem Linear time algorithms Optimal solutions Partial order Precedence constraints Time complexity

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A learning method in Hopfield neural network for combinatorial optimization problem

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NEUROCOMPUTING 2002年第1-4期48卷 1021-1024页

作者： Rong, LW Zheng, T Qi, PC Toyama Univ Fac Engn Toyama 9308555 Japan Tateyama Syst Inst Toyama 9300001 Japan

In this letter, we utilize the Hopfield network learning method to adjust the balance between constraint term and cost term of the energy function so that the local minimum that the network once falls into vanishes and the network can continue updating in a gradient descent direction of energy. We applied the proposed learning method to the traveling salesman problem to show that the method is capable of finding an optimal solution or a near-optimal solution in a shorter time. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： combinatorial optimization problems traveling salesman problem Hopfield neural network learning method

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Traveling Salesman Problem via Swarm Intelligence 12th

Traveling Salesman Problem via Swarm Intelligence

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12th International Conference on Swarm Intelligence (ICSI)

作者： Yen, Pei-Chen Phoa, Frederick Kin Hing Acad Sinica Inst Stat Sci Taipei Taiwan

ISBN: (纸本)9783030787424;9783030787431

Traveling Salesman Problem (TSP) is one of the most classic combinatorial optimization problems. It can be widely applied in many real-world applications. In this paper, we propose an efficient method via swarm intelligence to handle the traveling salesman problem, which may not be suitable for the standard particle swarm optimization due to its domain's discrete nature. Compared to the classic Ant Colony optimization method, the SIB method performs well in terms of efficiency and accuracy in the TSP problem. For TSP with cities size between 15 to 25, SIB has a significantly lower average executing time to obtain an adequate solution with close distance.

关键词： Traveling Salesman Problem Swarm intelligence Ant Colony optimization combinatorial optimization problems Metaheuristic method

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QUBO Coefficient Dynamic Ratio Shrinking Method for Quantum Annealers 5

QUBO Coefficient Dynamic Ratio Shrinking Method for Quantum ...

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2024 International Conference on Quantum Computing and Engineering

作者： Yachi, Yuta Tawada, Masashi Togawa, Nozomu Waseda Univ Dept Comp Sci & Commun Engn Tokyo Japan Waseda Univ Green Comp Syst Res Org Tokyo Japan

ISBN: (纸本)9798331541378

Quantum annealers search for optimal solutions to a combinatorial optimization problem by solving a quadratic unconstrained binary optimization (QUBO) model. Due to integrated control errors (ICEs), input QUBO coefficients are temporarily erroneous while a quantum annealer is running. Previous studies indicate that ICEs prevent quantum annealer from accurately running to obtain an optimal solution. This paper proposes a new method for reducing the ICE-induced noise effect. After a QUBO is input to a quantum annealer, the range of the QUBO coefficients is scaled within the hardware limitation. At that time, if the range is too large, the lowest absolute value (LAV) and near-LAV coefficients of the QUBO become too much small after scaling and these small coefficients can be more sensitive to the noise. To reduce the noise effect, our proposed method shrinks the range of QUBO coefficients by splitting it into multiple QUBOs. In splitting, LAV and near-LAV coefficients are left only in one QUBO, and the other coefficients are equally split so that each QUBO has a shrunk range. Finally, comparing the (quasi-)optimal solutions obtained from all split QUBOs, we obtain a solution closer to the original optimal solution. Experimental evaluation results show that the proposed method obtains more near-optimal solutions than the QUBO input as-is for all benchmarks.

关键词： quantum computing quantum annealing Ising machine QUBO combinatorial optimization problems ICE

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Chaotic neural networks and their applications

Chaotic neural networks and their applications

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3rd World Congress on Intelligent Control and Automation

作者： He, YY Wang, LP Northwestern Polytech Univ Coll Marine Engn Xian 710072 Shaanxi Peoples R China

ISBN: (纸本)7312012035

Many difficult combinatorial optimization problems arising from science and technology are often difficult to solve exactly Hence a great number of approximate algorithms for solving combinatorial optimization problems have been developed [10], [15]. Hopfield and Tank applied the continuous-time, continuous-output Hopfield neural network (CTCO-HNN) to TSP, thereby initiating a new approach to optimization problems. But Hopfield neural network is often trapped in local minima because of its gradient descent property. a number of modifications have been done on Hopfield neural network for escaping from local minima As so far, incorporating chaos into the Hopfield neural network has been proved to be successful approach to improve the convergent property of the HNNs. In this paper, we first review three chaotic neural network models, and then propose a novel approach to chaotic simulated annealing. Second, we apply all of them to 10 city TSP, respectively. The time evolutions of energy functions and outputs of neurons for each model are given. The features and effectiveness of four methods are discussed and evaluated according to the simulation results. We conclude that proposed neural network with simulated annealing has more powerful ability to obtain global minima than any other chaotic neural network model when applied to difficult combinatorial optimization problems.

关键词： combinatorial optimization problems Neural Networks Simulated Annealing Transient Chaos TSP

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A comparative study of metaheuristic algorithms for Dartboard Design

A comparative study of metaheuristic algorithms for Dartboar...

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5th International Conference on Information, Intelligence, Systems and Applications (IISA)

作者： Trichas, Ioannis Drosos, Christos Vlachos, Aristidis Univ Piraeus Dept Informat Piraeus Greece

ISBN: (纸本)9781479961726

The problem of optimally locating the numbers around a dartboard is a combinatorial optimization problem. In this paper, we're solving this problem using Ant System and Max-Min Ant System (MMAS) algorithm. The algorithm reinforces local search in neighborhood of the best solution found in each iteration while implementing methods to slow convergence and facilitate exploration. Both algorithms have been proved to be very effective in fmding optimum solution to hard combinatorial optimization problems.

关键词： combinatorial optimization problems Ant System (AS) Max-Min Ant System (MMAS) algorithm game of darts

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