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optimization problems ON GRAPHS WITH INDEPENDENT RANDOM EDGE WEIGHTS

SIAM JOURNAL ON COMPUTING 1981年第2期10卷 338-351页

作者： LUEKER, GS

optimization problems on complete graphs with edge weights drawn independently, from a fixed distribution, are considered. Several methods for analyzing these problems are discussed, including greedy methods, applications of Boole’s inequality, and exploitation of relationships with results about random unweighted graphs. These techniques are illustrated in the case in which the edge weights are drawn from a normal distribution; in particular, we investigate the expected behavior of the minimum weight clique on k vertices. We describe the asymptotic behavior (in probability and/or almost surely) of the random variable which describes the optimum; we also discuss the asymptotic behavior of its mean. Finally techniques are demonstrated by which we may determine an asymptotic description of the behavior of a greedy algorithm for this problem.

关键词： random graphs optimization problems normal distribution weighted graphs probabilistic analysis traveling salesman problem cliques Boole’s inequality greedy algorithms convergence in probability almost sure convergence

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optimization problems for Consecutive-k-out-of-n:G Systems with Exchangeable Components

Optimization Problems for Consecutive-k-out-of-n:G Systems w...

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International Symposium on Advanced Reliability and Maintenance Modeling (APARM)

作者： Zhou, Lei Yamamoto, Hisashi Xiao, Xiao Tokyo Metropolitan Univ Grad Sch Syst Design Tokyo Japan

ISBN: (纸本)9781728171029

In this paper, we focus on the optimization problems for a consecutive-k-out-of-n:G system with exchangeable components. A consecutive-k-out-of-n:G system consists of n components which are arranged in a line and the system works if and only if at least k consecutive components work. We first obtain the reliability and the number of failed components when system is working or fails. Then, we propose two optimization problems for this system, including the optimal number of components at system design stage, and the optimal replacement time at system operation stage.

关键词： consecutive k-out-of-n:G system exchangeable number of failed components optimization problems

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Convergence of discrete approximations to optimization problems of neutral functional-differential inclusions

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APPLIED MATHEMATICS AND COMPUTATION 2005年第2期165卷 375-391页

作者： Wang, LW Cent Missouri State Univ Dept Math & Comp Sci Warrensburg MO 64093 USA

This paper deals with the convergence of discrete approximations to the optimization problem (P) for a neutral functional-differential inclusion subject to general endpoint constraints. In the first part of the paper, discrete approximations to the neutral functional-differential inclusion are constructed using Enter finite difference methods and the convergence of discrete approximations is proved. In the second part of the paper, a family of discrete optimization problems (P-N) to (P) is provided and the strong convergence of optimal solutions for (P-N) to the optimal solution of (P) is discussed. (c) 2004 Elsevier Inc. All rights reserved.

关键词： convergence optimization problems neutral functional-differential inclusions discrete approximations

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Number of Failed Components in Consecutive-k-out-of-n :G Systems and Their Applications in optimization problems

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2022年第6期E105A卷 943-951页

作者： Zhou, Lei Yamamoto, Hisashi Tokyo Metropolitan Univ Fac Syst Design Hino Tokyo 1910065 Japan Yamaguchi Univ Grad Sch Sci & Technol Innovat Ube Yamaguchi 7558611 Japan

In this paper, we study the number of failed components in a consecutive-k-out-of-n:G system. The distributions and expected values of the number of failed components when system is failed or working at a particular time t are evaluated. We also apply them to the optimization problems concerned with the optimal number of components and the optimal replacement time. Finally, we present the illustrative examples for the expected number of failed components and give the numerical results for the optimization problems.

关键词： consecutive-k-out-of-n:G system signature number of failed components optimization problems

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Necessary optimality conditions for optimization problems with variational inequality constraints

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MATHEMATICS OF OPERATIONS RESEARCH 1997年第4期22卷 977-997页

作者： Ye, JJ Ye, XY SUNY ALBANY SCH PUBL HLTHDEPT BIOMETRY & STATALBANYNY 12222

In this paper we study optimization problems with variational inequality constraints in mine finite dimensional spaces. Kuhn-Tucker type necessary optimality conditions involving coderivatives are given under certain constraint qualifications including one that ensures nonexistence of nontrivial abnormal multipliers. The result is applied to bilevel programming problems to obtain Kuhn-Tucker type necessary optimality conditions. The Kuhn-Tucker type necessary optimality conditions are shown to be satisfied without any constraint qualification by the class of bilevel programming problems where the lower level is a parametric linear quadratic problem.

关键词： optimization problems variational inequality constraints necessary optimality conditions derivatives of set-valued maps nonsmooth analysis

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A general iterative method for addressing mixed equilibrium problems and optimization problems

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第5期73卷 1180-1202页

作者： Jaiboon, Chaichana Kumam, Poom KMUTT Dept Math Fac Sci Bangkok 10140 Thailand RMUTR Fac Appl Liberal Arts Dept Math Bangkok 10100 Thailand

In this paper, we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem (MEP), the set of fixed points of an infinite family of nonexpansive mappings {T(n)}(n=1)(infinity) and the set of solutions of variational inequalities for a xi-inverse-strongly monotone mapping in Hilbert spaces. Furthermore, we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions, which solves some optimization problems. Our results extend and improve the recent results of Yao et al. [Y. Yao, M. A. Noor, S. Zainab, Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl. 354 (2009) 319-329;Y. Yao, M. A. Noor, Y. C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479-509] and many others. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Mixed equilibrium problem Fixed point Variational inequality Nonexpansive mapping optimization problems

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A Hybrid Approach for Solving optimization problems on Small Quantum Computers

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COMPUTER 2019年第6期52卷 18-26页

作者： Shaydulin, Ruslan Ushijima-Mwesigwa, Hayato Negre, Christian F. A. Safro, Ilya Mniszewski, Susan M. Alexeev, Yuri Clemson Univ Comp Sci Clemson SC 29631 USA Clemson Univ Sch Hlth Res Clemson SC 29631 USA Fujitsu Labs Amer Sunnyvale CA USA Los Alamos Natl Lab Los Alamos NM USA Argonne Natl Lab Argonne IL 60439 USA

Solving larger-sized problems is an important area of research in quantum computing. Designing hybrid quantum-classical algorithms is a promising approach to solving this. We discuss decomposition-based hybrid approac... 详细信息

关键词： Computational Complexity Optimisation Quantum Computing Quantum Computers Quantum Computing Hybrid Quantum Classical Algorithms Decomposition Based Hybrid Approaches optimization problems Hybrid Approach Community Detection Computers Qubit Hardware optimization Logic Gates Annealing

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A novel bat algorithm with dynamic membrane structure for optimization problems

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APPLIED INTELLIGENCE 2021年第4期51卷 1992-2017页

作者： Alsalibi, Bisan Abualigah, Laith Khader, Ahamad Tajudin Univ Sains Malaysia Sch Comp Sci George Town 11800 Malaysia Amman Arab Univ Fac Comp Sci & Informat Amman 11953 Jordan

To improve the optimization efficiency for different optimization problems and take advantage of the dynamic membrane computing framework, this paper proposes an improved bat algorithm, namely, Dynamic Membrane-driven Bat Algorithm (DMBA). The dynamic construction of the DMBA algorithm aims at enhancing population diversity by balancing the exploration-exploitation tradeoff. Unlike the static membrane algorithms, the membranes in DMBA will be dynamically evolved by using merging and separation rules which help in maintaining the diversity of the population. The experimental results on a set of well-known benchmark functions including CEC 2005, CEC 2011, and CEC 2017 clearly prove the effectiveness of the proposed DMBA algorithm in terms of maintaining the diversity and exploitation capabilities compared to that of the others. It is shown that the proposed DMBA algorithm is superior to recent variants of the bat algorithm and other well-known algorithms in terms of solution accuracy and convergence speed.

关键词： Dynamic membrane structure Parallel membrane framework Bat algorithm optimization problems

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Linear fractional multi-objective optimization problems subject to fuzzy relational equations with a continuous Archimedean triangular norm

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INFORMATION SCIENCES 2014年 267卷 225-239页

作者： Khorram, E. Ezzati, R. Valizadeh, Z. Islamic Azad Univ Dept Math Karaj Branch Karaj Iran Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

In this paper, linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FREs) using the max-Archimedean triangular norm composition are considered. First, some theorems and results are presented to simplify systems of fuzzy relational equations. Next, the feasible set of the optimization problem is reduced. Then, the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski's approach. Furthermore, the efficient solutions are obtained by applying the improved c-constraint method. In addition, we design an algorithm to generate consistent systems of fuzzy relational equations, randomly, using the covering problem. Finally, the proposed method is effectively tested by solving a randomly generated consistent test problem. (C) 2014 Published by Elsevier Inc.

关键词： Fuzzy relational equation Archimedean t-norm Linear fractional multi-objective optimization problems The improved a-constraint method The covering problem

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An Enhanced Firefly Algorithm Using Pattern Search for Solving optimization problems

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IEEE ACCESS 2020年 8卷 148264-148288页

作者： Wahid, Fazli Zia, M. Sultan Bin Rais, Rao Naveed Aamir, Muhammad Butt, Umair Muneer Ali, Mubashir Ahmed, Adeel Ali Khan, Imran Khalid, Osman Univ Haripur Dept Informat Technol Haripur 22620 Pakistan Univ Lahore Fac Comp Sci & Informat Technol Gujrat Campus Lahore 50700 Pakistan Ajman Univ Coll Engn & Informat Technol Dept Elect & Comp Engn Ajman 34 U Arab Emirates Univ Tun Hussein Onn Malaysia Fac Comp Sci & Informat Technol Johor Baharu 86400 Malaysia Univ Sains Malaysia George Town Sch Comp Sci George Town 11800 Malaysia Univ Bergamo Sch Engn & Appl Sci I-24129 Bergamo Italy Quaid I Azam Univ Dept Comp Sci Islamabad 15320 Pakistan COMSATS Univ Islamabad Dept Comp Sci Abbottabad Campus Khyber Pakhtunkhwa 22060 Pakistan

Firefly Algorithm (FA) is one of the most recently introduced stochastic, nature-inspired, meta-heuristic approaches used for solving optimization problems. The conventional FA use randomization factor during generation of solution search space and fireflies position changing, which results in imbalanced relationship between exploration and exploitation. This imbalanced relationship causes in incapability of FA to find the most optimum values at termination stage. In the proposed model, this issue has been resolved by incorporating PS at the termination stage of standard FA. The optimized values obtained from the FA are set as the initial starting points for the PS algorithm and the values are further optimized by PS to get the most optimal values or at least better values than the values obtained by conventional FA during its maximum number of iterations. The performance of the newly developed FA-PS model has been tested on eight minimization functions and six maximization functions by considering various performance evaluation parameters. The results obtained have been compared with other optimization algorithms namely genetic algorithm (GA), standard FA, artificial bee colony (ABC), ant colony optimization (ACO), differential equations (DE), bat algorithm (BA), grey wolf optimization (GWO), Self-Adaptive Step Firefly Algorithm (SASFA), and FA-Cross algorithm in terms of convergence rate and various numerical performance evaluation parameters. A significant improvement has been observed in the solution quality by embedding PS in the standard FA at the termination stage. The result behind this improvement is the better exploration and exploitation of the solution search space at this stage.

关键词： optimization Search problems Genetic algorithms Artificial intelligence Particle swarm optimization Programming Firefly algorithm pattern search rich exploration and exploitation optimization problems fast convergence minimization and maximization functions

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