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Eliciting dual interval probabilities from interval comparison matrices

INFORMATION SCIENCES 2012年 190卷 17-26页

作者： Guo, Peijun Wang, Yuanbin Yokohama Natl Univ Fac Business Adm Hodogaya Ku Yokohama Kanagawa 2408501 Japan

In recent years, dealing with uncertainty using interval probabilities, such as combination, marginalization, condition, Bayesian inferences, has received considerable attention. However, how to elicit interval probabilities from subjective judgment is still a fundamental problem in applications of interval probabilities. In this paper, interval-valued pairwise comparisons of events are used to characterize the judgment of a person about which one is more likely to occur between each pair of events. From the interval comparison matrix, we elicit the dual interval probabilities by linear programming problems. The ratios of the estimated interval probabilities are used to approximate the interval comparison values from the outside and the inside of them. In other words, the inclusion relations between the interval comparison values and the ratios of the obtained interval probabilities hold. A numerical example concerning a new product development is presented to illustrate how to estimate dual interval probabilities and use interval probabilities to make a decision. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Interval probabilities Uncertainty modeling linear programming problem

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A SIMPLE VARIANT OF THE MIZUNO-TODD-YE PREDICTOR-CORRECTOR ALGORITHM AND ITS OBJECTIVE-FUNCTION-FREE COMPLEXITY

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SIAM JOURNAL ON OPTIMIZATION 2013年第3期23卷 1890-1903页

作者： Kitahara, Tomonari Tsuchiya, Takashi Tokyo Inst Technol Grad Sch Decis Sci & Technol Meguro Ku Tokyo 1528552 Japan Natl Grad Inst Policy Studies Minato Ku Tokyo 1068677 Japan

In this paper, we propose a simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. Our variant employs a simple and a natural scaling-invariant search direction aiming at finite-termination, and, even if finite-termination fails, the same direction is occasionally used instead of the ordinary predictor step. Our algorithm is scaling-invariant, is easy to implement, and enjoys an objective-function-free polynomial-time complexity for a linear program with bounded feasible region.

关键词： linear programming problem interior point method layered least squares interior point method iteration complexity strong polynomiality

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Shape Optimization of a Nozzle with Specified Flow Field Including Viscosity Effect

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ACTA APPLICANDAE MATHEMATICAE 2008年第3期104卷 243-256页

作者： Farhadinia, B. Farahi, M. H. Esfahani, J. A. Univ Mohaghegh Ardabili Dept Math Ardebil Iran Ferdowsi Univ Mashhad Mashhad Iran

In this article we intend to find the optimal shape of a nozzle respecting to some given target flow fields including viscosity effect. Via an approach based on measure theory which is not an iterative method and need not to any initial guess, each shape optimization problems are solved and consequently each geometry of the nozzle corresponding to prescribed flow fields is determined. Analyzing several case studies make us to confident on the use of the presented approach, because the obtained results give entirely the same as what we expect physically.

关键词： Navier-Stokes equations Optimal shape design (OSD) Optimal control Measure theory linear programming problem

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APPLICATION OF SPHERE PACKING THEORY IN FINANCIAL MANAGEMENT

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第5期19卷 3436-3443页

作者： Chuluunbaatar, Ankhbayar Galaa, Burmaa Rentsen, Enkhbat Natl Univ Mongolia Sch Business Ulaanbaatar 14192 Mongolia Mongolian Acad Sci Inst Math & Digital Technol Ulaanbaatar 13330 Mongolia

The paper illustrates an application of sphere packing theory based on the capital structure of financial management. The entire process is mod-elled as a new optimization problem formulated as the sphere packing prob... 详细信息

关键词： Financial ratios capital structure linear programming problem

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Reliability evaluation of hybrid power markets based on multiple transaction matrix and optimal transaction curtailment

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IET GENERATION TRANSMISSION & DISTRIBUTION 2007年第1期1卷 65-71页

作者： Goel, L. Viswanath, P. A. Wang, P. Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

A Monte Carlo simulation technique evaluates the reliability indices of restructured power systems with a hybrid market. A model for optimal transaction curtailment for a contingency state in a hybrid market is developed to incorporate the changes brought about by deregulation. The objective of the contingency optimal transaction curtailment for each individual generation company is to minimise its revenue loss. The problem is formulated as a linear programming problem and solved using an optimisation technique. Customer load curtailment, which is the basic parameter for reliability evaluation, is determined using a load-shedding philosophy which is based on the results of the optimal transaction curtailment by the genco. Supply and demand transactions of the market participants are represented by a transaction matrix. The impact of the firm and nonfirm bilateral and reserve contracts on customer reliabilities have been studied. The technique has been illustrated by application to the IEEE Reliability Test System.

关键词： power system reliability firm contracts reserve contracts reliability indices evaluation Power system management, operation and economics linear programming Optimisation techniques power markets Monte Carlo simulation technique linear programming problem supply and demand hybrid power markets IEEE Reliability Test System customer load curtailment nonfirm bilateral contracts optimisation technique restructured power systems load-shedding philosophy load shedding Monte Carlo methods optimal transaction curtailment multiple transaction matrix contingency state supply and demand transactions power system simulation deregulation

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An Architecture and a MAC Protocol for Throughput Improvement in Light Trail Networks

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IEICE TRANSACTIONS ON COMMUNICATIONS 2012年第7期E95B卷 2330-2343页

作者： Chen, Wenjie Fukushima, Yukinobu Yokohira, Tokumi Okayama Univ Grad Sch Nat Sci & Technol Okayama 7008530 Japan

Light trail architecture is attracting attention as a new optical wavelength-division multiplexing network architecture that can be built with currently available devices and can achieve bandwidth allocation with granularity finer than a wavelength. Because a light trail is a shared medium, we need a medium access control (MAC) protocol to prevent collisions. Although MAC protocols using token passing can prevent collisions, the bandwidths of links that are located upstream of the token holding node are kept idle. We first propose a dynamic light trail splitting method for increasing throughput of a light trail by using such idle bandwidths. Our method splits a trail into upstream and downstream trails at the token holding node, and independent data transmission on the two trails are permitted. As a result, we expect that the split trail architecture will achieve higher throughput than the original non-split trail architecture. The degree of performance improvement with the split trail architecture depends on how appropriately we determine the upstream and downstream token holding times of every transmission node. Thus, we formulate a problem in which we optimize the token holding times to accommodate requested traffic volume as a linear programming problem. We then derive the throughput of the split trail architecture by solving the problem using the NUOPT solver and investigate the degree of improvement over the original architecture. In addition, we evaluate the end-to-end delay of the split trail architecture by simulation. According to numerical examples, the split trail architecture achieves 1) almost the same throughput as the original one for the worst-case traffic pattern where every transmission node sends data to the terminating node of the trail only, 2) about 1.6 times higher throughput for a uniform traffic pattern where every node pair requests the same traffic volume and an extremely unbalanced traffic pattern where only a few node pairs request huge

关键词： light trail network medium access control (MAC) token passing linear programming problem

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Recursive Algorithm for L1 Norm Estimation in linear Models

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JOURNAL OF SURVEYING ENGINEERING 2011年第1期137卷 1-8页

作者： Khodabandeh, A. Amiri-Simkooei, A. R. Univ Tehran Dept Surveying & Geomat Engn Geodesy Div Fac Engn Tehran Iran Delft Univ Technol Delft Inst Earth Observat & Space Syst Fac Aerosp Engn NL-2629 HS Delft Netherlands Univ Isfahan Dept Surveying Engn Fac Engn Esfahan 81744 Iran

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which is based on Dikin's method. The method can be considered as an appropriate alternative for the classical simplex method, which is sometimes time-consuming. The proposed method, compared with the simplex method, is thus easier for implementation and faster in performance. Furthermore, a recursive form of the Dikin's method is derived, which resembles the recursive least-squares method. Two simulated numerical examples show that the proposed algorithm gives as accurate results as the simplex method but in considerably less time. When dealing with a large number of observations, this algorithm can thus be used instead of the iteratively reweighted least-squares method and the simplex method.

关键词： Iteratively reweighted least squares linear programming problem Interior point methods Simplex method Affine method of Dikin Robust estimation L1 norm minimization Recursive algorithm

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linear optimization and fuzzy-based clustering for WSNs assisted internet of things

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MULTIMEDIA TOOLS AND APPLICATIONS 2023年第4期82卷 5161-5185页

作者： Maratha, Priti Gupta, Kapil Natl Inst Technol Kurukshetra Dept Comp Applicat Kurukshetra Haryana India

Wireless data transmission on the Internet of Things (IoT) needs data-aware communication protocols. Clustering is one of the effective network management approaches that enhance the lifetime of IoT. The primary challenge in the data transmission across IoT is designing an energy-efficient clustering mechanism. Existing protocols struggle with the non-optimal selection of CHs and frequent re-clustering on IoT, which leads to significant energy consumption. If the cluster head (CH) lifetime of the devices (nodes) is known prior, then re-clustering can be avoided to a reasonable extent. Therefore, in this paper, we estimate the lifetime of devices as CHs by solving a linear optimization problem to extend the first node death as much as possible and also, stalls the frequent re-clustering process to minimize the energy consumption. We also apply the uniform distribution of CHs to ensure balanced energy consumption on IoT devices. The proposed clustering technique named ECFEL (Efficient Clustering using Fuzzy logic based on Estimated Lifetime) for IoT outperforms the existing protocols, namely Low Energy Adaptive Clustering Hierarchy (LEACH), MODified LEACH (MOD-LEACH), Dynamic k-LEACH (DkLEACH), Novel-PSO-LEACH, FM-SCHEL, and M-IWOCA techniques in terms of first node death (FND), half node death (HND), last node death (LND). Our simulation results showcase that ECFEL is having a better lifetime in terms of FND, HND, and LND, respectively. Furthermore, the experiments also confirm that ECFEL consumes less energy while maintaining a packet delivery ratio for a more extended period.

关键词： Sensor networks Network lifetime Fuzzy logic Residual energy Node centrality linear programming problem

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Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2021年第10期36卷 6066-6100页

作者： Seikh, Mijanur R. Dutta, Shibaji Li, Deng-Feng Kazi Nazrul Univ Dept Math Asansol 713340 W Bengal India Univ Elect Sci & Technol China Sch Management & Econ Chengdu Peoples R China

Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual-layer information. In real-life problems, there are many situations where players of a matrix game cannot assess their pay-offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay-offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.

关键词： expected value linear programming problem matrix game rough interval

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On the minimum average distance of binary codes: linear programming approach

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DISCRETE APPLIED MATHEMATICS 2001年第3期111卷 263-281页

作者： Fu, FW Wei, VK Yeung, RW Nankai Univ Dept Math Tianjin 300071 Peoples R China Chinese Univ Hong Kong Dept Informat Engn Shatin Hong Kong Peoples R China

Ahlswede and Katona posed the following average distance problem: For every n and 1 less than or equal to M less than or equal to 2(n), determine the minimum average Hamming distance beta (n,M) of binary codes with length n and size M. In this paper. improved lower bounds for B(n,M) are found with the help of linear programming. As a corollary, beta (n, 2(n-2) +/- 1), beta (n, 2(n-1) + 2(n-2) +/-1), beta (n, 2(n-2)), beta (n, 2(n-1) + 2(n-2)), beta (n, 2(n-1) +/- 2) and beta (n, 2(n) - 2) are determined. Furthermore, an upper bound for beta (n, M) is obtained by constructing a binary code with length n and size M. This upper bound is tight for some cases, but not in general. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： binary codes average Hamming distance distance enumerator MacWilliams-Delsarte identity linear programming problem

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