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A new simplex algorithm for interval-valued Fermatean fuzzy Linear programming problems

COMPUTATIONAL & APPLIED MATHEMATICS 2025年第1期44卷 1-36页

作者： Bihari, Rakhi Jeevaraj, S. Kumar, Ajay Atal Bihari Vajpayee Indian Inst Informat Technol Gwalior 474015 Madhya Pradesh India Atal Bihari Vajpayee Indian Inst Informat Technol Math Gwalior 474015 Madhya Pradesh India

Today, in most cases, such as transportation, management, artificial intelligence, industries, decision-making, and in many real-life situations, we deal with uncertainty, imprecise boundaries, and qualitative information. In order to deal with these kinds of critical circumstances, we need to solve an optimization problem with interval-valued Fermatean fuzzy (IVFF) information. A few works have been done on transportation problems with Interval-valued Fermatean fuzzy sets (IVFFSs). In this paper, we first introduce a few new arithmetic operations on the set of IVFFSs. Second, we propose a linear programming problem (LPP) model under an interval-valued Fermatean fuzzy environment and study its Mathematical properties by establishing various theorems. Third, we propose a new simplex algorithm to solve a fully interval-valued Fermatean fuzzy Linear programming (IVFFLPP) problem and solve a few numerical problems to show the applicability of our proposed algorithm. Fourth, we discuss the formulation of the interval-valued Fermatean fuzzy assignment problem (IVFFAP) as a particular case of IVFFLPP and study its properties. Fifth, we establish a new algorithm for solving IVFFAP and solve two numerical problems to discuss the applicability, importance of the proposed algorithms.

关键词： simplex algorithm Interval-valued Fermatean fuzzy sets Arithmetic operations Complete ranking principle Interval-valued Fermatean fuzzy linear programming problem Interval-valued Fermatean fuzzy assignment problem

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simplex algorithm for Countable-State Discounted Markov Decision Processes

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OPERATIONS RESEARCH 2017年第4期65卷 1029-1042页

作者： Lee, Ilbin Epelman, Marina A. Romeijn, H. Edwin Smith, Robert L. Univ Alberta Alberta Sch Business Edmonton AB T6G 2R6 Canada Univ Michigan Ann Arbor MI 48109 USA Georgia Inst Technol Atlanta GA 30332 USA

We consider discounted Markov decision processes (MDPs) with countablyinfinite state spaces, finite action spaces, and unbounded rewards. Typical examples of such MDPs are inventory management and queueing control problems in which there is no specific limit on the size of inventory or queue. Existing solution methods obtain a sequence of policies that converges to optimality in value but may not improve monotonically, i.e., a policy in the sequence may be worse than preceding policies. Our proposed approach considers countably-infinite linear programming (CILP) formulations of the MDPs (a CILP is defined as a linear program (LP) with countably-infinite numbers of variables and constraints). Under standard assumptions for analyzing MDPs with countably-infinite state spaces and unbounded rewards, we extend the major theoretical extreme point and duality results to the resulting CILPs. Under additional mild assumptions, which are satisfied by several applications of interest, we present a simplex-type algorithm that is implementable in the sense that each of its iterations requires only a finite amount of data and computation. We show that the algorithm finds a sequence of policies that improves monotonically and converges to optimality in value. Unlike existing simplex-type algorithms for CILPs, our proposed algorithm solves a class of CILPs in which each constraint may contain an infinite number of variables and each variable may appear in an infinite number of constraints. A numerical illustration for inventory management problems is also presented.

关键词： simplex algorithm infinite linear programs dynamic programming

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simplex algorithm for deep-level transient spectroscopy:: simplex-DLTS

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JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS BRIEF COMMUNICATIONS & REVIEW PAPERS 2004年第11A期43卷 7376-7380页

作者： Benchenane-Mehor, H Benzohra, M Idrissi-Benzohra, M Olivie, F Saïdane, A Univ Rouen Lab Elect Microtechnol & Instrumentat F-76821 Mont St Aignan France Univ Rouen Lab Etud & Caracterisat Amorphes & Polymeres F-76801 St Etienne France CNRS LAAS F-31077 Toulouse France Ecole Natl Super Enseignement Tech Mnaouer Oran 1523 Algeria

The Nelder-Mead simplex algorithm improved by Lagarias for low-dimension functions is introduced for the first time on transient capacitance signal analysis to decrease noise sensitivity and increase the resolution of deep-level transient spectroscopy method (DLTS). The application of the resolution figure of merit in predetermining the success of DLTS analyses' ability to resolve defects has shown that the performances of the simplex-DLTS developed in this work are significantly better than those of matrix pencil-DLTS method (MP-DLTS) published in 1998. Comparing experimentally the two methods in analyzing the signals generated by the same 150 keV germanium preamorphized p(+)n samples, we found that the simplex-DLTS method detects six defects in which some show very close activation energy values, while the MP-DLTS method found only two defects. Hence, the superiority of the simplex-DLTS method is proved;it reveals deep levels in which the emission process is carried out in the same temperature range.

关键词： transient capacitance deep-level transient spectroscopy DLTS resolution simplex algorithm

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A primal deficient-basis simplex algorithm for linear programming

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期196卷 898-912页

作者： Pan, Ping-Qi Southeast Univ Dept Math Nanjing 210096 Peoples R China

The standard basis, which plays a fundamental role in simplex methodology, was recently extended to include a deficient case (with fewer columns than rows) by taking advantage of primal degeneracy. Computational results have been favorable with dense implementations. In this paper, we propose a primal simplex algorithm using sparse LU factors of deficient bases. Amenable to real-world linear programming problems, which are often degenerate or even highly degenerate, the algorithm would solve them with potentially improved stability compared to the simplex algorithm. The proposed algorithm has been implemented and tested on a set of 50 Netlib test problems as well as a set of 15 much larger real-world problems, including 8 Kennington and 5 BPMPD problems. It significantly outperformed MINOS 5.3 in terms of both iteration counts and run time. In particular,. these results reveal that there is no inevitable correlation between an algorithm's inefficiency and degeneracy (contradicting common belief). (C) 2007 Elsevier Inc. All rights reserved.

关键词： large-scale linear programming simplex algorithm primal degeneracy deficient-basis LU factorization

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GPU accelerated pivoting rules for the simplex algorithm

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JOURNAL OF SYSTEMS AND SOFTWARE 2014年 96卷 1-9页

作者： Ploskas, Nikolaos Samaras, Nikolaos Univ Macedonia Sch Informat Sci Dept Appl Informat Thessaloniki 54006 Greece

simplex type algorithms perform successive pivoting operations (or iterations) in order to reach the optimal solution. The choice of the pivot element at each iteration is one of the most critical step in simplex type algorithms. The flexibility of the entering and leaving variable selection allows to develop various pivoting rules. In this paper, we have proposed some of the most well-known pivoting rules for the revised simplex algorithm on a CPU-GPU computing environment. All pivoting rules have been implemented in MATLAB and CUDA. Computational results on randomly generated optimal dense linear programs and on a set of benchmark problems (Netlib-optimal, Kennington, Netlib-infeasible, Meszaros) are also presented. These results showed that the proposed GPU implementations of the pivoting rules outperform the corresponding CPU implementations. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Linear programming simplex algorithm Pivoting rules Graphical Processing Unit MATLAB Compute Unified Device Architecture

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Fractional factorial design and simplex algorithm for optimizing sequential injection analysis (SIA) and second order calibration

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2006年第2期83卷 127-132页

作者： Pasamontes, Alberto Callao, Pilar Univ Rovira & Virgili Dept Quim Analit & Quim Organ Tarragona 43007 Spain

In this study, we report a method for finding an analytical sequence that allows to simultaneously determine two analytes with very similar physical and chemical characteristics, such as amoxicillin and clavulanic acid, using sequential injection analysis (SIA) with a diode-array spectrophotometric detector and multivariate curve resolution with alternating least squares (MCR-ALS). This method comprises two stages. In the first stage, a fractional factorial design (2(6-2)) is carried out in order to address the responses, reduce later experimentation and study how the factors, though confounded, interact with each other. In the second stage, optimization is carried out using the simplex algorithm. This method has advantages over response surface modelling, for example, when the number of significant factors is high. If simplex is begun in a suitable zone, the number of experiments may be considerably reduced. (c) 2006 Elsevier B.V All rights reserved.

关键词： fractional factorial design simplex algorithm MCR-ALS SIA amoxicillin clavulanic acid desirability function

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A simplex algorithm for a class of Leontief flow problems

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MATHEMATICAL AND COMPUTER MODELLING 1996年第7期24卷 69-75页

作者： Ng, PH Wagner, DK OFF NAVAL RES DIV MATH COMP & INFORMAT SCIARLINGTONVA 22217

A matrix N is Leontief if it has exactly one positive entry per column and there exists a nonnegative x such that Nx > 0. A Leontief flow problem is a linear-programming problem of the form min{c(inverted perpendicular)x\Nx = b;x greater than or equal to 0}, where N is a certain type of Leontief matrix. It is shown that for b > 0 this problem can be solved in O(n(2)U log npU) pivots by the simplex method using Dantzig's rule for choosing the entering variable, where n is the number of variables, p is the largest entry of N in absolute value, and U is a valid upper bound on any extreme-point solution. Classes of problems where this is a strongly polynomial bound are identified.

关键词： linear programming simplex algorithm Leontief matrices network flows computational complexity

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A new pivot selection rule for the network simplex algorithm

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MATHEMATICAL PROGRAMMING 1997年第2期78卷 149-158页

作者： Sokkalingam, PT Sharma, P Ahuja, RK INDIAN INST TECHNOL DEPT IND & MANAGEMENT ENGNKANPUR 208016UTTAR PRADESHINDIA INDIAN INST TECHNOL DEPT MATHKANPUR 208016UTTAR PRADESHINDIA

We present a new network simplex pivot selection rule, which we call the minimum ratio pivot rule, and analyze the worst-case complexity of the resulting network simplex algorithm. We consider networks with n nodes, m arcs, integral arc capacities and integral supplies/demands of nodes. We define a {0,1}-valued penalty for each are of the network. The minimum ratio pivot rule is to select that eligible are as the entering are whose addition to the basis creates a cycle with the minimum cost-to-penalty ratio. We show that the so-defined primal network simplex algorithm solves minimum cost how problem within O(n Delta) pivots and in O(Delta(m + n log n)) time, where Delta is any upper bound on the sum of all are flows in every feasible flow. For assignment and shortest path problems, our algorithm runs in O(n(2)) pivots and O(nm + n(2) log n) time. (C) 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

关键词： networks simplex algorithm minimum cost flow problem assignment problem shortest path problem

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A polynomial time primal network simplex algorithm for minimum cost flows

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MATHEMATICAL PROGRAMMING 1997年第2期78卷 109-129页

作者： Orlin, JB Sloan School of Management MIT 02139 Cambridge MA USA

Developing a polynomial time primal network simplex algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n(2)m log nC,n(2)m(2) log n)) time, where n is the number of nodes in the network, m is the number of arcs, and C denotes the maximum absolute are costs if are costs are integer and proportional to otherwise. We first introduce a pseudopolynomial variant of the network simplex algorithm called the ''premultiplier algorithm''. We then develop a cost-scaling version of the premultiplier algorithm that solves the minimum cost flow problem in O(min(nm log nC, nm(2) log n)) pivots. With certain simple data structures, the average time per pivot can be shown to be O(n). We also show that the diameter of the network polytope is O(nm log n). (C) 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

关键词： minimum cost flows network simplex polynomial time simplex algorithm premultipliers

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The simplex algorithm for Best-Estimate of Magnetic Parameters Related to Simple Geometric-Shaped Structures

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MATHEMATICAL GEOSCIENCES 2015年第3期47卷 301-316页

作者： Tlas, M. Asfahani, J. Atom Energy Commiss Damascus Syria

This paper introduces a practical approach to interpret magnetic anomalies related to simple geometric-shaped models such as thin dike and horizontal cylinder. This approach is mainly based on both the deconvolution technique and on the simplex algorithm for linear programming to best-estimate the model parameters, for example the depth to the top or to the center of a buried structure, the effective magnetization angle and the amplitude coefficient from magnetic anomaly profile. This approach has been tested first on synthetic data sets corrupted by different white Gaussian random noise levels to demonstrate the capability and the reliability of the method. The results acquired show that the estimated parameter values derived by this approach are close to the assumed true values of parameters. The validity of this approach is also demonstrated using real field magnetic anomalies from the United States and Brazil. A comparable and acceptable agreement is shown between the results derived by this approach and those from the real field data information.

关键词： Magnetic anomaly Thin dike-like structure Horizontal cylinder-like structure Deconvolution technique simplex algorithm

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