Статті в журналах: "LINEAR PROGRAMMING PROBLEM (LPP)"

1

Borza, Mojtaba, and Azmin Sham Rambely. "A Linearization to the Sum of Linear Ratios Programming Problem." Mathematics 9, no. 9 (April 29, 2021): 1004. http://dx.doi.org/10.3390/math9091004.

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Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

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2

Mustafa, Rebaz B., and Nejmaddin A. Sulaiman. "A New Approach to Solving Linear Fractional Programming Problem with Rough Interval Coefficients in the Objective Function." Ibn AL- Haitham Journal For Pure and Applied Sciences 35, no. 2 (April 20, 2022): 70–83. http://dx.doi.org/10.30526/35.2.2809.

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This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples for promising.

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3

Kucukbay, Fusun, and Ceyhun Araz. "Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6, no. 2 (April 20, 2016): 121–28. http://dx.doi.org/10.11121/ijocta.01.2016.00284.

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Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP) technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP). Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

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4

Bharati, S. K., and S. R. Singh. "Interval-Valued Intuitionistic Fuzzy Linear Programming Problem." New Mathematics and Natural Computation 16, no. 01 (March 2020): 53–71. http://dx.doi.org/10.1142/s1793005720500040.

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In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind of uncertainty. Interval-valued intuitionistic fuzzy sets (IV-IFS) is a perfect key for handling uncertainty and hesitation than FS and IFS. In this paper, we define an interval-valued intuitionistic fuzzy number (IV-IFN) and its expected interval and expected values. We also introduce the concept of interval-valued intuitionistic fuzzy linear programming problem (IV-IFLPP). Further, we find the solutions of IV-IFLPP and compare the obtained optimal solutions with existing methods [D. Dubey and A. Mehra, Linear programming with Triangular Intuitionistic Fuzzy Numbers, in Proc. of the 7th Conf. and of the European Society for Fuzzy Logic and Technology (EUSFLAT-LFA 2011), R. Parvathi and C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets 18 (2012) 48–56]. Proposed technique may be used successfully in various areas in the formulation of our country’s five year plans, these include transportation, food-grain storage, urban development, national, state and district level plans, etc., The Indian Railways may use IV-IFLPP technique for linking different railway zones in more realistic way. Agricultural research institutes may use proposed technique for crop rotation mix of cash crops, food crops and fertilizer mix. Airlines can apply IV-IFLPP in the selection of routes and allocation of aircrafts to different routes. Private and public sector oil refineries may use IV-IFLPP for blending of oil ingredients to produce finished petroleum products.

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5

Mitlif, Rasha Jalal. "An Application Model for Linear Programming with an Evolutionary Ranking Function." Ibn AL-Haitham Journal For Pure and Applied Sciences 35, no. 3 (July 20, 2022): 146–54. http://dx.doi.org/10.30526/35.3.2817.

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One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (RF) with the trapezoidal fuzzy number (TFN) is devised in this study. The fuzzy quantities are de-fuzzified by applying the proposed ranking function (RF) transformation to crisp value linear programming problems (LPP) in the objective function (OF). Then the simplex method (SM) is used to determine the best solution (BS). To demonstrate our findings, we provide a numerical example (NE).

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6

Khalifa, Hamiden Abd El-Wahed, Majed Alharbi, and Pavan Kumar. "A new method for solving quadratic fractional programming problem in neutrosophic environment." Open Engineering 11, no. 1 (January 1, 2021): 880–86. http://dx.doi.org/10.1515/eng-2021-0088.

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Abstract In the current study, a neutrosophic quadratic fractional programming (NQFP) problem is investigated using a new method. The NQFP problem is converted into the corresponding quadratic fractional programming (QFP) problem. The QFP is formulated by using the score function and hence it is converted to the linear programming problem (LPP) using the Taylor series, which can be solved by LPP techniques or software (e.g., Lingo). Finally, an example is given for illustration.

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7

Junaid Basha, M., and S. Nandhini. "A fuzzy based solution to multiple objective LPP." AIMS Mathematics 8, no. 4 (2023): 7714–30. http://dx.doi.org/10.3934/math.2023387.

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<abstract>This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.</abstract>

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8

Mitlif, Rasha Jalal, Raghad I. Sabri, and Eman Hassan Ouda. "A Novel Algorithm to Find the Best Solution for Pentagonal Fuzzy Numbers with Linear Programming Problems." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 2 (April 20, 2023): 301–5. http://dx.doi.org/10.30526/36.2.2957.

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Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking function (RF) approaches for solving fuzzy linear programming problems (FLPP) with a pentagonal fuzzy number (PFN) have been proposed, based on new ranking functions (N RF). The simplex method (SM) is very easy to understand. Finally, numerical examples (NE) are used to demonstrate the suggested approach's computing process.

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9

Carutasu, Vasile. "Considerations on Cycling in the Case of Linear Programming Problem (Lpp)." International conference KNOWLEDGE-BASED ORGANIZATION 24, no. 3 (June 1, 2018): 14–19. http://dx.doi.org/10.1515/kbo-2018-0130.

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Abstract Ever since the onset of algorithms for determining the optimal solution or solutions for a linear programming problem (LPP), the question of the possibility of occurrence of cycling when one or other of these algorithms are applied was born. Thus, the fundamental question regarding this issue is under what conditions the cyclic phenomenon appears for a problem of linear programming and how to construct examples in which to do so, and as a continuation of it, which methods can be developed to avoid this phenomenon. In this study we will present some aspects regarding this issue starting from the primal simplex algorithm, by highlighting some general aspects that occur when this phenomenon happens

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10

Güzel, Nuran. "A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/435030.

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We have proposed a new solution to the Multiobjective Linear Fractional Programming Problem (MOLFPP). The proposed solution is based on a theorem that deals with nonlinear fractional programming with single objective function and studied in the work by Dinkelbach, 1967. As a new contribution, we have proposed that is an efficient solution of MOLFPP if is an optimal solution of problem , where is for all . Hence, MOLFPP is simply reduced to linear programming problem (LPP). Some numerical examples are provided in order to illustrate the applications of the proposed method. The optimization software package, namely, WinQSB (Chang, 2001), has been employed in the computations.

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11

Prajapati, Raju, Om Prakash Dubey, and Randhir Kumar. "IMPROVED PARTICLE SWARM OPTIMIZATION FOR NON-LINEAR PROGRAMMING PROBLEM WITH BARRIER METHOD." International Journal of Students' Research in Technology & Management 5, no. 4 (November 30, 2017): 72–80. http://dx.doi.org/10.18510/ijsrtm.2017.5410.

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The Non-Linear Programming Problems (NLPP) are computationally hard to solve as compared to the Linear Programming Problems (LPP). To solve NLPP, the available methods are Lagrangian Multipliers, Sub gradient method, Karush-Kuhn-Tucker conditions, Penalty and Barrier method etc. In this paper, we are applying Barrier method to convert the NLPP with equality constraint to an NLPP without constraint. We use the improved version of famous Particle Swarm Optimization (PSO) method to obtain the solution of NLPP without constraint. SCILAB programming language is used to evaluate the solution on sample problems. The results of sample problems are compared on Improved PSO and general PSO.

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12

Mallia, B., M. Das, and C. Das. "Fundamentals of Transportation Problem." International Journal of Engineering and Advanced Technology 10, no. 5 (June 30, 2021): 90–103. http://dx.doi.org/10.35940/ijeat.e2654.0610521.

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Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem

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13

Hussain, Mohammad Rashid, Mohammed Qayyum, and Mohammad Equebal Hussain. "Transportation Problem of LPP Involving Probability Density Function." International Journal of Recent Contributions from Engineering, Science & IT (iJES) 7, no. 1 (March 22, 2019): 42. http://dx.doi.org/10.3991/ijes.v7i1.9909.

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In Linear Programming Problem (LPP), Transportation Problem (TP) is an application which is used to optimize through the probability density function of statistical approach. The main objective of this paper is to reduce complexity in Maximization problem of LPP, by fulfilling the relation between the objective function and constraints with the largest value. Here, we used non-negative integer and complex number of linear combination of form xmeλx. It has been decided with reasonably great probability, decision region, fundamental probabilities and Laplace Transform (LT). To obtain proposed results we applied probability density function over transportation problem. According to our proposed method we implemented mathematical model through the probability density function of statistical tools. Categorically, probability density function is an approach in our proposed method to obtain the feasible solution of transportation problem, which perform better than the existing methods.

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14

Aliyu, U. M. "Application of Linear Programming Technique for Optimal Production in Profit Maximization." International Journal of Science for Global Sustainability 7, no. 3 (November 30, 2021): 7. http://dx.doi.org/10.57233/ijsgs.v7i3.16.

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In this paper, we are concerned with applying linear programming technique to determine optimum product mix of Gusau Sweet Factory Limited to maximize profit. Data on the quantity of major raw materials used in the production of the three different sweets: Toffee. Lollipop and Candy, cost and selling prices and the profit of each product were collected from the extract of the financial record of the company. The problem was formulated as a linear programming problem (LPP) and solved using the revised simplex algorithm. The results show that Toffee and lollipop should be produced daily for the company to realize an optimum profit.

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15

Ziaei, E., and M. H. Farahi. "The approximate solution of non-linear time-delay fractional optimal control problems by embedding process." IMA Journal of Mathematical Control and Information 36, no. 3 (July 27, 2018): 713–27. http://dx.doi.org/10.1093/imamci/dnx063.

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Abstract In this paper, a class of time-delay fractional optimal control problems (TDFOCPs) is studied. Delays may appear in state or control (or both) functions. By an embedding process and using conformable fractional derivative as a new definition of fractional derivative and integral, the class of admissible pair (state, control) is replaced by a class of positive Radon measures. The optimization problem found in measure space is then approximated by a linear programming problem (LPP). The optimal measure which is representing optimal pair is approximated by the solution of a LPP. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to non-linear TDFOCPs. The usefulness of the used idea in this paper is that the method is not iterative, quite straightforward and can be applied to non-linear dynamical systems.

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16

Stepanov, Gleb D. "Solving Linear Programming Problems by Reducing to the Form with an Obvious Answer." Modeling and Analysis of Information Systems 28, no. 4 (December 18, 2021): 434–51. http://dx.doi.org/10.18255/1818-1015-2021-4-434-451.

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The article considers a method for solving a linear programming problem (LPP), which requires finding the minimum or maximum of a linear functional on a set of non-negative solutions of a system of linear algebraic equations with the same unknowns. The method is obtained by improving the classical simplex method, which when involving geometric considerations, in fact, generalizes the Gauss complete exclusion method for solving systems of equations. The proposed method, as well as the method of complete exceptions, proceeds from purely algebraic considerations. It consists of converting the entire LPP, including the objective function, into an equivalent problem with an obvious answer. For the convenience of converting the target functional, the equations are written as linear functionals on the left side and zeros on the right one. From the coefficients of the mentioned functionals, a matrix is formed, which is called the LPP matrix. The zero row of the matrix is the coefficients of the target functional, $a_{00}$ is its free member. The algorithms are described and justified in terms of the transformation of this matrix. In calculations the matrix is a calculation table. The method under consideration by analogy with the simplex method consists of three stages. At the first stage the LPP matrix is reduced to a special 1-canonical form. With such matrices one of the basic solutions of the system is obvious, and the target functional on it is $ a_{00}$, which is very convenient. At the second stage the resulting matrix is transformed into a similar matrix with non-positive elements of the zero column (except $a_{00}$), which entails the non-negativity of the basic solution. At the third stage the matrix is transformed into a matrix that provides non-negativity and optimality of the basic solution. For the second stage the analog of which in the simplex method uses an artificial basis and is the most time-consuming, two variants without artificial variables are given. When describing the first of them, along the way, a very easy-to-understand and remember analogue of the famous Farkas lemma is obtained. The other option is quite simple to use, but its full justification is difficult and will be separately published.

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17

Hanif, Muhammad, and Farzana Sultana Rafi. "A New Method for Optimal Solutions of Transportation Problems in LPP." Journal of Mathematics Research 10, no. 5 (August 9, 2018): 60. http://dx.doi.org/10.5539/jmr.v10n5p60.

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The several standard and the existing proposed methods for optimality of transportation problems in linear programming problem are available. In this paper, we considered all standard and existing proposed methods and then we proposed a new method for optimal solution of transportation problems. The most attractive feature of this method is that it requires very simple arithmetical and logical calculation, that’s why it is very easy even for layman to understand and use. Some limitations and recommendations of future works are also mentioned of the proposed method. Several numerical examples have been illustrated, those gives the clear idea about the method. A programming code for this method has been written in Appendix of the paper.

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18

Nagalakshmi, T., and G. Uthra. "A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 360. http://dx.doi.org/10.14419/ijet.v7i4.10.20935.

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This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming.

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19

Mustafaf, Muna Mansoor. "Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method." Baghdad Science Journal 17, no. 1(Suppl.) (March 18, 2020): 0342. http://dx.doi.org/10.21123/bsj.2020.17.1(suppl.).0342.

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In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.

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20

Olufemi Aderemi, Ayansola. "Comparative Study of Efficiency of Integer Programming, Simplex Method and Transportation Method in Linear Programming Problem (LPP)." American Journal of Theoretical and Applied Statistics 4, no. 3 (2015): 85. http://dx.doi.org/10.11648/j.ajtas.20150403.13.

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21

Prajapati, Raju, and Om Prakash Dubey. "ANALYSING THE IMPACT OF PENALTY CONSTANT ON PENALTY FUNCTION THROUGH PARTICE SWARM OPTIMIZATION." International Journal of Students' Research in Technology & Management 6, no. 2 (March 1, 2018): 01–06. http://dx.doi.org/10.18510/ijsrtm.2018.621.

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Non Linear Programming Problems (NLPP) are tedious to solve as compared to Linear Programming Problem (LPP). The present paper is an attempt to analyze the impact of penalty constant over the penalty function, which is used to solve the NLPP with inequality constraint(s). The improved version of famous meta heuristic Particle Swarm Optimization (PSO) is used for this purpose. The scilab programming language is used for computational purpose. The impact of penalty constant is studied by considering five test problems. Different values of penalty constant are taken to prepare the unconstraint NLPP from the given constraint NLPP with inequality constraint. These different unconstraint NLPP is then solved by improved PSO, and the superior one is noted. It has been shown that, In all the five cases, the superior one is due to the higher penalty constant. The computational results for performance are shown in the respective sections.

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22

Mohanambal, S. "A Design and Solving LPP Method for Binary Linear Programming Problem Using DNA Approach." International Journal of Information Sciences and Techniques 2, no. 2 (March 31, 2012): 11–21. http://dx.doi.org/10.5121/ijist.2012.2202.

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23

Saif, Nagib M. A., and Gerhard-Wilhelm Weber. "Inverse Linear Goal Programming Problem." Thamar University Journal of Natural & Applied Sciences 3, no. 3 (January 28, 2023): 67–76. http://dx.doi.org/10.59167/tujnas.v3i3.1284.

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This paper considers the inverse linear goal programming problem of multi-objective function in case the change in coefficient of the objective function. Let denote the set of feasible solutions points of linear goal programming problem of a multi-objective function, and let be the positive and negative deviation variables of the maximum and minimum goals respectively, be a specified cost vector, be given feasible solution vector, and be given tow vectors denoted the feasible positive deviation and the feasible negative deviation points of the max or min goals, respectively. The inverse linear goal programming problem of multi-objective function is as follows: Consider the change of the cost vectors as less as possible such that the vectors feasible solution becomes an optimal solution of LGP of multi-objective function under the new cost vectors and is minimal, where is some selected -norm. In this paper, we consider the inverse version ILGP of LGMP. under the -norm where the objective is to minimize , with denoting the index set of variables . We show that the inverse version of the considered under -norm reduces to solving a problem for the same kind; that is, an inverse multi-objective assignment problem reduces to an assignment problem.

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24

Vilisov, V. Ya. "Algorithm for optimal allocation of limited resources based on the game iteration method." Informacionno-technologicheskij vestnik, no. 2 (July 30, 2019): 89–99. http://dx.doi.org/10.21499/2409-1650-2019-2-89-99.

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The article proposes an algorithm for solving a linear programming problem (LPP) based on the use of its representation in the form of an antagonistic matrix game and the subsequent solution of the game by an iterative method. The algorithm is implemented as a computer program. The rate of convergence of the estimates of the solution to the actual value with the required accuracy has been studied. The software implementation shows a high speed of obtaining the LPP solution with acceptable accuracy in fractions or units of seconds. This allows the use algorithm in embedded systems for optimal control.

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25

Oltean, Mihai. "Evolving Evolutionary Algorithms Using Linear Genetic Programming." Evolutionary Computation 13, no. 3 (September 2005): 387–410. http://dx.doi.org/10.1162/1063656054794815.

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A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.

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26

Carutasu, Vasile. "Aspects of the Cycling Phenomenon in the Linear Programming Problem (Lpp) Through the Example of Marshall and Suurballe." International conference KNOWLEDGE-BASED ORGANIZATION 24, no. 3 (June 1, 2018): 20–25. http://dx.doi.org/10.1515/kbo-2018-0131.

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Abstract A complete analysis of the cycling phenomenon in the case of the linear programming problem (LPP) is far from being achieved. Even if [5] states that the answer to the fundamental question of this problem is found, the proposed solution is very difficult to apply, being necessary to find a solution of a complex system of inequalities. Additionally, it is difficult to recognize a problem that, by applying the primal simplex algorithm, leads us to the occurrence of this phenomenon. The example given by Marshall and Suurballe, but also the example given by Danzig, lead us to draw some useful conclusions about this phenomenon, whether the given problem admits the optimal solution or has an infinite optimal solution

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27

Chowdhury, S. M. Atiqur Rahman, and Sanwar Uddin Ahmad. "A Computer Technique for Solving LP Problems with Bounded Variables." Dhaka University Journal of Science 60, no. 2 (July 31, 2012): 163–68. http://dx.doi.org/10.3329/dujs.v60i2.11487.

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Linear Programming problem (LPP)s with upper bounded variables can be solved using the Bounded Simplex method (BSM),without the explicit consideration of the upper bounded constraints. The upper bounded constraints are considered implicitly in this method which reduced the size of the basis matrix significantly. In this paper, we have developed MATHEMATICA codes for solving such problems. A complete algorithm of the program with the help of a numerical example has been provided. Finally a comparison with the built-in code has been made for showing the efficiency of the developed code.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11487 Dhaka Univ. J. Sci. 60(2): 163-168, 2012 (July)

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Nagesh Kumar, G. V., B. Sravana Kumar, B. Venkateswara Rao, P. V. S. Sobhan, and K. Appala Naidu. "Linear programming technique based optimal relay coordination in a radial distribution system." International Journal of Engineering & Technology 7, no. 1.8 (February 9, 2018): 51. http://dx.doi.org/10.14419/ijet.v7i1.8.9450.

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Now-a-days to ensure power continuity and system’s reliability the protection system is to be designed properly for distribution systems to handle the faults to avoiding the damage to the equipments and to the service engineers. Different types of relays with different working principles are used to detect different types of faults in the system. In order to avoid mal operation of relays, proper coordination is to be carried out. The objective of this paper is to maintain the relay coordination as well as to decrease the working time of relays by optimizing the values of time dial setting (TDS) using linear programming problem technique (LPP). The inequality constraints guarantee the coordination margin for each primary or backup relay pairs having a fault very close to the primary relay. Simulation is carried out on a IEEE 15 bus balanced radial distribution system with 3 different types of relays namely standard inverse, extremely inverse and very inverse relay and the results are presented and analyzed.

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29

Zhou, Xue-Gang, and Bing-Yuan Cao. "A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/984168.

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A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducingpauxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian duality theory. The proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. Some examples are given to illustrate the feasibility of the present algorithm.

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30

Ahmad, Sanwar Uddin, M. Babul Hasan, and M. Ainul Islam. "Algorithm to Perform a Complete RHS Parametric Analysis for LPP with Bounded Variables." Dhaka University Journal of Science 60, no. 2 (August 3, 2012): 217–22. http://dx.doi.org/10.3329/dujs.v60i2.11521.

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Linear Programming problem (LPP)s with upper bounded variables can be solved using the Bounded Simplex method, without the explicit consideration of the upper bounded constraints. One can consider the upper bounded constraints explicitly and perform the regular righthand- side parametric analysis of LPPs with bounded variables. This paper develops a method to perform the parametric analysis where the upper bounded constraints are considered implicitly, thus reduce the size of the basis matrix.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11521 Dhaka Univ. J. Sci. 60(2): 217-222, 2012 (July)

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31

Abo-Sinna, Mahmoud A., and Ibrahim A. Baky. "Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/148975.

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This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.

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32

Chakroborty, Sajal, and Md Babul Hasan. "A Computer Technique for Solving Linear Fractional Programming Problems by Using Dinkelbach’s Algorithm." Dhaka University Journal of Science 64, no. 2 (July 31, 2016): 121–25. http://dx.doi.org/10.3329/dujs.v64i2.54487.

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In this paper, we introduce a computer oriented technique for solving linear fractional programming (LFP) problems by converting it into a single linear programming (LP) problem. We have used the idea of Dinkelbach’s algorithm. We use a mathematical programming language (AMPL) to develop computer code. A number of numerical examples are used to demonstrate the technique. Dhaka Univ. J. Sci. 64(2): 121-125, 2016 (July)

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33

Zhao, Yingfeng, and Ting Zhao. "Global Optimization for Generalized Linear Multiplicative Programming Using Convex Relaxation." Mathematical Problems in Engineering 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/9146309.

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Applications of generalized linear multiplicative programming problems (LMP) can be frequently found in various areas of engineering practice and management science. In this paper, we present a simple global optimization algorithm for solving linear multiplicative programming problem (LMP). The algorithm is developed by a fusion of a new convex relaxation method and the branch and bound scheme with some accelerating techniques. Global convergence and optimality of the algorithm are also presented and extensive computational results are reported on a wide range of problems from recent literature and GLOBALLib. Numerical experiments show that the proposed algorithm with a new convex relaxation method is more efficient than usual branch and bound algorithm that used linear relaxation for solving the LMP.

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34

Mustafa, Rebaz, and Nejmaddin Sulaiman. "Efficient Ranking Function Methods for Fully Fuzzy Linear Fractional Programming problems via Life Problems." WSEAS TRANSACTIONS ON MATHEMATICS 21 (October 10, 2022): 707–17. http://dx.doi.org/10.37394/23206.2022.21.83.

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In this paper, we propose two new ranking function algorithms to solve fully fuzzy linear fractional programming (FFLFP) problems, where the coefficients of the objective function and constraints are considered to be triangular fuzzy numbers (TrFN) s. The notion of a ranking function is an efficient approach when you want to work on TrFNs. The fuzzy values are converted to crisp values by using the suggested ranking function procedure. Charnes and Cooper’s method transforms linear fractional programming (LFP) problems into linear programming (LP) problems. The suggested ranking functions methods' applicability to actual problems of daily life, which take data from a company as an example, is shown, and it presents decision-making and exact error with the main value problem. The study aims to find an efficient solution to the FFLFP problem, and the simplex method is employed to determine the efficient optimal solution to the original FFLFP problem.

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35

ABO-SINNA, MAHMOUD A., and Azza H. Amer. "An Interactive Dynamic Fuzzy Goal Programming for Bi-level Multiobjective Linear Fractional Programming Problems." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 12 (February 28, 2017): 6991–7007. http://dx.doi.org/10.24297/jam.v12i12.3720.

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This paper presents an interactive dynamic fuzzy goal programming (DFGP) approach for solving bi-level multiobjective linear fractional programming (BL MOLFP) problems with the characteristics of dynamic programming (DP). In the proposed approach, the membership function of the objective goals of a problem with fuzzy aspiration levels are defined first as the membership function for vector of fuzzy goals of the decision variables controlled by firstâ€“level decision maker are developed first in the model formulation of the problem. The method of variable change, on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model, is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Then, under the framework of preemptive priority based GP, a multi stage DP model of the problem is used for achievement of the highest degree (unity) of each of the membership functions. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution and the suggested algorithm to simplify the solution procedure by DP at each stage is proposed. This paper is considered as an extension work of Mahmoud A. Abo-Sinna and Ibrahim A. Baky (2010) by using dynamic approach. Finally, this approach is illustrated by a given numerical example.

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36

Darvay, Zsolt, and Ágnes Füstös. "Numerical Results for the General Linear Complementarity Problem." Műszaki Tudományos Közlemények 11, no. 1 (October 1, 2019): 43–46. http://dx.doi.org/10.33894/mtk-2019.11.07.

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Abstract In this article we discuss the interior-point algorithm for the general complementarity problems (LCP) introduced by Tibor Illés, Marianna Nagy and Tamás Terlaky. Moreover, we present a various set of numerical results with the help of a code implemented in the C++ programming language. These results support the efficiency of the algorithm for both monotone and sufficient LCPs.

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37

Paidipati, Kiran Kumar, Hyndhavi Komaragiri, and Christophe Chesneau. "Pre-Emptive and Non-Pre-Emptive Goal Programming Problems for Optimal Menu Planning in Diet Management of Indian Diabetes Mellitus Patients." International Journal of Environmental Research and Public Health 18, no. 15 (July 24, 2021): 7842. http://dx.doi.org/10.3390/ijerph18157842.

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Diet management or caloric restriction for diabetes mellitus patients is essential in order to reduce the disease’s burden. Mathematical programming problems can help in this regard; they have a central role in optimal diet management and in the nutritional balance of food recipes. The present study employed linear optimization models such as linear, pre-emptive, and non-pre-emptive goal programming problems (LPP, PGP and NPGP) to minimize the deviations of over and under achievements of specific nutrients for optimal selection of food menus with various energy (calories) levels. Sixty-two food recipes are considered, all selected because of being commonly available for the Indian population and developed dietary intake for meal planning through optimization models. The results suggest that a variety of Indian food recipes with low glycemic values can be chosen to assist the varying glucose levels (>200 mg/dL) of Indian diabetes patients.

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38

Khalifa, Hamiden Abd El Wahed, and Pavan Kumar. "A method to solve two-player zero-sum matrix games in chaotic environment." Independent Journal of Management & Production 12, no. 1 (February 1, 2021): 115–26. http://dx.doi.org/10.14807/ijmp.v12i1.1295.

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This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System.

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39

Akram, Muhammad, Syed Muhammad Umer Shah, Mohammed M. Ali Al-Shamiri, and S. A. Edalatpanah. "Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets." AIMS Mathematics 8, no. 1 (2022): 924–61. http://dx.doi.org/10.3934/math.2023045.

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<abstract>Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.</abstract>

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40

Mohanty, B. K., and Mahima Gupta. "Product Selection in E-Commerce Under Fuzzy Environment: A MADM Game Theoretic Model." International Game Theory Review 17, no. 01 (March 2015): 1540008. http://dx.doi.org/10.1142/s0219198915400083.

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This paper introduces a methodology based on fuzzy game theory to determine the buyer's priority of the attributes and select a product in the e-business system. The game theory model developed in our paper considers the prioritization of attributes as strategies for the player (player 1) in one side and selection of the products for the opponent player (player 2). The fuzzy probabilities of the strategies in the game theory are obtained by using the concepts of similarities between the fuzzy numbers. The e-business system devises strategies for the player 1 by attaching appropriate priority levels to product attributes for maximum gain. On the other hand the opponent player 2 select the products as the strategies accordingly. The payoffs obtained in the game theory model as fuzzy numbers are subsequently converted to their equivalent probabilistic mean intervals. This process leads to transform the game theory model into a linear programming problem (LPP) with interval coefficients. The solution to LPP gives us the optimal strategies. These probability of strategies are considered as attributes' weights to determine ranking of the products in e-business system. The methodology is illustrated with the help of a numerical example.

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41

Sahoo, Prasan Kumar, Sudhir Ranjan Pattanaik, and Shih-Lin Wu. "A Novel Synchronous MAC Protocol for Wireless Sensor Networks with Performance Analysis." Sensors 19, no. 24 (December 6, 2019): 5394. http://dx.doi.org/10.3390/s19245394.

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Synchronous medium access control (MAC) protocols are highly essential for wireless sensor networks (WSN) to support transmissions with energy saving, quality services, and throughput in industrial, commercial and healthcare applications. In this paper, a synchronous channel access mechanism is designed, where sensors can reserve the contention free data transmission slots in different available channels. To reduce the delay of data transmission among the nodes in the mesh topology, a linear programming problem (LPP) model is designed to select suitable relay nodes. Moreover, the performance of the proposed MAC is analyzed and our models are validated with simulation and analytical results. The results show that our proposed MAC protocol outperforms the IEEE 802.15.4e MAC mechanism in terms of throughput, reliability, delay, energy, packet drop rate and transmission success rate.

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42

Nawkhass, Maher Ali, and Nejmaddin Ali Sulaiman. "Modify Symmetric Fuzzy Approach to Solve the Multi-Objective Linear Fractional Programming Problem." International Journal of Fuzzy System Applications 11, no. 1 (January 1, 2022): 1–17. http://dx.doi.org/10.4018/ijfsa.312243.

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The property of fuzzy sets is approached as an instrument for the construction and finding of the value of the multi-objective linear fractional programming problem (MOLFPP), which is one of the systems of decision problems that are covered by fuzzy dealings. The paper introduces an approach to convert and solve such a problem by modifying the symmetric fuzzy approach, suggesting an algorithm, and demonstrating how the fuzzy linear fractional programming problem (FLFPP) can be answered without raising the arithmetic potency. Also, it introduces a technique that uses an optimal mean to convert MOLFPP to a single LFPP by modifying the symmetric fuzzy approach. A numeric sample is provided to clarify the qualification of the suggested approach and compare the results with other techniques, which are solved by using a computer application to test the algorithm of the above method, indicating that the results obtained by the fuzzy environment are promising.

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43

Wang, Chun-Feng, and Yan-Qin Bai. "Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method." Scientific Programming 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/3204368.

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This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

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44

Tantawy, Said. "An Iterative Method for Solving Linear Fraction Programming (LFP) Problem with Sensitivity Analysis." Mathematical and Computational Applications 13, no. 3 (December 1, 2008): 147–51. http://dx.doi.org/10.3390/mca13030147.

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45

Das, Sapan Kumar. "An approach to optimize the cost of transportation problem based on triangular fuzzy programming problem." Complex & Intelligent Systems 8, no. 1 (October 15, 2021): 687–99. http://dx.doi.org/10.1007/s40747-021-00535-2.

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AbstractIn this article, we address a fully fuzzy triangular linear fractional programming (FFLFP) problem under the condition that all the parameters and decision variables are characterized by triangular fuzzy numbers. Utilizing the computation of triangular fuzzy numbers and Lexicographic order (LO), the FFLFP problem is changed over to a multi-objective function. Consequently, the problem is changed into a multi-objective crisp problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP issues. Lead from real-life problems, a couple of mathematical models are considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

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46

Alhussein, Sabah F. Abd. "Dominant cell method for the best linear assignment." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012015. http://dx.doi.org/10.1088/1742-6596/2322/1/012015.

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Abstract This research aims to present a new method for best solution (B.S) of assignment problem (A.P) in linear programming (L.P). It is like the method by which one can find the (B.S) of transportation problem (T.P) using the dominant cells (D.C) that was called (D.C.T) method.Since the (A.P) is different from (T.P) in some features, the researcher has made changes in the conditions of (D.C.T) in order to determine the dominant cell for assignment (D.C.A). At last, the researcher has applied his method of (D.C.A) beside Hungarian method on several (A.P) and found it to be the best.

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47

Naseer, Muhammad Muzammal, and Wail A. Mousa. "Linear complementarity problem: A novel approach to design finite-impulse response wavefield extrapolation filters." GEOPHYSICS 80, no. 2 (March 1, 2015): S55—S63. http://dx.doi.org/10.1190/geo2014-0244.1.

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In this paper, the problem of complex valued finite impulse response (FIR) wavefield extrapolation filter design was considered as a linear complementarity problem (LCP). LCP is not an optimization technique because there is no objective function to optimize; however, quadratic programming, one of the applications of LCP, can be used to find an optimal solution for the 1D FIR wavefield extrapolation filter. Quadratic programs are an extremely important source of applications of LCP; in fact, several algorithms for quadratic programs are based on LCP. We found that FIR wavefield extrapolation filter design problem can be written as a quadratic program and then, finally, to an equivalent LCP. There are two families of algorithms available to solve for LCP: (1) direct (pivoting-based) algorithms and (2) indirect (iterative) algorithms. In this study, the LCP has been solved using direct and indirect algorithms. To show the effectiveness of the proposed method, the SEG/EAGE salt velocity model data have been extrapolated via wavefield extrapolation FIR filters designed by our LCP approach, which resulted with practically stable seismic images.

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48

Kowaliw, Taras, and René Doursat. "Bias-variance decomposition in Genetic Programming." Open Mathematics 14, no. 1 (January 1, 2016): 62–80. http://dx.doi.org/10.1515/math-2016-0005.

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AbstractWe study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the variance between runs is primarily due to initialization rather than the selection of training samples, (b) parameters can be reasonably optimized to obtain gains in efficacy, and (c) functions detrimental to evolvability are easily eliminated, while functions well-suited to the problem can greatly improve performance—therefore, larger and more diverse function sets are always preferable.

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49

Saha, Sumon Kumar, Md Rezwan Hossain, Md Kutub Uddin, and Rabindra Nath Mondal. "A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm." Open Journal of Optimization 04, no. 03 (2015): 74–86. http://dx.doi.org/10.4236/ojop.2015.43010.

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50

Syed, Mujahid N., and Uthman Baroudi. "Tactile Routing for Location Privacy Preservation in Wireless Sensor Networks: A Game Theoretic Approach." Sensors 22, no. 19 (September 27, 2022): 7334. http://dx.doi.org/10.3390/s22197334.

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Location Privacy Preservation (LPP) in Wireless Sensor Networks (WSNs) during the era of the Internet of things and smart systems is a critical element in the success of WSNs. LPP in WSN can be stated as: given a WSN with an adversary aiming to unravel the location of critical nodes of a WSN, the goal of the WSN manager is to enshroud the location of the critical nodes via routing and/or encryption mechanisms. Typical research in the LPP of WSN routing involves developing and/or estimating the performance of a fixed routing protocol under a given attack mechanism. Motivated by advancements in network softwarization, in this work, we propose an approach where the WSN manager as well as the WSN adversary can deploy multiple routing and attack mechanisms, respectively. Initially, the proposed approach is formulated as a repeated two-player zero-sum game. The formulation is further extended to handle multiple objectives and incomplete information in the game matrix. In this work, the multiple objectives are handled via the epsilon constraint method. The presence of incomplete information in the formulation is modeled as interval based uncertainty. To sum, the proposed formulation ultimately boils down to linear programming problems, which can be efficiently solved. Numerical case studies to showcase the applicability of the proposed approach are illustrated in this work. Finally, discussion on obtaining the required data from any given WSN, discussion and interpretation of the formulation’s results, and future research direction of the current work is presented.

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