Solving Quadratic Fractional Programming Problem

Sulaiman, Najmaddin A.; Nawkhass, Maher A.

doi:10.14419/ijamr.v2i2.838

Cited by 7 publications

(2 citation statements)

References 7 publications

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“…Ibaraki et al [15] presented two algorithms for solving the quadratic fractional programming problem, one is the parameter programming technique based on quadratic programming, the other is Dinkelbach-based method [8]. Suleimann and Nawkhass [38] improved the simplex method by using the idea of Wolfe methods, which were utilized to solve the problem QCQFP. Tantawy [40] studied the feasible direction method, which also solved the QCQFP.…”

Section: Introductionmentioning

confidence: 99%

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Zhang¹,

Gao²,

Huang³

2024

JCM

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The mixed-integer quadratically constrained quadratic fractional programming (MIQC-QFP) problem often appears in various fields such as engineering practice, management science and network communication. However, most of the solutions to such problems are often designed for their unique circumstances. This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP. We first convert the MIQC-QFP into an equivalent generalized bilinear fractional programming (EIGBFP) problem with integer variables. Secondly, we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively, and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator. After that, combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure, an efficient algorithm for solving MIQCQFP globally is proposed. Finally, a series of test problems are given to illustrate the effectiveness, feasibility and other performance of this algorithm.

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Section: Introductionmentioning

confidence: 99%

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Zhang¹,

Gao²,

Huang³

2024

JCM

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“…To evaluate the function in the equation, a problem of minimizing a nonconvex quadratic function subject to two quadratic constraints is solved by an iterative algorithm. Suleiman and Nawkhass [25] considered the QFP problem with linear constraints and presented an algorithm based on Wolfe's method [26] and a new modified simplex approach. In addition, they [27] considered this problem with a linear denominator and solved it by a new modified simplex method.…”

Section: Introductionmentioning

confidence: 99%

Efficient algorithms for solving nonlinear fractional programming problems

Dolatnezhadsomarin

Khorram

Pourkarimi

2019

Filomat

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In this paper, an efficient algorithm based on the Pascoletti-Serafini scalarization (PS) approach is proposed to obtain almost uniform approximations of the entire Pareto front of bi-objective optimization problems. Five test problems with convex, non-convex, connected, and disconnected Pareto fronts are applied to evaluate the quality of approximations obtained by the proposed algorithm. Results are compared with results of some algorithms including the normal constraint (NC), weighted constraint (WC), Benson type, differential evolution (DE) with binomial crossover, non-dominated sorting genetic algorithm-II (NSGA-II), and S metric selection evolutionary multiobjective algorithm (SMS-EMOA). The results confirm the effectiveness of the presented bi-objective algorithm in terms of the quality of approximations of the Pareto front and CPU time. In addition, two algorithms are presented for approximately solving fractional programming (FP) problems. The first algorithm is based on an objective space cut and bound method for solving convex FP problems and the second algorithm is based on the proposed bi-objective algorithm for solving nonlinear FP problems. In addition, several examples are provided to demonstrate the performance of these suggested fractional algorithms.

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A new modified simplex method to solve quadratic fractional programming problem and compared it to a traditional simplex method by using pseudoaffinity of quadratic fractional functions

Suleiman¹,

Nawkhass²

2013

ams

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In this paper, we defined a new modified simplex method to solve quadratic fractional programming problem (QFPP) and suggested an algorithm for it. The algorithm of usual simplex method is also reported. The special case for this problem was solved by Converting objective function to pseudoaffinity of quadratic fractional functions (PQFF) to a linear programming problem to be solved by simplex method. Then the result is compared with a result, which obtained by new modified simplex method. These methods demonstrated by numerical examples. This work confirms that our techniques is valid and can be used to solve this particular type of QFPP.

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Solving Quadratic Fractional Programming Problem

Cited by 7 publications

References 7 publications

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Efficient algorithms for solving nonlinear fractional programming problems

A new modified simplex method to solve quadratic fractional programming problem and compared it to a traditional simplex method by using pseudoaffinity of quadratic fractional functions

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