A practicable contraction approach for the sum of the generalized polynomial ratios problem

Shen, Peiping; Zhu, Zeyi; Xiao, Chen

doi:10.1016/j.ejor.2019.03.014

Cited by 11 publications

(4 citation statements)

References 40 publications

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“…On the one hand, it is because the IQPP has a wide range of applications in management science, optimal control, financial optimization, engineering design, production plan, and so on [1,2]. On the other hand, it is because many nonlinear and nonconvex optimization problems can be transformed into this form of the IQPP [3][4][5][6], such as linear multiplicative programs problem, generalized linear multiplicative programs problem, and 0-1 programs problem. In addition, since the IQPP usually produces many local optimum solutions which are not global optimum, which puts forward many important theories and computational difficulties, that it is very necessary to propose a feasible and effective algorithm for globally solving the IQPP.…”

Section: Introductionmentioning

confidence: 99%

[Retracted] Branch‐and‐Reduction Algorithm for Indefinite Quadratic Programming Problem

2021

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This paper presents a rectangular branch-and-reduction algorithm for globally solving indefinite quadratic programming problem (IQPP), which has a wide application in engineering design and optimization. In this algorithm, first of all, we convert the IQPP into an equivalent bilinear optimization problem (EBOP). Next, a novel linearizing technique is presented for deriving the linear relaxation programs problem (LRPP) of the EBOP, which can be used to obtain the lower bound of the global optimal value to the EBOP. To obtain a global optimal solution of the EBOP, the main computational task of the proposed algorithm involves the solutions of a sequence of LRPP. Moreover, the global convergent property of the algorithm is proved, and numerical experiments demonstrate the higher computational performance of the algorithm.

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Section: Introductionmentioning

confidence: 99%

[Retracted] Branch‐and‐Reduction Algorithm for Indefinite Quadratic Programming Problem

2021

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“…This method was using an equivalent transformation and a new linear relaxation technique to found global solutions. Shen et al [14] proposed a practicable contraction algorithm to solve the sum of the generalized polynomial ratios problem. Liu et al [7] proposed a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale by using A output-space branch and bound algorithm.…”

Section: Introductionmentioning

confidence: 99%

An improved Evaporation Rate-Water Cycle Algorithm based Genetic Algorithm for solving generalized ratio problems

Veeramani

Sharanya

2021

RAIRO-Oper. Res.

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This paper presents an efficient metaheuristic approach for optimizing the generalized ratio problems such as the sum and multiplicative of linear or nonlinear ratio objective function with affine constraints. This paper focuses on the significance of hybrid techniques, which are implemented by using GA and ER-WCA to increase efficiency and robustness for solving linear and nonlinear generalized ratio problems. Initially, GA starts with an initial random population and it is processed by genetic operators. ER-WCA will observe and preserve the GAs fittest chromosome in each cycle and every generation. This Genetic ER-WCA algorithm is provided with better optimal solutions while solving constrained ratio optimization problems. Also, the effectiveness of the proposed genetic ER-WCA algorithm is analyzed while solving the large scale ratio problems. The results and performance of the proposed algorithm ensures a strong optimization and improves the exploitative process when compared to the other existing metaheuristic techniques. Numerical problems and applications are used to test the performance of the convergence and the accuracy of the approached method. The behavior of this Genetic ER-WCA algorithm is compared with those of evolutionary algorithms namely Neural Network Algorithm, Grey Wolf Optimization, ER-WCA, Water Cycle Algorithm, Firefly algorithm, Cuckoo search algorithm. The evaluated results show that the proposed algorithm increases the convergence and accuracy more than other existing algorithms.

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“…Their problem formulation was a SGP problem and the GP method has been used to solve their model. Shen et al (2019) proposed a practicable contraction approach for solving the sum of the generalized polynomial ratios problem with generalized 4 polynomial constraints. In their proposed approach, simple transformation and contraction strategies have been utilized to reduce the original nonconvex problem as a standard GP problem.…”

Section: Introductionmentioning

confidence: 99%

Global optimisation for a developed price discrimination model: A signomial geometric programming-based approach

Moradi

Omrani

Emrouznejad

2020

Journal of the Operational Research Society

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This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer objective is to maximize the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set up costs and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions.

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A practicable contraction approach for the sum of the generalized polynomial ratios problem

Cited by 11 publications

References 40 publications

[Retracted] Branch‐and‐Reduction Algorithm for Indefinite Quadratic Programming Problem

[Retracted] Branch‐and‐Reduction Algorithm for Indefinite Quadratic Programming Problem

An improved Evaporation Rate-Water Cycle Algorithm based Genetic Algorithm for solving generalized ratio problems

Global optimisation for a developed price discrimination model: A signomial geometric programming-based approach

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