A Linearization to the Sum of Linear Ratios Programming Problem

Abstract

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.

Healing Herbs (Belladonna, Yarrow): The Scholarly Denominative Model and the Folk Model

“…a1ii On the other hand, we find the term Achillea in various plant species: Achillea cartilaginea, Achillea collina, Achillea crithmifolia, Achillea distans, Achillea neilreichii, Achillea pannonica, Achillea ptarmica, Achillea shurii, Achillea setacea 27 .…”

A new efficient approach to tackle multi objective linear fractional problem with flexible constraints

“…It was proven that the solution obtained from the algorithm is an efficient solution for the main problem. It should be mentioned that in each step, the method proposed by Borza and Rambely [4] was used to change the S-LFPP into the linear programming problem. Four examples were solved to illustrate the method and comparisons were made with competitive methods of [18,24,31], genetic algorithm (GA), and gamultiobj documentation.…”

“…If (Y, λ) ∈ Ω, then Y λ ∈ S. Theorem 2.6. [4]. Let (Y * , λ * ) is the optimal solution of the 7, then X * = Y * λ * is the global optimal solution of the (5).…”

“…Afterward the weighted sum technique is applied to reach a single objective programming problem of the kind S-LFPP. Subsequently, we modify the recent work of Borza and Rambely [4] and then employ it to tackle the single objective programming problem. It is demonstrated that the outcomes of this research are efficient to the main problem.…”