Bi-level Linear Fractional Programming Problems Research Articles

Centroid for Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients by Utilizing MO-Technique

This paper presents an efficient and straightforward methodology with less computational complexities to title the bi-level objective linear fractional programming problem with fuzzy interval coefficients (BILOLFPP with FIC). To construct the methodology, the concept of mean technique is utilized to tackle the fuzzy numbers in addition to adding to α = [mean (ai) , mean (bi)] , i = 1, …, n, then. Accordingly, the fuzzy programming issue is converted into a single objective linear fractional programming problem (SOLFPP with FIC) by the utilize of weight function. The fuzzy technique has significant structural transform metamorphosis during the recent decades. Numerous to mention introduced have been undertaken to explanation fuzzy methodology for linear, non-linear programming issues. While, the previous finding that introduced have been conflicting, recent studies of competitive situations indicate that LFPP with fuzzy interval coefficients (LFPP with FIC) has an advantageous effect mostly on comparison situation. One of the suggestions which we found is interval approximations, closed interval approximation of sequential fuzzy number for resolving fuzzy number LFPP without changing it to a crisp issue. A new variant of modified simplex methodology is studied here just for resolving fuzzy number LFPP utilizing fuzzy arithmetic. Consequently, fuzzy representation of some important theories of fuzzy LFPP has been reproved. A fuzzy LFPP with FIC is worked out as numerical examples illustrate to the suggested methodology. On iterative processes, it decreases the overall processing time to explain, the modified simplex methodology for solving BILLFPP with FIC with out to crisp by taking numerical examples and compare with Nasseri, Verdegay and Mahmoudi methodology changing it to a crisp issue [9].

Solving bi-level linear fractional programming problems with fuzzy interval coefficients using game matrix

Solving bi-level linear fractional programming problems with fuzzy interval coefficients using game matrix

A Novel Technique for Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients

A Novel Technique for Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients

Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients Using Game Matrix

Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients Using Game Matrix

A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems

ABSTRACT We propose a new two-level vertex-searching algorithm framework that finds a global optimal solution to the continuous bilevel linear fractional programming problem over a compact polyhedron, in which both the upper and the lower objectives are linear fractional. Our solution method adopts the vertex-searching approach on the polyhedron, and the search space is determined by the set of candidates of optimal base to the lower level problem. In order to search base, a modified enumerative scheme, that is a new upper bound filter scheme inserted into the classical enumerative scheme, is proposed. The main solution procedure is designed on solving a sequence of upper and lower level mathematical programs; instead of a single-level problem reformulation approach, which is popularly and widely used in literature. An extension on general upper level objective functions such as quasiconvex/quasiconcave for the proposed vertex-searching approach is discussed. Numerical experiments show that our algorithm leads us to a global optimum. We conclude that our proposed algorithm framework has the simplest solution procedure and has potential efficiency advantages, which may reduce the complexity of enumerative schemes for medium or large-scale problems, while comparing with existing global algorithms such as the Kth-best algorithm (a two-level vertex-searching algorithm) and the single-level duality-based reformulation algorithm (a single-level vertex-searching algorithm).

A global optimization algorithm for solving the bi-level linear fractional programming problem

In this paper, we obtain the solution to bi-level linear fractional programming problem (BLFP) by means of an optimization algorithm based on the duality gap of the lower level problem. In our algorithm, the bi-level linear fractional programming problem is transformed into an equivalent single level programming problem by forcing the dual gap of the lower level problem to zero. Then, by obtaining all vertices of a polyhedron, the single level programming problem can be converted into a series of linear fractional programming problems. Finally, the performance of the proposed algorithm is tested on a set of examples taken from the literature.

Bilevel Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach

This paper presents fuzzy goal programming approach for bilevel linear fractional programming problem with a single decision maker at the upper level and a single decision maker at the lower level. Here, each level has single objective function, which are fractional in nature and the system constraints are linear functions. In the proposed approach, we first construct fractional membership functions by determining individual best solution of the objective functions subject to the system constraints. The fractional membership functions are then transformed into equivalent linear membership functions by first order Taylor polynomial series. Since the objectives of both level decision makers are potentially conflicting in nature, a possible relaxation of both level decisions is considered for avoiding decision deadlock. Then, the fuzzy goal programming approach is used for achieving highest degree of each of the membership goals to the maximum possible by minimizing the negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is solved and Euclidean distance function is used to obtain compromise optimal solution. General Terms Bi-level programming.

Weighting method for bi-level linear fractional programming problems

In this paper we consider the solution of a bi-level linear fractional programming problem (BLLFPP) by weighting method. A non-dominated solution set is obtained by this method. In this article decision makers (DMs) provide their preference bounds to the decision variables that is the upper and lower bounds to the decision variables they control. We convert the hierarchical system into scalar optimization problem (SOP) by finding proper weights using the analytic hierarchy process (AHP) so that objective functions of both levels can be combined into one objective function. Here the relative weights represent the relative importance of the objective functions.

A note on ‘bilevel linear fractional programming problem’

In this note, the bilevel linear fractional programming problem is considered. We examine a previous paper published by Thirwani and Arora [Cah. CERO 35 (1993) 135]. We show that several proofs in that paper are incorrect and provide alternative proofs.