Integer Linear Fractional Programming Problem Research Articles

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Reformulation of bilevel linear fractional/linear programming problem into a mixed integer programming problem via complementarity problem

The bilevel programming problem is a static version of the Stackelberg's leader follower game in which Stackelberg strategy is used by the higher level decision maker called the leader given the rational reaction of the lower decision maker called the follower. The bilevel programming problem (BLPP) is a two-level hierarchical optimisation problem and is non-convex. This paper deals with finding links between the bilevel linear fractional/linear programming problem (BF/LP), the generalised linear fractional complementarity problem (GFCP) and mixed integer linear fractional programming problem (MIFP). The (BF/LP) is reformulated as a (GFCP) which in turn is reformulated as an (MIFP). The method is supported with the help of a numerical example.

Generating the efficient set of MultiObjective Integer Linear plus Linear Fractional Programming Problems

The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn’t possess any convexity propriety. In this paper, we propose a method that generates the set of the efficient solutions of multiobjective integer linear plus linear fractional programming problem. Our method consists in Branch-and-Bound exploration combined with cutting plane technique that allows to remove from search inefficient solutions. The cutting plane technique takes into account the inefficiency of a solution in another problem that implies the inefficiency of that solution in our problem and uses this link to reduce the exploration’s domain.

Quadratic optimization over a discrete pareto set of a multi-objective linear fractional program

ABSTRACT In the present paper, an exact algorithm is proposed for maximizing a quadratic function over the efficient set of a multi-objective integer linear fractional programming problem. This method uses a branch and bound search in the decision space and a cutting plane which will significantly shorten the search. A sequence of quadratic programs are solved, the feasible region is iteratively partitioned with two branching constraints or reduced using a cutting plane. We establish theoretical results which prove the effectiveness of this exact method. For illustration, a numerical example and some computational experiments are reported.

On solving fuzzy rough multiobjective integer linear fractional programming problem

On solving fuzzy rough multiobjective integer linear fractional programming problem

A parametric approach to integer linear fractional programming: Newton’s and Hybrid-Newton methods for an optimal road maintenance problem

In this paper we study a parametric approach, one of the resolution methods for solving integer linear fractional programming (ILFP) problems in which all functions in the objective and constraints are linear and all variables are integers. We develop a novel complexity bound of Newton’s method applied to ILFP problems when variables are bounded. The analytical result for the worst-case performance shows that the number of iterations of Newton’s algorithm to find an optimal solution of the ILFP problem is polynomially bounded. We also propose a Hybrid-Newton algorithm and empirically show that it is relatively faster and more robust than the Newton algorithm under various data scenarios. To illustrate the applicability of our algorithm and provide concrete managerial prescriptions, we consider a case study of a road maintenance planning problem in Seoul, Korea. The results show that our fractional efficiency measure is capable of obtaining the maximum cost-efficient lifetime of a road given a limited maintenance budget.

Solving a Fully Rough Integer Linear Fractional Programming Problem

In this paper, a fully rough integer linear fractional programmingproblem is introduced, in which all coefficients and decision variablesin the objective function and the constraints are rough intervals. Theoptimal value of decision rough variables is rough interval. In order tosolve this problem, we will construct four crisp integer linear fractionalprogramming problems. Via these four crisp problems the roughoptimal integer solution is obtained. An illustrative numerical exampleis given for the developed theory.

Constrained integer fractional programming problem with box constraints

This paper deals with constrained integer linear fractional programming problem with box constraints whose integer solution is required to satisfy any h out of given set of l constraints. An iterative algorithm has been proposed for ranking and scanning of all the integer points of this problem to find an optimal solution. Numerical illustration is included in support of theory.

An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

We describe an improvement of Chergui and Moulaï’s method (2008) that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality) one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

English

English

Additive Algorithm for Solving 0-1 Integer Linear Fractional Programming Problem

In this paper, we present additive algorithm for solving a class of 0-1 integer linear fractional programming problems (0-1 ILFP) where all the coefficients at the numerator of the objective function are of same sign. The process is analogous to the process of solving 0-1 integer linear programming (0-1 ILP) problem but the condition of fathoming the partial feasible solution is different from that of 0-1 ILP. The procedure has been illustrated by two examples. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17066 Dhaka Univ. J. Sci. 61(2): 173-178, 2013 (July)

On Some Stability Notions of Multiobjective Integer Linear Fractional Programming Problem under Randomness

In this paper a solution algorithm to chance-constrained multiobjective integer linear fractional programming problem is suggested. We assume that there is randomness in the right-hand side of the constraints only and that the random variables are normally distributed. Some stability notions for the problem of concern are defined and characterized. An illustrative numerical example is provided to clarify the developed theory and the suggested solution algorithm.

A New Approach for Easy Computation by using ?-Matrix for solving Integer Linear Fractional Programming Problems

A New Approach for Easy Computation by using ?-Matrix for solving Integer Linear Fractional Programming Problems

On swarm-level resource allocation in BitTorrent communities

BitTorrent is a peer-to-peer computer network protocol for sharing content in an efficient and scalable way. Modeling and analysis of the popular private BitTorrent communities has become an active area of research. In these communities users are strongly incentivized to contribute their resources, i.e., to share their files. In BitTorrent terminology, users who have finished downloading files and stay online to share these files with others in the network are called seeders. The combination of seeders and downloaders of a file is called a swarm. In this paper we examine and evaluate the efficiency of the resource allocation of seeders in multiple swarms. This is formulated as an integer linear fractional programming problem. The evaluation is done on traces representing two existing BitTorrent communities. We find that in communities, particularly with low users-to-files ratio (which is typically the case), there is room for improvement

An Exact Method for a Discrete Multiobjective Linear Fractional Optimization

Integer linear fractional programming problem with multiple objective (MOILFP) is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.

Ranking in Integer Programming with Bounded Variables

An algorithm is developed which ranks the feasible solutions of an integer linear and linear fractional programming problems with bounded variables in decreasing order of objective values. Numerical illustration is also included.

Fuzzy weighted averages revisited

The fuzzy weighted average operations are common operations in risk and decision analysis. Based on Zadeh's extension principle, Dong and Wang (Fuzzy Sets and Systems 21 (1987) 183) proposed a FWA method: a method based on the α-cut representation of fuzzy sets and interval analysis. The FWA method provides a discrete approximation of the α-cuts of fuzzy weighted average. The FWA method has an exponential complexity. Subsequently, Liou and Wang (Fuzzy Sets and Systems 49 (1992) 307) proved that indeed the FWA method can be simplified to be a nonconstrainted linear fractional programming problem with lower and upper bounds for each of the variables. They proposed an improved algorithm, called IFWA, which is of O(N 2) complexity, where N is the number of decision variables in IFWA. Guh et al. (Comput. Math. Appl. 32 (8) (1996) 115) proposed a “max–min paired elimination method” (PFWA). They claimed their PFWA was of order N in complexity. Yet, the PFWA is a heuristic method lacking any proof of convergence. In 1997, Lee and Park proposed an algorithm (EFWA) which is of O(N log N) complexity. Most recently, Kao and Liu (Fuzzy Sets and Systems 120 (2001) 435) solved the FWA by transforming the fractional program into a linear program. In this note, we shall relate the IFWA framework with the nonconstrainted 0–1 integer linear fractional programming problem. In the mathematical programming literature, several O(N)-time algorithms have been existing, for instance, Robillard (Naval Res. Logist. Quart. 18 (1971) 47) and Hansen et al. (Math. Programming 52 (1991) 255). The algorithm of Hansen et al. will be presented for easy reference.

An algorithm for the integer linear fractional bilevel programming problem

The bilevel programming problem is an example of a two stage, non co-operative game in which the first player can influence but not control the actions of the second. In this paper we examine the case when the objective functions are linear fractional and present an algorithm for solving the integer case. We begin by solving the leader’s objective function and finding its integral optimal solution. Using the ranking in integer linear fractional programming problem, we are able to solve the given bilevel programming problem

A model of an urban transportation system formulated as a multiobjective mathematical programming problem under uncertainty

AbstractAn urban transportation system formulated in terms of a multiobjective mixed integer linear fractional programming (MOMILFP) problem under uncertainty is considered. The system is based on two means of public transportation i.e., trams and buses. One takes into account the factors of both passengers' and operator's concern, whose objectives are, generally, in conflict. The real uncertainty and imprecision of data is modeled by L‐R type fuzzy numbers. To solve the fuzzy MOMILFP problem an interactive method is utilized. As an illustration of that approach an application to Poznan's urban transportation system is presented.

Multi-criteria integer linear fractional programming problem

In the present paper an algorithm, based on cutting plane approach, is developed which seeks all the efficient r-tuples to multi-criteria integer linear fractional programming problem. A single objective integer linear fractional programming problem with any one of the objectives is considered and a cutting plane technique is used to this single objective programming problem. The cut developed in the present paper scans and truncates whole of an edge of the feasible region. The numerical illustrations are included in support of the algorithm developed.