25,774 research outputs found
A linear fractional optimization over an integer efficient set
Mathematical optimization problems with a goal function, have many applications in
various fields like financial sectors, management sciences and economic applications.
Therefore, it is very important to have a powerful tool to solve such problems when the
main criterion is not linear, particularly fractional, a ratio of two affine functions. In
this paper, we propose an exact algorithm for optimizing a linear fractional function over
the efficient set of a Multiple Objective Integer Linear Programming (MOILP) problem without
having to enumerate all the efficient solutions. We iteratively add some constraints, that
eliminate the undesirable (not interested) points and reduce, progressively, the
admissible region. At each iteration, the solution is being evaluated at the reduced
gradient cost vector and a new direction that improves the objective function is then
defined. The algorithm was coded in MATLAB environment and tested over different
instances randomly generated
Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem
The problem of optimizing a real valued function over an efficient set of the Multiple Objective Linear Fractional Programming problem (MOLFP) is an important field of research and has not received as much attention as did the problem of optimizing a linear function over an efficient set of the Multiple Objective Linear Programming problem
(MOLP).In this work an algorithm is developed that optimizes an arbitrary linear function over an integer efficient set of problem (MOLFP) without explicitly having to enumerate all the efficient solutions. The proposed method is based on a simple selection technique that improves the linear objective value at each iteration.A numerical illustration is included to explain the proposed method
Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem
The problem of optimizing a real valued function over an efficient set of the Multiple Objective Linear Fractional Programming problem (MOLFP) is an important field of research and has not received as much attention as did the problem of optimizing a linear function over an efficient set of the Multiple Objective Linear Programming problem
(MOLP).In this work an algorithm is developed that optimizes an arbitrary linear function over an integer efficient set of problem (MOLFP) without explicitly having to enumerate all the efficient solutions. The proposed method is based on a simple selection technique that improves the linear objective value at each iteration.A numerical illustration is included to explain the proposed method
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
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
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