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

An Algorithm For Solving Multiple Objective Integer Linear Programming Problem

In the present paper a complete procedure for solving Multiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one

A possibilistic optimization over an integer efficient set within a fuzzy environment

Optimizing a linear function over the efficient set of a Multiple Objective Integer Linear Programming (MOILP) problem is known as a difficult problem to deal with, since a discrete efficient set is generally not convex and not explicitly known. Such problem becomes more and more difficult when parameters are defined with uncertainty. In this work, we deal with problems of this type for which parameters are imprecise and are assumed to be trapezoidal fuzzy numbers. The method is based on possibility and necessity measures introduced in the literature by D. Dubois and H. Prade

A genetics algorithms for optimizing a function over the integer efficient set

In this paper, we propose an algorithm called Directional Exploration Genetic Algorithm (DEGA) to resolve a function (Phi) over the efficient set of a multi-objective integer linear programming problem (MOILP). DEGA algorithm belongs to evolutionary algorithms, which operate on the decision space by choosing the fastest improving directions that improve the objectives functions and (Phi) function. Two variants of this algorithm and a basic version of the genetic algorithm (BVGA) are performed and implemented in Python. Several benchmarks are carried out to evaluate the algorithm\u27s performances and interesting results are obtained and discussed

Multiple objective optimization Applied to Speech enhancement problem

Enhancement of speech corrupted by broadband noise is subject of interest in many applications. For several years, the investigation of methods of denoising the vocal signal has yielded very satisfactory results, but certain problems and questions still remain. The term speech quality in speech enhancement is associated with clarity and intelligibility. So, one of these issues is to reach a compromise between noise reduction, signal distortion and musical noise. In this paper, we studied one of the classical techniques based on the spectral subtraction developed by Boll and improved by Berouti where two parameters α and β to control the effects of the distortion and the musical noise are introduced. However, the choice on these parameters (α and β) remains empirical. Our works is to find a compromise between these two parameters to obtain an optimal solution depending on the environment, the unknown noise and its level. Moreover, we propose in this paper, an algorithm based on bi-objective approach precisely Particle Swarm Optimization (PSO) technique in association with speech enhancement technique proposed by Berouti et al. Comparative results show that the performance of our proposed method with several types of noise, depending on the environment and on various noise levels, are better than those of spectral subtraction methods of Boll or Berouti

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