An unconstrained binary quadratic programming for the maximum independent set problem

For a given graph G = (V, E) the maximum independent set problem is to find the largest subset of pairwise nonadjacent vertices. We propose a new model which is a reformulation of the maximum independent set problem as an unconstrained quadratic binary programming, and we resolve it afterward by means of a genetic algorithm. The efficiency of the approach is confirmed by results of numerical experiments on DIMACS benchmarks

Solving the graph coloring problem via hybrid genetic algorithms

Let G = (V,E) an undirected graph, V corresponds to the set of vertices and E corresponds to the set of edges, we focus on the graph coloring problem (GCP), which consist to associate a color to each vertex so that two vertices connected do not possess the same color. In this paper we propose a new hybrid genetic algorithm based on a local search heuristic called DBG to give approximate values of χ(G) for GCP. The proposed algorithm is evaluated on the DIMACS benchmarks and numerical results show that the proposed approach achieves highly competitive results, compared with best existing algorithms

Gene selection

Gene expression data (DNA microarray) enable researchers to simultaneously measure the levels of expression of several thousand genes. These levels of expression are very important in the classification of different types of tumors. In this work, we are interested in gene selection, which is an essential step in the data pre-processing for cancer classification. This selection makes it possible to represent a small subset of genes from a large set, and to eliminate the redundant, irrelevant or noisy genes. The combinatorial nature of the selection problem requires the development of specific techniques such as filters and Wrappers, or hybrids combining several optimization processes. In this context, we propose two hybrid approaches (RBPSO-1NN and FBPSO-SVM) for the gene selection problem, based on the combination of the filter methods (the Fisher criterion and the ReliefF algorithm), the BPSO metaheuristic algorithms and the Backward algorithm using the classifiers (SVM and 1NN) for the evaluation of the relevance of the candidate subsets. In order to verify the performance of our methods, we have tested them on eight well-known microarray datasets of high dimensions varying from 2308 to 11225 genes. The experiments carried out on the different datasets show that our methods prove to be very competitive with the existing works

A New Steganographic Method For Grayscale Image Using Graph Coloring Problem

Statistical steganalysis schemes detect the existence of secret information embedded by steganography. The χ 2 detection and Regular-Singular (RS)-attack methods are two well known statistical steganalysis schemes used against LSB (least significant bit) steganography. The embedded message length can be estimated accurately by these two steganalysis schemes. For secret communication, the resistance of steganography against steganalysis is very important for information security. To avoid the enemy’s attempts, the statistical features between stego-images and cover images should be as similar as possible for better resistance to steganalysis. To ensure the security against the RS and χ 2 analysis, we presents in this paper a new steganographic method based on graph coloring problem (GCP). Before embedding the secret message in LSB (least significant bit) of the cover image, we use a (GCP) algorithm to locate the optimal positions of the pixels in the cover image. Thus, the existence of the secret message is hard to be detected by the RS analysis. Meanwhile, better visual quality can be achieved by the proposed algorithm. The experimental results demonstrate the proposed algorithm’s effectiveness in resistance to steganalysis with better visual qualit