Search

Bandwidth consecutive multicoloring problem is also known as a b-coloring problem. Let G = (V, E) be a graph where V is the set of vertices and E is the set of edges. Let each vertex v of V has a positive integer weight b (v) and each edge (v, w) of E has a non-negative integer weight b (v, w). A bandwidth consecutive multicoloring of a graph is a problem of assigning b (v) consecutive positive integers to each vertex v of V in such a manner that the difference between all the integers of vertex v and all the integers of vertex w is greater than b (v, w). The maximum integer assigned in this coloring is called the span of the coloring. The b-coloring is the problem of minimizing this span. No metaheuristic is proposed for general graphs so far for this problem till date as it is strongly NP-hard. In this paper, we proposed three heuristics for the problem including a greedy randomized adaptive search procedure (GRASP). The efficiency of these algorithms is tested on benchmark graphs and their performance is compared among themselves. Experimental results showed that among all three proposed heuristics, GRASP performed well for the given problem. [ABSTRACT FROM AUTHOR]

This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal k-coloring of that fuzzy graph such that the degree of the sum of incompatible vertices and edges is minimized. TFGC is also converted into an equivalent binary programming problem and solved using a CPLEX solver. The performance of both methods is examined on randomly generated fuzzy graphs and computational results are reported. An application based on TFGC is also explored and solved using both proposed methods. [ABSTRACT FROM AUTHOR]

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples. [ABSTRACT FROM AUTHOR]