Solving Graph Coloring Problem Using an Enhanced Binary Dragonfly Algorithm

2019 ◽  
Vol 10 (3) ◽  
pp. 23-45 ◽  
Author(s):  
Karim Baiche ◽  
Yassine Meraihi ◽  
Manolo Dulva Hina ◽  
Amar Ramdane-Cherif ◽  
Mohammed Mahseur
Keyword(s):  
Graph Coloring ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Random Parameters ◽  
Dragonfly Algorithm ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Graph Coloring Problem ◽  
Np Hard Problem ◽  
The Right

The graph coloring problem (GCP) is one of the most interesting classical combinatorial optimization problems in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. In this article, the authors propose a new enhanced binary dragonfly algorithm to solve the graph coloring problem. The binary dragonfly algorithm has been enhanced by introducing two modifications. First, the authors use the Gaussian distribution random selection method for choosing the right value of the inertia weight w used to update the step vector (∆X). Second, the authors adopt chaotic maps to determine the random parameters s, a, c, f, and e. The aim of these modifications is to improve the performance and the efficiency of the binary dragonfly algorithm and ensure the diversity of solutions. The authors consider the well-known DIMACS benchmark graph coloring instances to evaluate the performance of their algorithm. The simulation results reveal the effectiveness and the successfulness of the proposed algorithm in comparison with some well-known algorithms in the literature.

A Modified Binary Crow Search Algorithm for Solving the Graph Coloring Problem

2020 ◽  
Vol 11 (2) ◽  
pp. 28-46 ◽  
Author(s):  
Yassine Meraihi ◽  
Mohammed Mahseur ◽  
Dalila Acheli
Keyword(s):  
Graph Coloring ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Distribution Method ◽  
Local Optima ◽  
Coloring Problem ◽  
Graph Coloring Problem ◽  
Np Hard Problem ◽  
The Right

The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve the graph coloring problem. First, the binary crow search algorithm is obtained from the original crow search algorithm using the V-shaped transfer function and the discretization method. Second, we use chaotic maps to choose the right values of the flight length (FL) and the awareness probability (AP). Third, we adopt the Gaussian distribution method to replace the random variables used for updating the position of the crows. The aim of these contributions is to avoid the premature convergence to local optima and ensure the diversity of the solutions. To evaluate the performance of our algorithm, we use the well-known DIMACS benchmark graph coloring instances. The simulation results reveal the efficiency of our proposed algorithm in comparison with other existing algorithms in the literature.

A Binary Cuckoo Search Algorithm for Graph Coloring Problem

2014 ◽  
Vol 5 (3) ◽  
pp. 42-56 ◽  
Author(s):  
Halima Djelloul ◽  
Abdesslem Layeb ◽  
Salim Chikhi
Keyword(s):  
Combinatorial Optimization ◽  
Graph Coloring ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Hybrid Approaches ◽  
Graph Coloring Problem

The Graph Coloring Problem (GCP) is one of the most interesting, studied, and difficult combinatorial optimization problems. That is why several approaches were developed for solving this problem, including exact approaches, heuristic approaches, metaheuristics, and hybrid approaches. This paper tries to solve the graph coloring problem using a discrete binary version of cuckoo search algorithm. To show the feasibility and the effectiveness of the algorithm, it has used the standard DIMACS benchmark, and the obtained results are very encouraging.

scholarly journals The Hybrid ColorAnt-RT Algorithms and an Application to Register Allocation

2015 ◽  
Vol 18 (55) ◽  
pp. 81
Author(s):  
Mauro Mulati, ◽  
Carla Lintzmayer ◽  
Anderson Da Silva
Keyword(s):  
Ant Colony Optimization ◽  
Graph Coloring ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Register Allocation ◽  
Ant Colony ◽  
Frequency Assignment ◽  
It Use ◽  
Combinatorial Optimization Problems ◽  
Ant Colony Optimization Algorithms

Ant Colony Optimization is a metaheuristic used to create heuristic algorithms to find good solutions for combinatorial optimization problems. This metaheuristic is inspired on the effective behavior present in some species of ants of exploring the environment to find and transport food to the nest. Several works have proposed using Ant Colony Optimization algorithms to solve problems such as vehicle routing, frequency assignment, scheduling and graph coloring. The graph coloring problem essentially consists in finding a number k of colors to assign to the vertices of a graph, so that there are no two adjacent vertices with the same color. This paper presents the hybrid ColorAnt-RT algorithms, a class of algorithms for graph coloring problems which is based on the Ant Colony Optimization metaheuristic and uses Tabu Search as local search. The experiments with ColorAnt-RT algorithms indicate that changing the way to reinforce the pheromone trail results in better results. In fact, the results with ColorAnt-RT show that it is a promising option in finding good approximations of k. The good results obtained by ColorAnt-RT motivated it use on a register allocation based on Ant Colony Optimization, called CARTRA. As a result, this paper also presents CARTRA, an algorithm that extends a classic graph coloring register allocator to use the graph coloring algorithm ColorAnt-RT. CARTRA minimizes the amount of spills, thereby improving the quality of the generated code.

scholarly journals Message passing for the coloring problem: Gallager meets Alon and Kahale

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Sonny Ben-Shimon ◽  
Dan Vilenchik
Keyword(s):  
Message Passing ◽  
Optimization Problems ◽  
Decoding Algorithm ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Message Passing Algorithm ◽  
Graph Coloring Problem ◽  
Message Passing Algorithms ◽  
International Audience ◽  
Threshold Regime

International audience Message passing algorithms are popular in many combinatorial optimization problems. For example, experimental results show that \emphsurvey propagation (a certain message passing algorithm) is effective in finding proper k-colorings of random graphs in the near-threshold regime. In 1962 Gallager introduced the concept of Low Density Parity Check (LDPC) codes, and suggested a simple decoding algorithm based on message passing. In 1994 Alon and Kahale exhibited a coloring algorithm and proved its usefulness for finding a k-coloring of graphs drawn from a certain planted-solution distribution over k-colorable graphs. In this work we show an interpretation of Alon and Kahale's coloring algorithm in light of Gallager's decoding algorithm, thus showing a connection between the two problems - coloring and decoding. This also provides a rigorous evidence for the usefulness of the message passing paradigm for the graph coloring problem.

scholarly journals Exact Algorithms for the Graph Coloring Problem

2018 ◽  
Vol 25 (4) ◽  
pp. 57
Author(s):  
Alane Marie De Lima ◽  
Renato Carmo
Keyword(s):  
Graph Coloring ◽  
Independent Sets ◽  
Exact Algorithms ◽  
Coloring Problem ◽  
The Third ◽  
Graph Coloring Problem ◽  
Np Hard Problem ◽  
Definition Of ◽  
Maximal Independent Sets ◽  
Exact Version

The graph coloring problem is the problem of partitioning the vertices of a graph into the smallest possible set of independent sets. Since it is a well-known NP-Hard problem, it is of great interest of the computer science finding results over exact algorithms that solve it. The main algorithms of this kind, though, are scattered through the literature. In this paper, we group and contextualize some of these algorithms, which are based in Dynamic Programming, Branch-and-Bound and Integer Linear Programming. The algorithms for the first group are based in the work of Lawler, which searches maximal independent sets on each subset of vertices of a graph as the base of his algorithm. In the second group, the algorithms are based in the work of Brelaz, which adapted the DSATUR procedure to an exact version, and in the work of Zykov, which introduced the definition of Zykov trees. The third group contains the algorithms based in the work of Mehrotra and Trick, which uses the Column Generation method.

A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

2021 ◽  
pp. 1-11
Author(s):  
Zhaocai Wang ◽  
Dangwei Wang ◽  
Xiaoguang Bao ◽  
Tunhua Wu
Keyword(s):  
Time Complexity ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Vertex Coloring ◽  
Intelligent Computing ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Computing Algorithm ◽  
Vertex Coloring Problem ◽  
Dna Algorithm

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

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