Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem

Mahmoudi, Shadi; Lotfi, Shahriar

doi:10.1016/j.asoc.2015.04.020

Cited by 64 publications

(34 citation statements)

References 37 publications

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“…But there are certain issues related to exact algorithms are observed. The main problem with the exact algorithms is that most of the exact algorithms are able to execute small size graphs which have less than 100 vertices [6] [7].…”

Section: Exact and Approximate Algorithmmentioning

confidence: 99%

A Novel Exact Heuristic Graph Coloring Algorithm based on Finding Independent Set

Agrawal¹,

Chhabra²

2017

IJCA

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Vertex coloring is a graph coloring technique which has a wide application area to provide solution for many real world problems. The high computational complexity of graph coloring algorithm led the development of exact heuristic algorithm which can be executed in optimal time. This paper explores some existing graph coloring algorithms to propose taxonomy of exact graph coloring algorithm which is capable to execute large graphs also. This paper presented experimental result on DIMACS graph instances. KeywordsGraph Coloring, independent set, exact algorithm, approximate algorithm, sequential algorithm and parallel algorithms.

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Section: Exact and Approximate Algorithmmentioning

confidence: 99%

A Novel Exact Heuristic Graph Coloring Algorithm based on Finding Independent Set

Agrawal¹,

Chhabra²

2017

IJCA

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“…Metaheuristic methods are becoming one of the important tools for producing robust and efficient methods that compute approximate solutions of problems with high quality in reasonable computation time. Therefore, metaheuristic methods are applied for solving real-world optimization problems [18,19,24,30,33,42,43]. Among those metaheuristic algorithms, tabu search (TS) [18] is one of the most efficient memory-based methods.…”

Section: Introductionmentioning

confidence: 99%

A directed tabu search method for solving controlled Volterra integral equations

Ebrahimzadeh

Khanduzi

2016

Math Sci

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This paper proposes a pseudo-spectral scheme for obtaining approximate optimal control and state. This computational scheme represents the solution of the optimal control problem (OCP) by an mth degree Lagrange interpolating polynomial, using Legendre nodes. Then, OCP of non-linear Volterra integral equation is transformed into an optimization problem. Directed tabu search (DTS) method is utilized to derive the solutions of the optimal control and state as well as the optimal value of the objective function. In the DTS method, two neighborhood-local search strategies based on Nelder-Mead method and adaptive pattern search are applied. In addition, a tabu list with anti-cycling rules, the so-called tabu regions and semi-tabu regions are used. In addition, diversification and intensification search schemes are employed. DTS is able to converge to the global optimum solutions of a set of numerical examples. Therefore, some good balance between the diversification and intensification ensures a faster and efficient convergence to get quality solutions. Numerical examples are provided which confirm the reliability and efficiency of the proposed method. Moreover, a comparison is made with optimal solutions obtained by the other numerical methods in the literature.

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“…These algorithms are called greedy algorithms because of the algorithms choice the best validy selection for every operation step. The greedy algorithms generally provide effective and sufficient results for vertex coloring [15]. In this study, we described First Fit (FF) [19], Largest Degree Ordering (LDO) [19], Welsh and Powell (WP) [5], Incidence Degree Ordering (IDO) [19], Recursive Largest First (RLF) [20] and Degree of Saturation (DSATUR) [21] algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS [22].…”

Section: Introductionmentioning

confidence: 99%

“…Huerictic algorithms generally can be used for a problem with fewer numbers of _______________________________________________________________________________________________________________________________________________________________ vertices. On the other hand, for the complex graphs metahueristic algorithms can find better solutions [15]. Tabu Search (TS) Algorithm [16], Simulated Annealing (SA) Algorithm [17], Genetic Algorithm (GA) [7], Ant Colony (ACO) Algorithm [18], Cuckoo (COA) Algorithm [15] are some of the meta heueristic algorithms used for graph coloring problem.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, for the complex graphs metahueristic algorithms can find better solutions [15]. Tabu Search (TS) Algorithm [16], Simulated Annealing (SA) Algorithm [17], Genetic Algorithm (GA) [7], Ant Colony (ACO) Algorithm [18], Cuckoo (COA) Algorithm [15] are some of the meta heueristic algorithms used for graph coloring problem. When the vertices in a graph are colored by means of the greedy algorithms, the coloring issue is performed with selecting and coloring methods of algorithms.…”

Section: Introductionmentioning

confidence: 99%

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A Performance Comparison of Graph Coloring Algorithms

ASLAN¹

2016

ijisae

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Graph coloring problem (GCP) is getting more popular to solve the problem of coloring the adjacent regions in a map with minimum different number of colors. It is used to solve a variety of real-world problems like map coloring, timetabling and scheduling. Graph coloring is associated with two types of coloring as vertex and edge coloring. The goal of the both types of coloring is to color the whole graph without conflicts. Therefore, adjacent vertices or adjacent edges must be colored with different colors. The number of the least possible colors to be used for GCP is called chromatic number. As the number of vertices or edges in a graph increases, the complexity of the problem also increases. Because of this, each algorithm can not find the chromatic number of the problems and may also be different in their executing times. Due to these constructions, GCP is known an NP-hard problem. Various heuristic and metaheuristic methods have been developed in order to solve the GCP. In this study, we described First Fit (FF), Largest Degree Ordering (LDO), Welsh and Powell (WP), Incidence Degree Ordering (IDO), Degree of Saturation (DSATUR) and Recursive Largest First (RLF) algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS. The performances of the algorithms were compared as their solution qualities and executing times. Experimental results show that while RLF and DSATUR algorithms are sufficient for the GCP, FF algorithm is generally deficient. WP algorithm finds out the best solution in the shortest time on Register Allocation, CAR, Mycielski, Stanford Miles, Book and Game graphs. On the other hand, RLF algorithm is quite better than the other algorithms on Leighton, Flat, Random (DSJC) and Stanford Queen graphs.

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Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem

Cited by 64 publications

References 37 publications

A Novel Exact Heuristic Graph Coloring Algorithm based on Finding Independent Set

A Novel Exact Heuristic Graph Coloring Algorithm based on Finding Independent Set

A directed tabu search method for solving controlled Volterra integral equations

A Performance Comparison of Graph Coloring Algorithms

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