A new memetic algorithm based on cellular learning automata for solving the vertex coloring problem

Mirsaleh, Mehdi Rezapoor; Meybodi, Mohammad Reza

doi:10.1007/s12293-016-0183-4

Cited by 23 publications

(4 citation statements)

References 36 publications

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“…One such kind of specific type of graph & its coloring solution reported for partition graph coloring problem [28]. Several more techniques based on the type graph & its uses in application area have discussed and found suitable for getting the graph coloring based solutions for specific class of problems [29][30].…”

Section: Algorithmmentioning

confidence: 99%

An Algorithm Based on Heap of Binary Search Tree to Solve Graph Coloring Problem

Shukla¹,

Bharti²,

Garg³

2019

IJRTE

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Graph coloring problem is one of most frequent studied problem in the graph theory due to its uses in different area of applications like simulation of biological networks, communication networks, register allocation and many more. This problem involves the coloring of the vertices of the given a graph G (V, E) with number of available colors in such a manner that adjacent vertices must assign colors different with each other. In this paper we present a hybrid approach to assign the colors to vertices of the given graph that is based on adjacency matrix and search tree data structure. The coloring process for a particular vertex in the graph will done by getting the feasible colors available in the color list. The feasible colors that may be assigned to a vertex, retrieved from the vertex-color binary search tree generated initially for available colors. The proposed solution for the graph coloring problem is efficient in terms of its running time complexity and it will work without affecting its complexity for any kind of graph.

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Section: Algorithmmentioning

confidence: 99%

An Algorithm Based on Heap of Binary Search Tree to Solve Graph Coloring Problem

Shukla¹,

Bharti²,

Garg³

2019

IJRTE

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“…Several other methodologies have also find in literature to solve the problem of coloring of graphs that involves: improved cuckoo optimization technique [28], using coupled oscillatory networks [29], using local anti-magic labeling in the graph [30], cellular learning automata based solution [31], solving graph-b coloring problem using hybrid genetic algorithms [32], Douglas-Rachford Algorithm based solution [33] for graph coloring problem and branch-and-cut algorithm for the equitable coloring problem [34].…”

Section: Algorithmmentioning

confidence: 99%

A Linked List-Based Exact Algorithm for Graph Coloring Problem

Shukla¹,

Bharti²,

Garag³

2019

RIA

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Graph coloring is an NP-hard problem. There is ample room to further reduce the number of colors being used under the strict constraints of the problem. This paper proposes an algorithm that stores the information of the vertices in the graph, together with the color and the next address field of a node in a singly linked list. The coloring of a particular vertex is decided on the content of color field of node corresponding to the searched vertex for coloring. The adjacency matrix of the graph was adopted to select the feasible color to be allocated to a vertex, without violating the constraints for coloring of the vertices in the graph. The proposed algorithm was tested on DIMACS benchmark graphs, using Python 3.6. The results show that our algorithm produced the result with the optimal number of colors required to solve the problem. This research provides a new strategy to find the optimal coloring solution for each type of graphs.

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“…Several works describe successful applications of MA to different hard optimization problems concerned with path planning or graph structures optimizations. Examples are path planning for mobile robots with bacterial MA [12], traveling car renter problem [13] or vertex coloring problem [14]. Other combinatorial optimization problems, such as job-shop scheduling problem [15] or knapsack problem [16], have also been successfully approached by MA.…”

Section: Memetic Algorithmsmentioning

confidence: 99%

Baldwin effect and Lamarckian evolution in a memetic algorithm for Euclidean Steiner tree problem

Bereta

2018

Memetic Comp.

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The study is concerned with the Baldwin effect and Lamarckian evolution in a memetic algorithm for Euclidean Steiner tree problem (ESTP). The main aim is to examine the importance of the proposed local search procedures for the ability of the algorithm to find solutions to ESTP. Two local search procedures are proposed as a part of an evolutionary algorithm for ESTP, and the effect of their use is carefully analyzed. The correction procedure modifies the given chromosome so that it satisfies the degree and angle conditions in ESTP. The improvement procedure actively adds new Steiner points to the evaluated solution. The modified solutions are accepted with varying probability, leading to a spectrum of algorithms with a Baldwin effect on one end and Lamarckian evolution on the other. The results are carefully analyzed using proper statistical procedures (Friedman test and post-hoc procedures). To further check the ability of the proposed algorithm to find the optimal or near optimal solutions, results for problems from OR-Lib are provided.

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A new memetic algorithm based on cellular learning automata for solving the vertex coloring problem

Cited by 23 publications

References 36 publications

An Algorithm Based on Heap of Binary Search Tree to Solve Graph Coloring Problem

An Algorithm Based on Heap of Binary Search Tree to Solve Graph Coloring Problem

A Linked List-Based Exact Algorithm for Graph Coloring Problem

Baldwin effect and Lamarckian evolution in a memetic algorithm for Euclidean Steiner tree problem

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