Abstract

The minimum weighted edge dominating set problem (MWEDS) generalizes both the weighted vertex cover problem and the problem of covering the edges of graph by a minimum cost set of both vertices and edges. In this paper, we propose a meta heuristic approach based on genetic algorithm and local search to solve the MWEDS problem. Therefore, the proposed method is considered as a memetic search algorithm which is called Memetic Algorithm with filtering scheme for minimum weighted edge dominating set, and called shortly (MAFS). In the MAFS method, three new fitness functions are invoked to effectively measure the solution qualities. The search process in the proposed method uses intensification scheme, called “filtering”, beside the main genetic search operations in order to achieve faster performance. The experimental results proves that the proposed method is promising in solving the MWEDS problem. (Less)

Highlights

  • The Minimum Edge Dominating Set (MEDS) is a subset of edges of minimum cardinality, where each edge is be in the edge dominating set, or adjacent to some edges in the edge dominating set [11], [12], [24]

  • We propose a memetic algorithm with filtering scheme for finding the minimum edge dominating set, called shortly Memetic Algorithm with Filtering Scheme (MAFS)

  • The results show that MAFS with (f it1) could not acquire the optimal total weight opw for all instances of the minimum weighted edge dominating set problem (MWEDS) problem especially when the number of edges increased proportionally with the graph size

Read more

Summary

INTRODUCTION

The Minimum Edge Dominating Set (MEDS) is a subset of edges of minimum cardinality, where each edge is be in the edge dominating set, or adjacent to some edges in the edge dominating set [11], [12], [24]. Meta-heuristics are powerful search methods which can be efficiently in providing satisfactory solutions to large and complex problems such as vertex cover [20], dominating set [14] and edge coloring [16] in a reasonable time. GAs are able to incorporate other techniques within its framework to produce a hybrid method that brings more promising one One direction of such hybridization is to use local search which can accelerate the search process in a pure GA. We propose a memetic algorithm with filtering scheme for finding the minimum edge dominating set, called shortly MAFS. It uses a 0-1 variable representation of solutions in searching for the MWEDS, and invokes three new fitness functions to measure the solution qualities.

PROBLEM FORMULATION AND RELATED WORKS
PROPOSED METHOD
Graph Representation
Solution Representation
Fitness Function
Genetic Operators
Local Search
Intensification Schemes
MAFS Algorithm
NUMERICAL EXPERIMENTS
Graph Generation
Comparison Results
RESULTS

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.