A memetic algorithm for the weighted feedback vertex set problem. Issue 4 (11th November 2014)

• Record Type: Journal Article
• Authors: Carrabs, Francesco; Cerrone, Carmine; Cerulli, Raffaele
• Is Part Of: Networks. Volume 64:Issue 4(2014:Dec.)
• Page Start: 339
• Page End: 356
• Publication Date: 2014-11-11
• Subjects: Network analysis (Planning) -- Periodicals; 658.4032
• DOI: 10.1002/net.21577
• Languages: English
• ISSNs: 0028-3045

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Given an undirected and vertex weighted graph <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2t6mn89x" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00283045:media:net21577:net21577-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>V</mml:mi><mml:mo>, </mml:mo><mml:mi>E</mml:mi><mml:mo>, </mml:mo><mml:mi>w</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>, the Weighted Feedback Vertex Set Problem consists of finding the subset <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2t6mn8xv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00283045:media:net21577:net21577-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> of vertices, with minimum weight, whose removal results in an acyclic graph. Finding the minimum feedback vertex set in a graph is an important combinatorial problem that has a variety of real applications. In this article, we introduce a memetic algorithm for this problem. We propose an efficient greedy procedure that quickly generates chromosomes with specific characteristics and a wise application of recent local search procedures based on <italic>k</italic>‐diamonds. Computational results show that the proposed algorithm outperforms the effectiveness of two other metaheuristics recently proposed in the literature for this problem. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(4), 339–356 2014</p> </abstract>