Applied Soft Computing 59 (2017) 644–658 Contents lists available at ScienceDirect Applied Soft Computing j ourna l ho me page: www.elsevier.com/locate /asoc Two population-based optimization algorithms for minimum weight connected dominating set problem Zuleyha Akusta Dagdeviren a,∗ , Dogan Aydin b , Muhammed Cinsdikici a a International Computer Institute, Ege University, 35100, Izmir, Turkey b Computer Engineering Department, Dumlupinar University, 43000, Kutahya, Turkey a r t i c l e i n f o Article history: Received 10 September 2016 Received in revised form 10 June 2017 Accepted 12 June 2017 Available online 22 June 2017 Keywords: Minimum weight connected dominating set Hybrid genetic algorithm Population-based iterated greedy algorithm Optimization heuristics Undirected graph a b s t r a c t Minimum weight connected dominating set (MWCDS) is a very important NP-Hard problem used in many applications such as backbone formation, data aggregation, routing and scheduling in wireless ad hoc and sensor networks. Population-based approaches are very useful to solve NP-Hard optimization problems. In this study, a hybrid genetic algorithm (HGA) and a population-based iterated greedy (PBIG) algorithm for MWCDS problem are proposed. To the best of our knowledge, the proposed algorithms are the first population-based algorithms to solve MWCDS problem on undirected graphs. HGA is a steady- state procedure which incorporates a greedy heuristic with a genetic search. PBIG algorithm refines the population by partially destroying and greedily reconstructing individual solutions. We compare the performance of the proposed algorithms with other greedy heuristics and brute force methods through extensive simulations. We show that our proposed algorithms perform very well in terms of MWCDS solution quality and CPU time. © 2017 Elsevier B.V. All rights reserved. 1. Introduction The dominating set (DS) 1 and its variants are popular graph theoretic structures which are used in many applications such as clustering, backbone formation and intrusion detection in wireless ad hoc and sensor networks (WASNs) [1–3], gateway placement in wireless mesh networks [4], deployment of wavelength divi- sion multiplexing in optical networks [5], information retrieval for multi-document summarization [6] and query selection for obtain- ing data from web databases [7]. For a given undirected graph (UG) G (V, E)where all edges are bidirectional, V is the set of vertices and E is the set of edges; the minimum dominating set (MDS) problem is to find a subset of ver- tices D ⊆ V where each node in V \ D is adjacent to at least one node in D. The nodes in D and V \ D are called as dominators and dominatees, respectively. Finding the minimum set of dominators for a given undirected graph is an NP-Hard problem. An example application of MDS problem is clustering a WASN where domina- tors are cluster heads and dominatees are cluster members. If D is a DS and each node pair (v i ,v j ) ∈ D has at least a path that consists of only nodes in D, then the D is defined as the connected dominating set (CDS). CDS is a very useful structure for backbone formation in ∗ Corresponding author. E-mail address: zuleyhaakusta@gmail.com (Z.A. Dagdeviren). 1 The acronyms used throughout the text are explained in Table 1. WASNs [2] such as data collected from dominatees are relayed by the dominators through CDS to the sink node. Similar to the MDS problem, finding the minimum CDS (MCDS) is an NP-Hard problem. Energy efficient operation is of utmost importance in WASNs since generally nodes are battery-powered. It is a well-known fact that the communication is the dominant factor of the energy consump- tion [8]. Hence, the nodes in the CDS backbone may exhaust their batteries very earlier than others since they are responsible for car- rying the data transmission. One of the solutions of this problem is selecting the nodes with high energies as dominators. To achieve this, a weighted connected dominating set (WCDS) backbone has been applied [9] in which the total weight of CDS is aimed to be minimized. Same as its unweighted version, finding the minimum WCDS (MWCDS) is in NP-Hard complexity class. There are approximation algorithms [9,10] based on heuristics to solve the MWCDS problem on unit disk graphs (UDGs) which are used to model WASNs. Although UDG can be an appropriate model to use the inherent geometrical properties of the ideal wire- less communication, the transmission range of a node may not be circular in some cases such as a network area that includes obstacles [11]. Hence, UG is a better model in this situation. In this paper, we propose two population-based optimization algorithms for MWCDS problem on UG. To the best of our knowl- edge, these are the first population-based algorithms proposed for MWCDS on UGs. Our first approach for solving this problem is a hybrid genetic algorithm (HGA). This algorithm is a heuristic based steady-state genetic algorithm which gives favorable results for http://dx.doi.org/10.1016/j.asoc.2017.06.023 1568-4946/© 2017 Elsevier B.V. All rights reserved.