An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS$_o$ performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS$_o$ that is suitable for solving the minimum weight dominating set problem. The application of RLS$_o$ in graph mining is also briefly demonstrated

An ACO Algorithm for Effective Cluster Head Selection

This paper presents an effective algorithm for selecting cluster heads in mobile ad hoc networks using ant colony optimization. A cluster in an ad hoc network consists of a cluster head and cluster members which are at one hop away from the cluster head. The cluster head allocates the resources to its cluster members. Clustering in MANET is done to reduce the communication overhead and thereby increase the network performance. A MANET can have many clusters in it. This paper presents an algorithm which is a combination of the four main clustering schemes- the ID based clustering, connectivity based, probability based and the weighted approach. An Ant colony optimization based approach is used to minimize the number of clusters in MANET. This can also be considered as a minimum dominating set problem in graph theory. The algorithm considers various parameters like the number of nodes, the transmission range etc. Experimental results show that the proposed algorithm is an effective methodology for finding out the minimum number of cluster heads.Comment: 7 pages, 5 figures, International Journal of Advances in Information Technology (JAIT); ISSN: 1798-2340; Academy Publishers, Finlan

The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation

A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem approximately by a local algorithm of generalized leaf removal and by a message-passing algorithm of belief propagation. These algorithms can construct near-optimal dominating sets or even exact minimum dominating sets for random digraphs and also for real-world digraph instances. We further develop a core percolation theory and a replica-symmetric spin glass theory for this problem. Our algorithmic and theoretical results may facilitate applications of dominating sets to various network problems involving directed interactions.Comment: 11 pages, 3 figures in EPS forma

Hybrid behavioural-based multi-objective space trajectory optimization

In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behaviorism, combinedwith the decomposition of the solutions pace was tested on a set of standard multi-objective optimization problems and on a simple but representative case of space trajectory design

A hybrid genetic algorithm and inver over approach for the travelling salesman problem

This article posted here with permission of the IEEE - Copyright @ 2010 IEEEThis paper proposes a two-phase hybrid approach for the travelling salesman problem (TSP). The first phase is based on a sequence based genetic algorithm (SBGA) with an embedded local search scheme. Within the SBGA, a memory is introduced to store good sequences (sub-tours) extracted from previous good solutions and the stored sequences are used to guide the generation of offspring via local search during the evolution of the population. Additionally, we also apply some techniques to adapt the key parameters based on whether the best individual of the population improves or not and maintain the diversity. After SBGA finishes, the hybrid approach enters the second phase, where the inver over (IO) operator, which is a state-of-the-art algorithm for the TSP, is used to further improve the solution quality of the population. Experiments are carried out to investigate the performance of the proposed hybrid approach in comparison with several relevant algorithms on a set of benchmark TSP instances. The experimental results show that the proposed hybrid approach is efficient in finding good quality solutions for the test TSPs.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/E060722/1

Multi agent collaborative search based on Tchebycheff decomposition

This paper presents a novel formulation of Multi Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent (individualistic moves). In this novel formulation the selection process is based on a combination of Tchebycheff scalarization and Pareto dominance. Furthermore, while in the previous implementation, social actions were applied to the whole population of agents and individualistic actions only to an elite sub-population, in this novel formulation this mechanism is inverted. The novel agent-based algorithm is tested at first on a standard benchmark of difficult problems and then on two specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi objective optimization algorithms. The results demonstrate that this novel agent-based search has better performance with respect to its predecessor in a number of cases and converges better than the other state-of-the-art algorithms with a better spreading of the solutions

Web Usage Mining with Evolutionary Extraction of Temporal Fuzzy Association Rules

In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets' boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries. The GA-based approach is enhanced from previous work by including a graph representation and an improved fitness function. A comparison of the GA-based approach with a traditional approach on real-world Web log data discovered rules that were lost with the traditional approach. The GA-based approach is recommended as complementary to existing algorithms, because it discovers extra rules. (C) 2013 Elsevier B.V. All rights reserved