Solving the Graph Bisection Problem with Imperialist Competitive
Algorithm
Hodais Soltanpoor
1
, Shirin Nozarian
1
and Majid VafaeiJahan
2
1
Young Researchers Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2
Department of Computer Engineering, Islamic Azad University, Mashhad Branch, Iran
Abstract. Imperialist competitive algorithm is a method in complementary calculations which is dealing
with finding an optimum response in different optimization problems. Though its initial versions are
introduced in order to solve the optimization problems, it is used in discrete problems, too. The Binary
discrete method is offered in this article on the basis of mentioned algorithm to solve the problem of Graph
Bisection. Graph Bisection means dividing the graph into two almost equal sections, with minimum
connection between them. Considering the results of other suggested methods and their comparison with
other optimization algorithms, such as genetic algorithm, particles swarm optimization, ant colony, tabu
search, and simulated annealing, it can be deduced that the Binary discrete imperialist competitive algorithm
performs better in different tests. Results cleared that this algorithm performs around 11% better than other
compared methods.
Keyword: Problem of Graph Bisection, Genetic Algorithm, Tabu Search, Simulated Annealing, Ant
Colony, Imperialist Competitive Algorithm.
1. Introduction
This article is dealing with solving the problem of graph bisection and comparing the genetic algorithm
(GA), ant colony (ACO), tabu search (TS), simulated annealing (SA), and imperialist competitive algorithm
(ICA). Dividing the graph is one of the most important problems which can be applied in different fields.
Some applications like scientific calculations, VLSI designing, tasks schedules, and geographical data
systems.
The problem can be defined as follow: dividing the graph into P sections almost equally, with minimum
connection between them. The efficient execution of most parallel algorithms usually needs a solution for
dividing the graph. As the apexes represent the calculations and the connections represent the transacted data.
Dividing the calculation graph into P sections is one solution for offering the tasks to P processors. Since this
division relates an equal number of calculation tasks to each processor, the performance will be balanced.
And since division makes the connection cut minimum, the costs of relating the processors will be the least,
too.
The problem of graph division classifies in NP-Complete problems. But many algorithms are designed
which offer appropriate divisions for that. Spectrum division methods [1] offer proper divisions of the graph,
but they are calculated complicatedly. Geometric division methods [2, 3] are quick, but offer weaker
divisions. Furthermore, geometric methods are applicable only when coordinating data are available. After
them, a new method is offered to divide the graph. These methods, known as Graph multi layer division, are
moderately complicated for calculation [1, 4, 5, 6]. Though the method of multilayer is quicker than
spectrum division, the paralleling in this method is more useful. Up to now, lots of researches are
accomplished to design the parallel algorithms for dividing the graphs [7, 8, 9].
Dividing the graph into two equal sections, with minimum connection between the apexes in different
sections has been one of the points in dividing the graph. Regarding the growing usage of graph bisection
problem, and also heuristic methods in solving complicated problems, this article is dealing with solving the
problem by genetic algorithm, ant colony, tabu search, simulated annealing, and imperialist competitive
algorithm.
2012 International Conference on System Engineering and Modeling (ICSEM 2012)
IPCSIT vol. 34 (2012) © (2012) IACSIT Press, Singapore
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