Multi-objective Genetic Algorithms for grouping problems

Abstract

Linear Linkage Encoding (LLE) is a convenient representational scheme for Genetic Algorithms (GAs). LLE can be used when a GA is applied to a grouping problem and this representation does not suffer from the redundancy problem that exists in classical encoding schemes. LLE has been mainly used in data clustering. One-point crossover has been utilized in these applications. In fact, the standard recombination operators are not suitable to be used with LLE. These operators can easily disturb the building blocks and cannot fully exploit the power of the representation. In this study, a new crossover operator is introduced for LLE. The operator which is named as group-crossover is tested on the data clustering problem and a very significant performance increase is obtained compared to classical one-point and uniform crossover operations. Graph coloring is the second domain where the proposed framework is tested. This is a challenging combinatorial optimization problem for search methods and no significant success has been obtained on the problem with pure GA. The experimental results denote that GAs powered with LLE can provide satisfactory outcomes in this domain, too.

A grouping hyper-heuristic framework: Application on graph colouring

“…Avanthay et al (2003) proposed a variable neighbourhood search algorithm for graph colouring problem. Studies in (Ülker et al, 2006;Ülker et al, 2008;Korkmaz, 2010) and (Kirovski and Potkonjak, 1998) apply generic GAs using some of the genetic representations discussed in section 2.1.1 to solve graph colouring problem.Ülker et al (2006) proposed special crossover operators for graph colouring, namely Lowest Index Max Crossover (LIMX), Greedy Partition Crossover Lowest Index (GPX-LI) and Greedy Partition Crossover Cardinality Based (GPX-CB). Külahçıoglu (2007) proposed two modified versions of the LLE representation which are Linear Linkage Encoding With Ending Node Links (LLE-e) and Linear Linkage Encoding With Backward Links (LLE-b), and both of them are tested using genetic operators.…”

“…It has been observed that the use of crossover operators are found to be very disruptive and tends to impair the search rather than guide it for grouping problems in (Falkenauer, 1998;Korkmaz, 2010). Additionally, the proposed framework performs single-point based search, hence, crossover operators are ignored.…”

“…In the table, the results denoted as RL-ILTA are the best colourings obtained by our framework. The results under M-LLE are obtained by a multi-objective genetic grouping algorithm described in (Korkmaz, 2010). Lowest Index Max Crossover (LIMX), Greedy Partition Crossover Lowest Index (GPX-LI) and Greedy Partition Crossover Cardinality Based (GPX-CB) graph colouring algorithms are proposed in (Ülker et al, 2006).…”

“…A redundant representation scheme which allows equivalent solutions yielding the same grouping creates a huge search space that might impair even the most powerful search algorithm. Many grouping approaches based on genetic algorithms (GAs) have been explored in the scientific literature providing various degrees of success (Falkenauer, 1998;Korkmaz, 2010). In previous studies, it has been observed that traditional operators are rather disruptive and, in many cases, counter productive, hence special operators that are tailored for grouping problems are needed.…”

Simultaneously construct IRT-based parallel tests based on an adapted CLONALG algorithm

“…The test construction problem is a combinatorial optimization problem [17,19,21,22], and now there is no polynomial time algorithm that exists for finding the optimal solution. An IRT-based test construction is composed of three steps.…”