Abstract

Estimation of distribution algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as genetic algorithms (GAs). This paper focuses on the problem of inexact graph matching which is NP-hard and requires techniques to find an approximate acceptable solution. This problem arises when a nonbijective correspondence is searched between two graphs. A typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images. EDA algorithms are well suited for this type of problems.

This paper proposes to use EDA algorithms as a new approach for inexact graph matching. Also, two adaptations of the EDA approach to problems with constraints are described as two techniques to control the generation of individuals, and the performance of EDAs for inexact graph matching is compared with the one of GAs.

Author Keywords: Inexact graph matching; Estimation of distribution algorithms; Bayesian networks; Genetic algorithms; Hybrid soft computing; Probabilistic reasoning; Evolutionary computing

Article Outline

1. Introduction

2. Graph matching as a combinational optimization problem with constraints

2.1. Representation of individuals

2.2. Definition of the fitness function

3. Estimation of distribution algorithms (EDAs)

3.1. Introduction

3.2. Notations

3.3. Bayesian networks

3.4. Existent EDA in combinatorial optimization

3.4.1. Without interdependencies

3.4.2. Pairwise dependencies

3.4.3. Multiple interdependencies

4. Proposed EDA approaches for inexact graph matching

4.1. Notation of EDAs applied to graph matching

4.2. Estimating the probability distribution

4.2.1. UMDA—univariate marginal distribution algorithm

4.2.2. MIMIC—mutual information maximization for input clustering

4.2.3. EBNA—estimation of Bayesian network algorithm

4.3. Adapting the simulation scheme

4.3.1. Techniques to obtain correct individuals

4.3.2. Controlling directly the simulation step

4.3.2.1. Last time manipulation (LTM)

4.3.2.2. All time manipulation (ATM)

4.3.3. Correction of individuals after the simulation step

4.3.4. Penalization of wrong individuals

5. Description of the experiment

5.1. The need to obtain correct individuals

5.2. Combining correction methods and algorithms

5.3. Experimental results

6. Conclusions and further work

Acknowledgements

References

Vitae