Convergence of a hill-climbing genetic algorithm for graph matching

Abstract This paper presents a convergence analysis for the problem of consistent labelling using genetic search. The work builds on a recent empirical study of graph matching where we showed that a Bayesian consistency measure could be efficiently optimised using a hybrid genetic search procedure which incorporated a hill-climbing step. In the present study we return to the algorithm and provide some theoretical justification for its observed convergence behaviour. The novelty of the analysis is to demonstrate analytically that the hill-climbing step significantly accelerates convergence, and that the convergence rate is polynomial in the size of the node-set of the graphs being matched.

[1]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[2]  David L. Waltz,et al.  Understanding Line drawings of Scenes with Shadows , 1975 .

[3]  Robert M. Haralick,et al.  A Metric for Comparing Relational Descriptions , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Alan L. Yuille,et al.  Twenty Questions, Focus of Attention, and A*: A Theoretical Comparison of Optimization Strategies , 1997, EMMCVPR.

[5]  Patrick Henry Winston,et al.  The psychology of computer vision , 1976, Pattern Recognit..

[6]  Francesco Palmieri,et al.  Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part II: Analysis of the diversification role of crossover , 1994, IEEE Trans. Neural Networks.

[7]  Fred W. Glover,et al.  Tabu search for graph partitioning , 1996, Ann. Oper. Res..

[8]  Edwin R. Hancock,et al.  A Bayesian interpretation for the exponential correlation associative memory , 1998, Pattern Recognit. Lett..

[9]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[10]  Andrew K. C. Wong,et al.  Entropy and Distance of Random Graphs with Application to Structural Pattern Recognition , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Edwin R. Hancock,et al.  Gauging relational consistency and correcting structural errors , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  Edwin R. Hancock,et al.  Genetic algorithm parameter sets for line labelling , 1997, Pattern Recognit. Lett..

[13]  Fred W. Glover,et al.  Tabu Search for Nonlinear and Parametric Optimization (with Links to Genetic Algorithms) , 1994, Discret. Appl. Math..

[14]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[16]  Yong Gao,et al.  Comments on "Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. I. Basic properties of selection and mutation" [and reply] , 1998, IEEE Trans. Neural Networks.

[17]  Edwin R. Hancock,et al.  Structural Matching with Active Triangulations , 1998, Comput. Vis. Image Underst..

[18]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Josef Kittler,et al.  Discrete relaxation , 1990, Pattern Recognit..

[20]  Edwin R. Hancock,et al.  Relational matching with dynamic graph structures , 1995, Proceedings of IEEE International Conference on Computer Vision.

[21]  Basilis Gidas,et al.  A Renormalization Group Approach to Image Processing Problems , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Josef Kittler,et al.  A Bayesian interpretation for the Hopfield network , 1993, IEEE International Conference on Neural Networks.

[23]  Fred W. Glover,et al.  Ejection Chains, Reference Structures and Alternating Path Methods for Traveling Salesman Problems , 1996, Discret. Appl. Math..

[24]  Edwin R. Hancock,et al.  Structural Matching by Discrete Relaxation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  KumarVipin.  Algorithms for constraint-satisfaction problems , 1992 .

[26]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[27]  Edwin R. Hancock,et al.  Inexact graph matching using genetic search , 1997, Pattern Recognit..

[28]  Edwin R. Hancock,et al.  Multiple line-template matching with the EM algorithm , 1997, Pattern Recognit. Lett..

[29]  Alan L. Yuille,et al.  Generalized Deformable Models, Statistical Physics, and Matching Problems , 1990, Neural Computation.

[30]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[31]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.