Hierarchical problem solving with the linkage tree genetic algorithm

Hierarchical problems represent an important class of nearly decomposable problems. The concept of near decomposability is central to the study of complex systems. When little a priori information is available, a black box problem solver is needed to optimize these hierarchical problems. The solver should be able to learn linkage information, and to preserve and test partial solutions at different levels in the hierarchy. Two well known benchmark functions - shuffled Hierarchical If-And-Only-If (HIFF) and shuffled Hierarchical Trap (HTRAP) functions - exemplify the challenges posed by hierarchical problems. Standard genetic algorithms are unable to solve these problems, and specific methods, like SEAM and hBOA, have been designed to address them. In this paper, we investigate how the recently developed Linkage Tree Genetic Algorithm (LTGA) performs on these hierarchical problems. We compare LTGA with SEAM and hBOA on HIFF and HTRAP functions. Results show that, although LTGA is a simple algorithm compared to SEAM and hBOA, it nevertheless is a very efficient, reliable, and scalable algorithm for solving the randomly shuffled versions of HIFF and HTRAP, two hard, hierarchical problems.

[1]  Shlomo Moran,et al.  Optimal implementations of UPGMA and other common clustering algorithms , 2007, Inf. Process. Lett..

[2]  J. Pollack,et al.  A computational model of symbiotic composition in evolutionary transitions. , 2003, Bio Systems.

[3]  Dirk Thierens,et al.  Pairwise and problem-specific distance metrics in the linkage tree genetic algorithm , 2011, GECCO '11.

[4]  Dirk Thierens,et al.  The Linkage Tree Genetic Algorithm , 2010, PPSN.

[5]  13th Annual Genetic and Evolutionary Computation Conference, GECCO 2011, Proceedings, Dublin, Ireland, July 12-16, 2011 , 2011, GECCO.

[6]  David E. Goldberg,et al.  A new method for linkage learning in the ECGA , 2009, GECCO '09.

[7]  Dirk Thierens,et al.  Predetermined versus learned linkage models , 2012, GECCO '12.

[8]  Dirk Thierens,et al.  Optimal mixing evolutionary algorithms , 2011, GECCO '11.

[9]  Dirk Thierens,et al.  Linkage neighbors, optimal mixing and forced improvements in genetic algorithms , 2012, GECCO '12.

[10]  Dirk Thierens,et al.  The roles of local search, model building and optimal mixing in evolutionary algorithms from a bbo perspective , 2011, GECCO.

[11]  Dirk Thierens,et al.  Hierarchical Genetic Algorithms , 2004, PPSN.

[12]  D. Goldberg,et al.  Escaping hierarchical traps with competent genetic algorithms , 2001 .

[13]  David E. Goldberg,et al.  Hierarchical Problem Solving and the Bayesian Optimization Algorithm , 2000, GECCO.

[14]  David E. Goldberg,et al.  Population sizing for entropy-based model building in discrete estimation of distribution algorithms , 2007, GECCO '07.

[15]  Jordan B. Pollack,et al.  Symbiotic Combination as an Alternative to Sexual Recombination in Genetic Algorithms , 2000, PPSN.

[16]  Dirk Thierens Linkage tree genetic algorithm: first results , 2010, GECCO '10.

[17]  Dirk Thierens,et al.  On the complexity of hierarchical problem solving , 2005, GECCO '05.

[18]  David E. Goldberg,et al.  Hierarchical Bayesian Optimization Algorithm , 2006, Scalable Optimization via Probabilistic Modeling.

[19]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[20]  David E. Goldberg,et al.  A hierarchy machine: Learning to optimize from nature and humans , 2003, Complex..

[21]  Franz Rothlauf,et al.  Evaluation-Relaxation Schemes for Genetic and Evolutionary Algorithms , 2004 .

[22]  Dirk Thierens,et al.  More concise and robust linkage learning by filtering and combining linkage hierarchies , 2013, GECCO '13.