1. Linkage Tree Genetic Algorithm Wei-Ming Chen

2.  The Linkage Tree Genetic Algorithm, Dirk Thierens, 2010  Pairwise and Problem-Specific Distance Metrics in the Linkage Tree Genetic Algorithm, Martin Pelikan, Mark W. Hauschild, Dirk Thierens, 2011 Papers

3.  The Linkage Tree Genetic Algorithm  Dirk Thierens  GECCO 2010

4. GA mechanism Initialization EvaluationSelection Crossover Mutation Replacement Until termination

5.  Construct the variables to a tree  Hierarchical Clustering  Assign each variable to a single cluster.  Repeat until one cluster left  Join two nearest clusters c i and c j into c ij Introduction

6.  Entropy H :  Distance D : Clustering

7.  Choose a pair of chromosome  Crossover mask : apart chromosome into two subsets  Replacement : If one of the offspring is better than both of the parents Genetic Algorithm

8. Example (1/4)

9. Example (2/4)

10. Example (3/4)

11. Example (4/4)

12.  Initial : Create initial population of size N  Repeat  Build the linkage tree  For every pair  while the tree is not fully traversed  traversed a step and set crossover mask  do crossover  do replacement if necessary Algorithm

13.  Test problems  Trap function  NK landscape  Result  The problems are solved in polynomial time  Similar with ECGA and DSMGA Result

14.  Pairwise and Problem-Specific Distance Metrics in the Linkage Tree Genetic Algorithm  Martin Pelikan, Mark W. Hauschild, Dirk Thierens  GECCO 2011

15.  To improves the quality of the solution  In first iteration, do local search before proceeding with the first iteration  Based on single-bit neighborhoods  choose the step which improves the quality of the solution most  Until find the local optimum local search

16.  Original :  Pairwise matrix :  Problem-Specific Metric  decomposable problem composed of m subproblems  prefer decompositions which minimize the sizes of subsets  If two variables in the same subset, the distance of them is 1 Speed up

17.  Test problems  Trap-5, Trap-6, Trap 7  NK landscape  2D spin glass  Result  The problems are solved in polynomial time  Trap functions : almost same  NK landscape : Original < Pairwise < Problem  2D spin glass : Original < Problem < Pairwise Result

18.  LTGA :  Small population size  Solve all the problems in low-order polynomial time  Future work :  Problem-specific metrics  Construct all the variables to only one tree ?  Change the minimum mask size ? Conclusion