```Linkage Tree Genetic Algorithm
Wei-Ming Chen
Papers
 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
 The Linkage Tree Genetic Algorithm
 Dirk Thierens
 GECCO 2010
GA mechanism
Evaluation
Selection
Initialization
Replacement
Until termination
Mutation
Crossover
Introduction
 Construct the variables to a tree
 Hierarchical Clustering
 Assign each variable to a single cluster.
 Repeat until one cluster left
 Join two nearest clusters
ci and cj into cij
Clustering
 Entropy H :
 Distance D :
Genetic Algorithm
 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
Example (1/4)
Example (2/4)
Example (3/4)
Example (4/4)
Algorithm
 Initial : Create initial population of size N
 Repeat
 For every pair

while the tree is not fully traversed

traversed a step and set crossover mask

do crossover

do replacement if necessary
Result
 Test problems
 Trap function
 NK landscape
 Result
 The problems are solved in polynomial time
 Similar with ECGA and DSMGA
 Pairwise and Problem-Speciﬁc Distance
Metrics in the Linkage Tree Genetic
Algorithm
 Martin Pelikan, Mark W. Hauschild,
Dirk Thierens
 GECCO 2011
local search
 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
Speed up
 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
Result
 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
Conclusion
 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 ?
```