1. Euclidean TSP EA Pseudo Code

2. What is a Euclidean TSP? 1 2 4 5 3 c ij 2 = (x i – x j ) 2 + (y i – y j ) 2

3. Individual Representation Permutation of the cities What permutation represents this tour? Solutions? 1 2 4 5 3 143523521412534

4. Permutation Creation 1. Create 1. Create array 2. Number 2. Number in-order 3. Loop 3. Loop i = 1 to N 1.j 1.j = random ≥ i 2.Swap(A[i], 2.Swap(A[i], A[j]) 123456423156436125 [Skiena1997], Generating Permutations

5. Individual Datastructure Generic solution is usually to have two data members –Genotype –Fitness This way fitness is stored once calculated

6. Fitness Calculation Sum up all the edge lengths Requires many slow sqrt() calls

7. Program Requirements Read from a parameter file Execute one or more runs Create a log file

8. Required Parameters (world) TSP world (logfile) Log file (popsize) Population size (offsize) Offspring per generation (maxeval) Maximum evaluations (runs) Number of runs (seed) Random seed

9. Setup Open configuration file Parse values into variables Read world file describing TSP world Seed random number generator

10. Random Number Generator Is a datastructure Updates internal variables every time a random number is requested Needs to be passed around by reference Seed only once Use the Mersenne Twister –http://www-personal.engin.umich.edu/~wagnerr/MersenneTwister.html http://www-personal.engin.umich.edu/~wagnerr/MersenneTwister.html

11. TSP World File Format Line 1: “TSP” Line 2: Number of cities Lines 3+: x-coordinate y-coordinate –Two ascii integers per line separated by a space

12. EA Run –Pass in all configuration data –Make sure the random number generator is passed by reference Allocate your data structures –population[popcount] –offspring[offcount] Initialize population with random individuals evalcount = popsize While(evalcount < maxevals) –For # of children Select two parents by two binary tournaments Recombine using cut-and-crossfill Mutate offspring Evaluate child’s fitness (evalcount++) –Sort and elitist survival selection

13. Parent Selection Create four random numbers a, b, c, d Parent 1 –max_fitness(population[a], population[b]) Parent 2 –max_fitness(population[c], population[d])

14. Recombination (“cut-and-crossfill”) 436125243156 Child 436215 [Eiben2003], p26

15. Recombination (“cut-and-crossfill”) 1. Used = boolean array of all false’s 2. XPoint = random from 1 to N 3. For (i = 1 to XPoint) 1.Child[i] = ParentA[i] 2.Used[Child[i]] = true 4. j = 0 5. For (i = XPoint to N) 1.While(Used[ParentB[j]]) 1. j++ 2.Child[i] = ParentB[j]

16. Mutation i = random from 1 to N j = random from 1 to N Swap(Child[i], Child[j]) Child 436215 [Eiben2003], p26

17. Survival Selection Combine populations SortCrop

18. TSPView Demo

19. References [Eiben2003] A.E. Eiben and J.E. Smith. Introduction to Evolutionary Computing. Spring-Verlag, Berlin Heidelberg, 2003, ISBN 3-540-40184-9. [Skiena1997] Steven S. Skiena. The Algorithm Design Manual. Springer-Verlag, New York, 1997. http://www2.toki.or.id/book/AlgDesignManual/ http://www2.toki.or.id/book/AlgDesignManual/