1. Torcs Simulator Presented by Galina Volkinshtein and Evgenia Dubrovsky

2. Overview  Torcs  Motivation  Optimization Algorithm  Results and Comparison

3. Torcs  Car Setup Optimization Competition @ EvoStar 2010.  The purpose is to find the best car setup.  The contest is divided into an optimization phase and an evaluation phase.  During the optimization phase, the optimization algorithm will be applied to search for the best parameter setting.  During the evaluation phase, the best solution will be scored according to the distance covered in a fixed amount of game time.

4. Overview  Torcs  Motivation  Optimization Algorithm  Results and Comparison

5. Motivation  The winner of the competition evostar2010 in April -Jorge Muñoz used a MOEA.  MOEA - Multiobjective evolutionary algorithm.  MOEAs:  Aggregation based – non-dominated solutions are obtained by a weighted sum of the individual objective functions.  Dominance based – use the dominance relation as a measure of the fitness of each individual.

6. Overview  Torcs  Motivation  Optimization Algorithm  Results and Comparison

7. NSGA-II Introduction.  The ranking-based evolutionary algorithm NSGA-II combines elitism and a mechanism to distribute the solutions as much as possible.  Multiobjective optimization elitism requires that some portion of the non-dominated solutions will survive.

8. NSGA-II Introduction (cont'd). -II  NSGA-II is based on dominance count.  Multiobjective optimization populations can search many local optima so a finite population tends to settle on a single good optimum, even if other equivalent optima exist.  Special mechanisms are required to prevent this occurring.  Niche induction methods promote the simultaneous sampling of several different optima by favoring diversity in the population.

9. NSGA-II Introduction (cont'd).  Individuals close to one another mutually decrease each other's fitness.  Isolated individuals are given a greater chance of reproducing, favoring diversification.

10. NSGA-II Components.  Dominance. Only non-dominated solutions are kept.  Crowding. Density less crowded regions are preferred to crowded regions.

11. NSGA-II Flow.  NSGA-II classifies a population in several classes which are called fronts.  The number of classes varies from generation to generation and the members in each class are equivalent.  That is, it cannot be stated which individual is better.  This classification which is called non-dominated sorting is implemented as follows.

12. NSGA-II Non-dominated Sorting.  All non-dominated individuals are classified into one category and assigned a dummy fitness value or rank.  These classified individuals are ignored and from the remaining members of the population the non-dominated individuals are selected for forming the next layer.  This process continues until all members are classified.  Individuals of the first layer have the highest fitness while members of the last layer are assigned the smallest fitness.  All individuals from the first layer produce more copies in the next generation.

13. NSGA-II Crowding distance.  An estimation of the density of solutions surrounding each member is calculated using the crowding distance:  The population is sorted in ascending order.  The solutions with the smallest and largest value are assigned a very large distance estimate to guarantee that they will be selected in the next generation.  All other solutions are assigned a distance value equal to the absolute difference in the function values of two adjacent solutions.

14. NSGA-II Elitism.  The elitism is used by combining together the population of children Q_t and the parent population P_t at generation t together.  A non-dominated sorting is applied and a new population is formed.  A population of children Q_t+1 from P_t+1 is formed using a binary crowded tournament selection, crossover and mutation.

15. Overview  Torcs  Motivation  Optimization Algorithm  Results and Comparison

16. Results and Comparison E-track instead of Poli-track

17. Results and Comparison trackElitist Optclient TOP SPEEDDISTANCE RACEDGenerationsTOP SPEEDDISTANCE RACEDGenerations CG track21746971414230618 Dirt-31255021513433312 E-Track 41965993517840219

18. The End Any Questions ?

19. The End Thank you ;)‏