1. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 1 International Graduate School of Dynamic Intelligent Systems Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm (T. Shibata and T. Fukuda) Chuan-Kang Ting

2. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 2 International Graduate School of Dynamic Intelligent Systems Path Planning for Multiple Robots 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 2 1 4 3 6 5 8 7 9

3. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 3 International Graduate School of Dynamic Intelligent Systems Selfish-planning 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10

4. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 4 International Graduate School of Dynamic Intelligent Systems Collision & Deadlock 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 Selfish Coordination

5. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 5 International Graduate School of Dynamic Intelligent Systems Setting Subject: path planning of multiple robots Purpose: optimize the path of each robot to avoid collisions, reduce waiting time, and decrease tour length Conditions: no global communication between robots but local sense to surrounding Method: apply genetic algorithm to optimize motion planning of each robot

6. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 6 International Graduate School of Dynamic Intelligent Systems Evolution in Nature Chromosomes Mutation Crossover Mating Survival of the Fittest

7. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 7 International Graduate School of Dynamic Intelligent Systems Genetic Algorithms Genetic Algorithm () { t := 0; init_population P(t); evaluate P(t); do { P’(t) := select_parents P(t); crossover P’(t); mutate P’(t); evaluate P’(t); P(t+1) := survive P(t), P’(t) t := t + 1; } while not terminated; } InitializationInitialization MutationMutation Evaluate & Survive Evaluate CrossoverCrossover SelectionSelection Terminated?

8. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 8 International Graduate School of Dynamic Intelligent Systems Chromosome - background MAKLINK –Construct the available free space between obstacles –Based on free links: whose two ends are either corners of polygonal obstacles or a point on the working-space boundary –Every node can allow only one robot at the same time

9. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 9 International Graduate School of Dynamic Intelligent Systems Chromosome - representation Chromosome –An encoded expression of potential solutions. (usually in the form of string) Path representation –Encode the order of visiting points as a string Example –0-1-2-6-9-11-15-17-22-25-26 –0-4-8-10-15-20-23-26

10. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 10 International Graduate School of Dynamic Intelligent Systems Chromosome - population Population – a set of chromosomes Chromosomes are generated randomly. i.e. the population contains a set of random solutions Each robot is equipped with one population 0-1-2-6-9-11-15-17-22-25-26 0-4-8-10-15-20-23-26

11. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 11 International Graduate School of Dynamic Intelligent Systems Operator - Crossover Exchange information from two selected chromosomes –Crossover point: the first identical node in both parents –Example: Parent1: 0-1-2-6-9-11- 15 -17-22-25-26 Parent2: 0-4-8-10- 15 -20-23-26 Child1: 0-1-2-6-9-11-15-20-23-26 Child2: 0-4-8-10-15-17-22-25-26

12. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 12 International Graduate School of Dynamic Intelligent Systems Operator - Mutation Mutation rate is low (for escaping local optimum) 1.Randomly selects one gene (node) to mutate 2.Its following nodes are picked randomly from sequentially connected nodes

13. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 13 International Graduate School of Dynamic Intelligent Systems Evaluation - Fitness Fitness = Tour Length + Waiting Time (Static) (Dynamic)

14. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 14 International Graduate School of Dynamic Intelligent Systems Evolution Flowchart

15. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 15 International Graduate School of Dynamic Intelligent Systems Experimental Results (1) Optimize the path for single robot (selfish- planning)

16. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 16 International Graduate School of Dynamic Intelligent Systems Experimental Results (2) Fitness variation of multiple robots

17. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 17 International Graduate School of Dynamic Intelligent Systems Experimental Results (3)

18. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 18 International Graduate School of Dynamic Intelligent Systems Experimental Results (4) 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9

19. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 19 International Graduate School of Dynamic Intelligent Systems Summary The paper proposes a strategy of coordinative motion planning for multi-agent systems. Without global communication, the robot uses Genetic Algorithm (GA) to search the feasible solutions, which consider the tour distance and waiting time at the same time. Simulation results demonstrate this strategy can avoid collisions and achieve coordination of multiple robots.

20. Coordinative Behavior in Evolutionary Multi-agent System by Genetic Algorithm Chuan-Kang Ting – Page: 20 International Graduate School of Dynamic Intelligent Systems Thank you