1. A Sensitive Metaheuristic for Solving a Large Optimization Problem
Camelia-M. Pintea,
Camelia Chira,
D. Dumitrescu and
Petrica C. Pop
Babes-Bolyai University and North University
Romania

2. Outline Stigmergy Ant Colony Systems Autonomous Robots
Sensitive Robots
Drilling Problem
Sensitive Robot Metaheuristic
Numerical experiments and Statistical analysis
Conclusions and further work

3. Stigmergy Collective behaviour of social individuals
Indirect interactions
an individual modifies the environment
other individuals respond to that change at a later time
The environment mediates the communication among individuals
Self-organization
stigmergic interactions

4. Stigmergy – ant systems

5. Ant System Ant System - proposed by M. Dorigo (1992)
Initially used for routing problems
Successfully applied now to a broad range of problems: Quadratic Assignment Problem, Scheduling problems, Recognizing Hamiltonian graphs, Dynamic graph search
Ants lay down pheromones as they travel
Experiments show that pheromone builds up more quickly on shorter paths
An optimal path should be the one with the strongest pheromone concentration after a certain amount of time

6. Basic concepts of Ant System
Cooperative
behavior
Positive
feedback
Negative
feedback
Time scale
Stagnation
Stigmergy
Cooperative behavior ant algorithms make use of the simultaneous exploration of
different solutions
Positive feedback build a solution using local solutions, by keeping good
solutions in memory
Negative feedback to avoid premature convergence - evaporate the pheromone
Time scale number of runs is critical
Stagnation avoid good, but not very good solutions from becoming
reinforced
Stigmergy the indirectly communication between agents using pheromones

7. Ant Colony Systems (ACS)
Systems based on agents
Inspiration: behavior of real ant colonies
Leonel Moura + Vitorino Ramos, 2002 A B
Ants deposit on ground pheromone (while walking between food sources and nest) and can smell pheromone
Ants tend to choose strong pheromone trails

8. Ant Colony Optimization
Path followed by an ant: candidate solution
Ants deposit pheromone along the path followed proportional to the quality of corresponding candidate solution
Paths with stronger pheromone trails are preferred
ACO metaheuristic
robust and versatile
Successfully applied to a range of
CO problems

9. Stigmergy and Autonomous Robots
No global plans
Bonabeau, E. et al.: Swarm intelligence from natural to artificial systems. Oxford, UK.
Stigmergy provides a general mechanism that relates individual and colony level behaviors
The behavior-based approach to design intelligent systems has produced promising results in a wide variety of areas: military applications, mining, space exploration, agriculture, factory automation, service industries, waste management, health care and disaster intervention.
Autonomous robots can accomplish real-world tasks without being told exactly how.

10. Sensitive Robots
Artificial entities with a Stigmergic Sensitivity Level (SSL) expressed by a real number in the unit interval [0, 1].
Robots with small SSL values
highly independent
environment explorers
potential to autonomously discover new promising regions of the search space
search diversification can be sustained.
Robots with high SSL values
intensively exploit the promising search regions already identified
the robot behavior emphasizes search intensification
The SSL value can increase or decrease according to the search space topology encoded in the robot experience.

11. Sensitive Robot Metaheuristic (SRM)
Combines stigmergic communication and autonomous robot search
Qualitative stigmergic mechanism
“Micro-rules” define action-stimuli pair for a robot

12. SRM for solving a Large Drilling problem
SRM implemented using two teams of robots
First team of robots with small SSL values
Small SSL-robots (sSSL robots)
Sensitive-explorer robots
Search diversification
Second team of robots with high SSL values
High SSL-robots (hSSL robots)
Sensitive-exploiter robots
Search intensification
Problem

13. Drilling Problem
The process of manufacturing the printed circuit board (PCB) is difficult and complex.
Drilling small holes require precision and is done with the use of an automated drilling machine driven by computer programs.
The large drilling problem is a particular class of Generalized Traveling Salesman Problem involving a large graph and finding the minimal tour for drilling on a large-scale PCB

14. The Generalized Traveling Salesman Problem (GTSP)
Nodes of complete undirected graph clustered
Find a minimum-cost tour passing through exactly one node from each cluster
A graphic representation of the Generalized Traveling Salesman problem solved with ant system.
Introduced by Laporte and Nobert in 1983 and Noon and Bean in 1991
Applications to location and telecommunication problems
C-M. Pintea, C.P. Pop, C. Chira: The Generalized Traveling Salesman Problem solved with Ant Algorithms (ACS for GTSP from numerical experiments) J.UCS, in press, 2008

15. Sensitive Robot Metaheuristic (SRM) for Large Drilling problem
SRM model relies on the reaction of virtual sensitive robots to different stigmergic variables
Each robot is endowed with a particular stigmergic sensitivity level to ensure a good balance between search diversification and intensification

16. Sensitive Robot Algorithm

17. Numerical experiments (1)
[1] Bixby, B., Reinelt, G.: (1995)

18. Comparisons Nearest Neighbor (NN)
Rule: always go next to the nearest as-yet-unvisited location
GI3 composite heuristic
Construction of an initial partial solution
Insertion of a node from each non-visited node subset
Solution improvement phase
Random Key Genetic Algorithm
Combines GA with a local tour improvement heuristic
Solutions encoded using random keys
ACS for GTSP

19. Numerical experiments (2)
[8] Renaud, J., Boctor, F.F.: An efficient composite heuristic for the Symmetric Generalized Traveling Salesman Problem. Euro. J. Oper.Res., (1998)
[9]. Snyder, L.V., Daskin, M.S.: A Random-Key Genetic Algorithm for the Generalized Traveling Salesman Problem. INFORMS, San Antonio, TX (2000).

20. Statistical analysis
The Expected Utility Approach technique has been employed to determine the accuracy of each heuristic
SRM has Rank 1 being the most accurate algorithm within the compared set of algorithms

21. Conclusions and further work
Bio-inspired robot-based model for complex travel robotic problems
Potential Improvements
Execution time
Parameter values
Efficient combination with other algorithms
Future Work
Variable SSL - learning
Numerical experiments - NP-hard problems
Search and optimization in dynamic complex networks

22. Optimal Route
Actual Route

23. Thank you for your attention