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A Sensitive Metaheuristic for Solving a Large Optimization Problem

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. Outline. Stigmergy Ant Colony Systems Autonomous Robots Sensitive Robots Drilling Problem

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A Sensitive Metaheuristic for Solving a Large Optimization Problem

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  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 pheromonesas 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. A B Leonel Moura + Vitorino Ramos, 2002 Ant Colony Systems (ACS) • Systems based on agents • Inspiration: behavior of real ant colonies • 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) • 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 • 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.

  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.: http://nhse.cs.rice.edu/softlib/catalog/tsplib.html (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 cchira@cs.ubbcluj.ro

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