SOFSEM 2008 A Sensitive Metaheuristic for Solving a

SOFSEM 2008 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 l Stigmergy l Ant Colony Systems l Autonomous Robots l Sensitive Robots l Drilling Problem l Sensitive Robot Metaheuristic l Numerical experiments and Statistical analysis l Conclusions and further work

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

Stigmergy – ant systems

Ant System l l l q q q 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

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

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

Ant Colony Optimization l 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 l ACO metaheuristic l l robust and versatile l Successfully applied to a range of CO problems l

Stigmergy and Autonomous Robots No global plans Bonabeau, E. et al. : Swarm intelligence from natural to artificial systems. Oxford, UK. l l l 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.

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

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

SRM for solving a Large Drilling problem SRM implemented using two teams of robots l 1. First team of robots with small SSL values l l l 2. Second team of robots with high SSL values l l Small SSL-robots (s. SSL robots) Sensitive-explorer robots Search diversification High SSL-robots (h. SSL robots) Sensitive-exploiter robots Search intensification Problem

Drilling Problem l l l 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

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 l l l 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 A graphic representation of the Generalized Traveling Salesman problem solved with ant system.

Sensitive Robot Metaheuristic (SRM) for Large Drilling problem l l 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

Sensitive Robot Algorithm

Numerical experiments (1) [1] Bixby, B. , Reinelt, G. : http: //nhse. cs. rice. edu/softlib/catalog/tsplib. html (1995)

Comparisons l l Nearest Neighbor (NN) l Rule: always go next to the nearest as-yet-unvisited location GI 3 composite heuristic l Construction of an initial partial solution l Insertion of a node from each non-visited node subset l Solution improvement phase Random Key Genetic Algorithm l Combines GA with a local tour improvement heuristic l Solutions encoded using random keys ACS for GTSP

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).

Statistical analysis l 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

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

Optimal Route Actual Route

Thank you for your attention cchira@cs. ubbcluj. ro