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 Stigmergy

Ant Colony Systems

Autonomous Robots

Sensitive Robots

Drilling Problem

Sensitive Robot Metaheuristic

Numerical experiments and Statistical analysis

Conclusions and further work

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

Stigmergy – ant systems

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

Basic concepts of Ant System

Key concepts

• 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

Cooperative behavior

Positive feedback

Negativefeedback

Time scale Stagnation Stigmergy

Leonel Moura + Vitorino Ramos, 2002

A B

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

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

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.

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.

Sensitive Robot Metaheuristic (SRM)

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

1. First team of robots with small SSL values Small SSL-robots (sSSL robots) Sensitive-explorer robots Search diversification

2. Second team of robots with high SSL values High SSL-robots (hSSL robots) Sensitive-exploiter robots Search intensification

Problem

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

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

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

• Nodes of complete undirected graph clustered• Find a minimum-cost tour passing through exactly one node from

each cluster

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

Sensitive Robot Algorithm

Numerical experiments (1)

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

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

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 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

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

Optimal Route

Actual Route

Thank you for your attention

cchira@cs.ubbcluj.ro