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
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Ant Colony Systems

Autonomous Robots

Sensitive Robots

Drilling Problem

Sensitive Robot Metaheuristic

Numerical experiments and Statistical analysis
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Conclusions and further work
Stigmergy
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Collective behaviour of social individuals
Indirect interactions
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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

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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)


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

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

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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.

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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
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highly independent

environment explorers
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potential to autonomously discover new promising regions of the search space

search diversification can be sustained.
Robots with high SSL values
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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)
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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
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1.
First team of robots with small SSL values
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2.
Second team of robots with high SSL values
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Small SSL-robots (sSSL robots)
Sensitive-explorer robots
Search diversification
High SSL-robots (hSSL robots)
Sensitive-exploiter robots
Search intensification
Problem
Drilling Problem

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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
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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
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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
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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
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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
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Potential Improvements
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Execution time
Parameter values
Efficient combination with other algorithms
Future Work
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Variable SSL - learning
Numerical experiments - NP-hard problems
Search and optimization in dynamic complex
networks
Optimal Route
Actual Route
Thank you for your attention
[email protected]