5. Simulated Annealing 5.1 Basic Concepts - IUST Personal Webpages

44 Pages·2011·0.33 MB·English

5. Simulated Annealing
5.1
Basic Concepts
Fall 2010
Instructor: Dr. Masoud Yaghini
Simulated Annealing: Part 1
Outline
(cid:1) Introduction
(cid:1) Real Annealing and Simulated Annealing
(cid:1) Metropolis Algorithm
(cid:1) Template of SA
(cid:1)(cid:1) AA SSiimmppllee EExxaammppllee
(cid:1) References
Introduction
Simulated Annealing: Part 1
What Is Simulated Annealing?
(cid:1) Simulated Annealing (SA)
SA is applied to solve optimization problems
–
SA is a stochastic algorithm
–
SA is escaping from local optima by allowing worsening
–
mmoovveess
SA is a memoryless algorithm, the algorithm does not use
–
any information gathered during the search
SA is applied for both combinatorial and continuous
–
optimization problems
SA is simple and easy to implement.
–
SA is motivated by the physical annealing process
–
Simulated Annealing: Part 1
SA vs Greedy Algorithms:
Ball on terrain example
Simulated Annealing: Part 1
History
(cid:1) Numerical simulation of annealing, Metropolis et al.
1953.
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller.
EEqquuaattiioonn ooff ssttaattee ccaallccuullaattiioonnss bbyy ffaasstt ccoommppuuttiinngg mmaacchhiinneess.. JJoouurrnnaall ooff
Chemical Physics, 21:1087–1092, 1953.
Simulated Annealing: Part 1
History
(cid:1) SA for combinatorial problems
Kirkpatrick et. al, 1986
–
Cerny, 1985
–
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated
annealing. Science, 220(4598):671–680, 1983.
V. Cerny, Thermodynamical approach to the traveling salesman problem : an
efficient simulation algorithm. J. of Optimization Theory and Applications,
45(1):41–51, 1985.
Simulated Annealing: Part 1
History
(cid:1) Originally, the use of simulated annealing in
combinatorial optimization
(cid:1) In the 1980s, SA had a major impact on the field of
heuristic search for its simplicity and efficiency in
ssoollvviinngg ccoommbbiinnaattoorriiaall ooppttiimmiizzaattiioonn pprroobblleemmss..
(cid:1) Then, it has been extended to deal with continuous
optimization problems
(cid:1) SA was inspired by an analogy between the
physical annealing process of solids and the
problem of solving large combinatorial optimization
problems.
Simulated Annealing: Part 1
Applications
(cid:1) Basic problems
Traveling Salesman Problem
–
Graph partitioning
–
Matching prob.
–
QQuuaaddrraattiicc AAssssiiggnnmmeenntt
––
Linear Arrangement
–
Scheduling
–
….
–
Simulated Annealing: Part 1
Applications
(cid:1) Engineering problem
VLSI: Placement, routing…
–
Facilities layout
–
Image processing
–
CCooddee ddeessiiggnn
––
Biology
–
Physics
–
….
–