Simulated Annealing [math]

428 Pages·2008·38.37 MB·English

by  C. Tan

Simulated Annealing

Simulated Annealing
Edited by
Cher Ming Tan
I-Tech
IV

Published by In-Teh

In-Teh is Croatian branch of I-Tech Education and Publishing KG, Vienna, Austria.

Abstracting and non-profit use of the material is permitted with credit to the source. Statements and
opinions expressed in the chapters are these of the individual contributors and not necessarily those of
the editors or publisher. No responsibility is accepted for the accuracy of information contained in the
published articles. Publisher assumes no responsibility liability for any damage or injury to persons or
property arising out of the use of any materials, instructions, methods or ideas contained inside. After
this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in
any publication of which they are an author or editor, and the make other personal use of the work.

© 2008 In-teh
www.in-teh.org
Additional copies can be obtained from:
[email protected]

First published September 2008
Printed in Croatia

A catalogue record for this book is available from the University Library Rijeka under no. 111224063
Simulated Annealing, Edited by Cher Ming Tan
p. cm.
ISBN 978-953-7619-07-7
1. Simulated Annealing. Cher Ming Tan
Preface

Optimization is important in all branches of engineering due to limited resources
available. Through optimization, maximum usage of the resource can be achieved.
However, global optimization can be difficult due to the requirement of the knowledge of
the system behavior under analysis and the possible large solution space. Without this
knowledge, the optimization thus obtained may only be a local optimization. Metaheuristic
algorithms, on the other hand, are effective in exploring the solution space. Often, they are
referred to as “black box” algorithms as they use very limited knowledge about the specific
system to be tackled, and often it does not require a mathematical model of the system
under study. Hence it can be used to solve a broad range of problem, and has thus receiving
increasing attention.
One of the commonly used metaheuristic algorithms is the Simulated Annealing (SA).
SA is an optimization algorithm that is not fool by false minima and is easy to implement. It
is also superior as compared to many other metaheuristic algorithms as presented in this
book. In this book, the different applications of the Simulated Annealing will be presented.
The first 11 chapters are devoted to the applications in Industrial engineering such as the
scheduling problem, decision making, allocation problem, routing problem and general
optimization problem.
The subsequent chapters of this book will focus on the application of the Simulated
Annealing in Material Engineering on porous material study, Electrical Engineering on
integrated circuit technology, Mechanical Engineering on mechanical structure design,
Structural Engineering on concrete structures, Computer Engineering on task mapping and
Bio-engineering on protein structure. The last three Chapters will be on the methodology to
optimize the Simulated Annealing, its comparison with other metaheuristic algorithms and
the various practical considerations in the application of Simulated Annealing.
This book provides the readers with the knowledge of Simulated Annealing and its vast
applications in the various branches of engineering. We encourage readers to explore the
application of Simulated Annealing in their work for the task of optimization.
Editor
Cher Ming Tan
Nanyang Technological University
Singapore

Contents

Preface V

1. Simulated Annealing as an Intensification Component in Hybrid 001
Population-Based Metaheuristics
Davide Anghinolfi and Massimo Paolucci

2. Multi-objective Simulated Annealing for a Maintenance Workforce 027
Scheduling Problem: A case Study
Nima Safaei, Dragan Banjevic and Andrew K.S. Jardine

3. Using Simulated Annealing for Open Shop Scheduling with Sum Criteria 049
Michael Andresen, Heidemarie Bräsel, Mathias Plauschin and Frank Werner

4. Real Time Multiagent Decision Making by Simulated Annealing 077
Dawei Jiang and Jingyu Han

5. Learning FCM with Simulated Annealing 089
M.Ghazanfari and S. Alizadeh

6. Knowledge-Informed Simulated Annealing for Spatial Allocation 105
Problems
Jiunn-Der Duh

7. An Efficient Quasi-Human Heuristic Algorithm for 119
Solving the Rectangle-Packing Problem
Wenqi Huang and Duanbing Chen

8. Application of Simulated Annealing to Routing Problems in City Logistics 131
Hisafumi Kokubugata and Hironao Kawashima

9. Theory and Applications of Simulated Annealing for 155
Nonlinear Constrained Optimization
Benjamin W. Wah, Yixin Chen and Tao Wang
VIII

10. Annealing Stochastic Approximation Monte Carlo for Global Optimization 187
Faming Liang

11. Application of Simulated Annealing on the Study of Multiphase Systems 207
Maurice G. Politis, Michael E. Kainourgiakis, Eustathios S. Kikkinides
and Athanasios K. Stubos

12. Simulated Annealing for Mixture Distribution Analysis and its Applications 227
to
Reliability Testing
Cher Ming Tan and Nagarajan Raghavan

13. Reticle Floorplanning and Simulated Wafer Dicing for Multiple-project 257
Wafers
by Simulated Annealing
Rung-Bin Lin, Meng-Chiou Wu and Shih-Cheng Tsai

14. Structural Optimization Using Simulated Annealing 281
Fazil O. Sonmez

15. Optimization of Reinforced Concrete Structures by Simulated Annealing 307
F. González-Vidosa, V. Yepes, J. Alcalá, M. Carrera, C. Perea and I. Payá-
Zaforteza

16. Best Practices for Simulated Annealing in Multiprocessor Task 321
Distribution Problems
Heikki Orsila, Erno Salminen and Timo D. Hämäläinen

17. Simulated Annealing of Two Electron Density Solution Systems 343
Mario de Oliveira Neto, Ronaldo Luiz Alonso, Fabio Lima Leite, Osvaldo N.
Oliveira Jr, Igor Polikarpov and Yvonne Primerano Mascarenhas

18. Improving the Neighborhood Selection Strategy in Simulated Annealing 363
using the Optimal Stopping Problem
Saed Alizamir, Steffen Rebennack and Panos M. Pardalos

19. A Comparison of Simulated Annealing, Elliptic and Genetic Algorithms 383
for Finding Irregularly Shaped Spatial Clusters
Luiz Duczmal, André L. F. Cançado, Ricardo H. C. Takahashi and Lupércio F.
Bessegato

20. Practical Considerations for Simulated Annealing Implementation 401
Sergio Ledesma, Gabriel Aviña and Raul Sanchez
1
Simulated Annealing as an Intensification
Component in Hybrid Population-Based
Metaheuristics
Davide Anghinolfi and Massimo Paolucci
Department of Communication, Computer and Systems Sciences
University of Genova
Italy
1. Introduction
The use of hybrid metaheuristics applied to combinatorial optimization problems received a
continuously increasing attention in the literature. Metaheuristic algorithms differ from
most of the classical optimization techniques since they aim at defining effective general
purpose methods to explore the solution space, avoiding to tailor them on the specific
problem at hand. Often metaheuristics are referred to as “black-box” algorithms as they use
limited knowledge about the specific problem to be tackled, instead usually taking
inspiration from concepts and behaviours far from the optimization field. This is exactly the
case of metaheuristics like simulated annealing (SA), genetic algorithm (GA), ant colony
optimization (ACO) or particle swarm optimization (PSO). Metaheuristics are based on a
subset of features (e.g., the use of exploration history as short or long term memory, that of
learning mechanisms or of candidate solution generation techniques) that represent a
general algorithm fingerprint which usually can be easily adapted to face different complex
real world problems. The effectiveness of any metaheuristic applied to a specific
combinatorial problem may depend on a number of factors: most of the time no single
dominating algorithm can be identified but several distinct mechanisms exploited by
different metaheuristics appear to be profitable for searching high quality solutions. For this
reason a growing number of metaheuristic approaches to combinatorial problems try to put
together several techniques and concepts from different methods in order to design new and
highly effective algorithms. Hybrid approaches in fact usually seem both to combine
complementary strengths and to overcome the drawbacks of single methods by embedding
in them one or more steps based on different techniques. As an example, in (Anghinolfi &
Paolucci, 2007a) the SA probabilistic candidate solution acceptance rule is coupled with the
tabu list and neighbourhood change mechanisms respectively characterizing tabu search
(TS) and variable neighbourhood search (VNS) approaches to face parallel machine total
tardiness scheduling problems. Several surveys exist proposing both classifications of
metaheuristics and unified views of hybrid metaheuristics (e.g., (Blum & Roli, 2003),
(Doerner et al., 2007), (Raidl, 2006) and (Talbi, 2002)). We would avoid to replicate here the
various definitions and classifications through which the different approaches can be
analysed and organized (the interested reader can for example refer to (Blum & Roli, 2003)
2 Simulated Annealing
for a valuable review). However, we should underline few basic concepts that allow us to
focus on the different characteristics of the kinds of methods used in the hybrid algorithms
presented in this chapter. SA, ACO and PSO are all stochastic algorithms, but SA is
commonly classified as a trajectory-based method since it determines at each iteration a new
single current solution, whereas ACO and PSO are population-based methods since they
explore at each iteration a set of distinct solutions which they make evolve iteration after
iteration. The concept behind these two population-based methods is that the overall
exploration process can be improved by learning from the single exploring experiences of a
population of very simple agents (the ants or the particles). As will be cleared in the
following of the chapter, ACO explicitly exploits a learning mechanism in order to identify,
iteration after iteration, which features should characterize good, i.e., the most promising,
solutions. If in ACO the communication among the exploring agents (the ants) is indirect,
PSO, on the other hand, drives the search of the population of agents (the swarm of
particles) on the basis of simple pieces of information (e.g., where the current best is
located), making the agents moving towards promising solutions. Therefore, both ACO and
PSO use memory structures, more complex in ACO, simpler in PSO, to elaborate their
exploration strategies; agents in ACO and PSO perform a learning or information driven
sampling of the solution space that could in general be considered wide but also quite
coarse, and that can be trapped in local optima (the so-called stagnation (Dorigo & Stutzle,
2004)). SA, on the other hand, is a memoryless method which combines the local search
aptitude of exploring in depth regions in the solution space with the ability, ruled by the
cooling schedule mechanism, of escaping from local optima. From this brief overview the
possible advantage of coupling the different complementary abilities of the two types of
metaheuristics should begin to emerge. Therefore in this chapter our purpose is to focus the
attention on hybrid population-based metaheuristic algorithms with a specific reference to
the use of SA as a hybridizing component. Then, according to the classification proposed in
(Raidl, 2006), the kind of hybrid algorithms here considered result from the combination of
two distinct metaheuristics (the “what is hybridized” aspect) among which a low-level
strong coupling is established (the “level of hybridization” aspect), in particular the
execution of SA is interleaved with the iterations of the population-based metaheuristics
(the “order of execution” aspect) so that SA can be viewed as an integrated component of
these latter (the “control strategy” aspect).
Several works recently appeared in the literature show the interest of embedding SA into
population-based approaches as ACO, PSO and GA. Examples of PSO hybridized by
incorporating SA intensification can be found in (Liu et al., 2008), where the proposed
hybrid PSO (HPSO), which includes a probabilistically applied local search (LS) and a
learning-guided multi-neighbourhood SA, is applied to makespan minimization in a
permutation flow shop scheduling problem with the limited buffers between consecutive
machines; in (He & Wang, 2007), where constrained optimization problems are faced by a
HPSO which applies the SA search from the best solution found by the swarm in order to
avoid the premature convergence; in (Li et al., 2006), where the hybrid algorithm, named
PSOSA, is used for non-linear systems parameter estimation; in (Ge et al., 2007) where the
HPSO is used to face the job shop scheduling. Differently, in (Xia & Wu, 2005) multi-
objective flexible job shop scheduling problems are confronted by a hierarchical approach
exploiting PSO to assign operations to machines and then SA to schedule operations on each
machine. Hybrid ACO approaches, which combine pheromone trail based learning