Soft Computing in Chemical and Physical Sciences: A Shift in Computing Paradigm

429 Pages·2018·13.125 MB·English

by  Kanchan Sarkar, Sankar Prasad Bhattacharyya

SOFT-COMPUTING
PHYSICAL

IN AND
CHEMICAL SCIENCES
A SHIFT IN COMPUTING PARADIGM

SOFT-COMPUTING
PHYSICAL

IN AND
CHEMICAL SCIENCES
A SHIFT IN COMPUTING PARADIGM
Kanchan Sarkar
Sankar Prasad Bhattacharyya
CRC Press
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Library of Congress Cataloging‑in‑Publication Data
Names: Bhattacharyya, S. P. (Sankar Pradad), author. | Sarkar, Kanchan,
author.
Title: Soft computing in chemical and physical sciences : a shift in
computing paradigm / S.P. Bhattacharyya, Kanchan Sarkar.
Description: Boca Raton : CRC Press, Taylor & Francis, 2018. | Includes
bibliographical references and index.
Identifiers: LCCN 2017048154| ISBN 9781498755931 (hardback : alk. paper) |
ISBN 9781315152899 (ebook)
Subjects: LCSH: Chemical engineering--Data processing. | Physics--Data
processing. | Soft computing.
Classification: LCC TP184 .B43 2018 | DDC 660--dc23
LC record available at https://lccn.loc.gov/2017048154
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
http://www.crcpress.com
Dedicated to the loving memory of Professor Mihir Chowdhury

Contents
Preface ...........................................................................................................................................xiii
Authors ...........................................................................................................................................xv
1. A New Computing Paradigm ...............................................................................................1
1.1 Introduction ...................................................................................................................1
1.2 What Is Soft Computing? .............................................................................................1
1.3 Why Soft Computing? ..................................................................................................3
1.4 Overview of the Topics Covered .................................................................................4
1.4.1 Genetic Algorithms .........................................................................................4
1.4.2 Evolutionary Algorithms and Genetic Computing ....................................5
1.4.3 Random Mutation Hill Climbing and Simulated Annealing ...................5
1.4.4 Artificial Neural Networks ............................................................................5
1.4.5 Swarm Intelligence Method ...........................................................................5
1.4.6 Fuzzy Logic and Fuzzy-Set-Based Systems .................................................6
1.4.7 Quantum Computing ......................................................................................6
1.5 Interfacing Soft Computing with Problem-Solving in Physics
and Chemistry ........................................................................................................6
References .................................................................................................................................7
2. Genetic Algorithms ................................................................................................................9
2.1 Introduction ...................................................................................................................9
2.2 What Are Genetic Algorithms? .................................................................................12
2.3 How Do the GAs Work? .............................................................................................13
2.3.1 Representation of Solutions ..........................................................................14
2.3.2 Fitness and Fitness Landscapes ...................................................................15
2.3.3 The Crossover Operator ................................................................................18
2.3.4 Mutation Operator .........................................................................................18
2.3.5 The Selection Operator ..................................................................................19
2.3.6 A Specific Choice ...........................................................................................20
2.4 Why Does GA Work? ..................................................................................................25
2.4.1 The Schemas (Schematas) and Their Attributes........................................25
2.4.2 The Schema Theorem ....................................................................................27
2.4.3 Effects of Crossover .......................................................................................29
2.4.4 Effects of Mutation .........................................................................................30
2.5 Other Theoretical Models of GA ..............................................................................31
2.5.1 GA as a Dynamical System .........................................................................31
2.5.2 GA: A Statistical Mechanical View .............................................................36
2.6 Variants of GA .............................................................................................................37
2.6.1 Variants of Crossover Operators .................................................................38
2.6.1.1 Simple Crossover ............................................................................38
2.6.1.2 Uniform Crossover .........................................................................39
2.6.1.3 Heuristic Crossover .......................................................................39
2.6.1.4 Linear Crossover ............................................................................39
vii
viii Contents
2.6.1.5 Arithmetic Crossover ....................................................................40
2.6.1.6 Simplex Crossover ..........................................................................40
2.6.1.7 BLX-α Crossover .............................................................................40
2.6.1.8 Similarity Crossover ......................................................................40
2.6.1.9 Cell Crossover .................................................................................41
2.6.1.10 Average Offspring Method ..........................................................41
2.6.1.11 Cut and Splice Crossover ..............................................................41
2.6.2 Variants of Mutation Operators ...................................................................42
2.6.2.1 Uniform Mutation ..........................................................................43
2.6.2.2 Nonuniform Mutation ...................................................................43
2.6.2.3 Gaussian Type Mutation ...............................................................44
2.6.2.4 Dynamic Random Mutation .........................................................44
2.6.2.5 Arithmetic Mutation ......................................................................45
2.6.2.6 Directed Random Mutation ..........................................................45
2.6.2.7 Wavelet Mutation ...........................................................................45
2.6.2.8 BGA Mutation .................................................................................46
2.6.2.9 Soft Mutation ..................................................................................46
2.6.3 Variants of Selection Operators ...................................................................47
2.6.3.1 Generational Replacement ............................................................47
2.6.3.2 Truncation Replacement ................................................................47
2.6.3.3 Stochastic Universal Sampling .....................................................47
2.6.3.4 Rank-Based Selection .....................................................................47
2.6.3.5 Tournament Selection ....................................................................48
2.6.3.6 Clonal Selection ..............................................................................48
2.6.3.7 Sexual Selection ..............................................................................48
References ...............................................................................................................................49
3. Evolutionary Computing ....................................................................................................53
3.1 Introduction .................................................................................................................53
3.2 Evolutionary Programming ......................................................................................54
3.2.1 The Basic Architecture ..................................................................................54
3.3 Evolutionary Strategy .................................................................................................56
3.4 Genetic Programming ................................................................................................58
3.4.1 The Parse Tree and Lisp Program ...............................................................59
3.5 Differential Evolution .................................................................................................62
3.6 Parallel GAs .................................................................................................................64
3.6.1 Designing an Optimal Master Slave GA ....................................................65
References ...............................................................................................................................68
4. Random Mutation Hill Climbing and Simulated Annealing Methods ...................71
4.1 Introduction .................................................................................................................71
4.2 The Random Mutation Hill Climbing Method (RMHCM) ...................................72
4.2.1 RMHC Pseudocode .......................................................................................72
4.2.2 Adaptive RMHC ............................................................................................73
4.2.3 Variants of RMHC .........................................................................................74
4.2.4 Analysis of RMHCM .....................................................................................76
4.3 The Simulated Annealing Method ...........................................................................78
4.4 The Method of Quantum Annealing (QA) ..............................................................87
Contents ix
4.5 Elementary Applications of SAM in Quantum Mechanics...................................88
4.5.1 The Generator Coordinate Method .............................................................95
4.5.2 (Multiconfiguration) Self-Consistent Field Calculation
and the SAM ............................................................................................96
4.6 Elementary Applications of RMHC in Cluster Physics .......................................100
4.6.1 The Problem and the Method ....................................................................101
4.7 Search for the Minima (Local and Global) in Model Potentials
and Spin Systems ......................................................................................................104
References .............................................................................................................................107
5. Swarm Intelligence ............................................................................................................109
5.1 Introduction ...............................................................................................................109
5.2 Particle Swarm Optimization .................................................................................111
5.2.1 The Algorithm ..............................................................................................112
5.3 Particle Swarm Optimization for Discrete Search Variables .............................114
5.4 Convergence of the PSO Algorithm .......................................................................116
5.5 The Fireflies Algorithm ............................................................................................118
5.5.1 The Algorithm ..............................................................................................118
5.6 Artificial Bee Colony Algorithms ...........................................................................121
5.6.1 Introduction ..................................................................................................121
5.7 Ant Colony Optimization Algorithms ..................................................................125
5.7.1 Introduction ..................................................................................................125
5.7.2 The Bridge Experiment ..............................................................................126
5.7.3 A Simple Ant Colony Algorithm ..............................................................128
5.8 Continuous Ant Colony Optimization ..................................................................131
References .............................................................................................................................133
6. Application of Soft Computing in Physics ....................................................................135
6.1 Introduction ..............................................................................................................135
6.2 Variational Principle, Energy Extremalization, and Diagonalization
of Hamiltonian by GA ..............................................................................................136
6.2.1 Stochastic or Soft Diagonalization by GA ................................................137
6.2.2 The Algorithm for Calculating the Lowest Eigenvalue .........................139
6.2.3 Computing the Largest Eigenvalue of H ..................................................142
6.2.4 Algorithms for Extracting Multiple Eigenvalues by GA ........................143
6.3 GA in solving the Partitioned Matrix Eigenvalue Problem ................................145
6.3.1 Energy-Dependent Partitioning: Search for the Ground State .............146
6.3.2 Applications ..................................................................................................150
6.3.3 Evolutionary Computing and Energy-Independent
Partitioned Matrix Eigenvalue Problem ...................................................151
6.3.4 Applications ..................................................................................................154
6.4 Computing Eigenvalues and Eigenvectors of a Hamiltonian Matrix
by GA Rayleigh Quotient Method ..........................................................................154
6.4.1 Sequential Search for Eigenvalues and Vectors.......................................155
6.4.1.1 Notes on Different Steps .............................................................156
6.4.2 Sequential Search for Higher Eigenvalues ...............................................157
6.4.3 Simultaneous Search for Multiple Eigenvalues .......................................158