139,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
- Veröffentlichungsjahr: 2021
This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them. The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 330
Ähnliche
Table of Contents
Cover
Title Page
Copyright
Preface
Acknowledgments
PART 1: Programmation
1 Linear Programming
1.1. Introduction
1.2. Definitions
1.3. Geometry of the linear program
1.4. Graphical solving of a linear program
1.5. Simplex algorithm
1.6. Initialization of the simplex algorithm
1.7. Interior-point algorithm
1.8. Duality
1.9. Relaxation
1.10. Postoptimal analysis
1.11. Application to an inventory problem
1.12. Using Matlab
2 Integer Programming
2.1. Introduction
2.2. Solving methods
2.3. Binary programming
2.4. Decomposition principle
2.5. Using Matlab
3 Dynamic Programming
3.1. Introduction
3.2. Solving strategy
3.3. Discrete DP
3.4. Continuous DP
3.5. Stochastic DP
3.6. Using Matlab
4 Stochastic Programming
4.1. Introduction
4.2. Presentation of the problem
4.3. Optimal feedback in an open loop
4.4. Stochastic linear programming
4.5. Stochastic linear programs with recourse
4.6. Nonlinear stochastic programming
4.7. Stochastic dynamic programming
4.8. Application to the reliability of mechanical systems
4.9. Using Matlab
PART 2: Optimization
5 Combinatorial Optimization
5.1. Introduction
5.2. Symmetric TSP
5.3. Asymmetric traveling salesman problem
5.4. Vehicle routing problem
5.5. Selective routing problem
5.6. Using Matlab
6 Unconstrained Nonlinear Programming
6.1. Introduction
6.2. Mathematical formulation
6.3. Optimality conditions
6.4. Quadratic problems
6.5. Newton’s algorithm
6.6. Methods of descent and linear search
6.7. Quasi-Newton methods
6.8. Relaxation method
6.9. Gradient method
6.10. Least squares problem
6.11. Direct search methods
6.12. Application to an identification problem
6.13. Using Matlab
7 Constrained Nonlinear Optimization
7.1. Introduction
7.2. Mathematical formulation
7.3. Lagrange multipliers
7.4. Optimization with inequality constraints
7.5. Constrained minimization algorithms
7.6. Newton algorithms: SQP method
7.7. Application to structure optimization
7.8. Using Matlab
Appendices
Appendix 1: Reminders from Linear Algebra
A1.1. Vector space
A1.2. Linear mappings
A1.3. Matrices
A1.4. Determinants
A1.5. Scalar product
A1.6. Vector norm
Appendix 2: Reminders about functions from ℝ
n
into ℝ
A2.1. Differentiability
A2.2. Convexity
A2.3. Quadratic function
Appendix 3: Optimization Toolbox
A3.1. Introduction
A3.2. Various functions
A3.3. Matlab’s optimization application
Appendix 4: Software
A4.1. Autonomous and multipurpose optimization software
A4.2. Packages for specific classes of problems
A4.3. Optimization software for design
A4.4. Solvers for stochastic optimization
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1. First simplex tableau
Table 1.2. Second simplex tableau
Table 1.3. Third simplex tableau
Chapter 3
Table 3.1. Table constructed to solve the problem
Table 3.2. List of n objects
Table 3.3. Results of the recursive formula
Table 3.4. Demand and purchase prices
Table 3.5. Solution of the stock problem
Chapter 4
Table 4.1. Characteristics of the random variables for the concrete beam
Table 4.2. Results obtained with the FORM method for the concrete beam
Chapter 6
Table 6.1. Material properties
Chapter 7
Table 7.1. Results calculated with Matlab
Table 7.2. Solution calculated with Matlab
Appendix 3
Table A3.1. Optimization problems supported by the optimization toolbox
List of Illustrations
Chapter 1
Figure 1.1. Bounded polyhedron (left) and unbounded polyhedron (right). For a co...
Figure 1.2. Graphical solution. For a color version of this figure, see www.iste...
Figure 1.3. Graphical solution with isoprofit lines. For a color version of this...
Chapter 2
Figure 2.1. Branch-and-bound method
Figure 2.2. Branch-and-cut method
Figure 2.3. Matrix A
Chapter 3
Figure 3.1. Different cities. For a color version of this figure, see www.iste.c...
Figure 3.2. DAG representing the dependencies between the different subproblems ...
Figure 3.3. Level-dependent multilevel DAG for the shortest path problem. For a ...
Figure 3.4. Level-independent multilevel DAG for the shortest path problem. For ...
Figure 3.5. Graph corresponding to this problem
Figure 3.6. Graph constructed from this problem
Figure 3.7. Decision-chance tree for the insurance contract problem. For a color...
Figure 3.8. Binary search tree for set A. For a color version of this figure, se...
Figure 3.9. Five possible binary trees for list S. For a color version of this f...
Chapter 4
Figure 4.1. Constructing a scenario tree. For a color version of this figure, se...
Figure 4.2. Example of a tree structure. For a color version of this figure, see...
Figure 4.3. Geometric representation of β
HL
for a problem with two random variab...
Figure 4.4. Most probable failure point. For a color version of this figure, see...
Figure 4.5. Illustration of FORM. For a color version of this figure, see www.is...
Figure 4.6. Diagram of the beam on simple supports of reinforced concrete
Chapter 5
Figure 5.1. Different possible trips. For a color version of this figure, see ww...
Figure 5.2. Problem with 85,900 towns. For a color version of this figure, see w...
Figure 5.3. Various solving methods
Figure 5.4. Traveling salesman’s route through n towns
Figure 5.5. VRP
Figure 5.6. Final tour of the traveling salesman. For a color version of this fi...
Chapter 6
Figure 6.1. Graphical solution. For a color version of this figure, see www.iste...
Figure 6.2. Identification process
Figure 6.3. Force/elongation for different optimization steps and plastic deform...
Chapter 7
Figure 7.1. Methodology for optimizing structures modeled by finite elements
Figure 7.2. Plate
Figure 7.3. Shape of the plate. For a color version of this figure, see www.iste...
Figure 7.4. Optimized plate. For a color version of this figure, see www.iste.co...
Figure 7.5. Triangular plate
Figure 7.6. Initial and optimal shape. For a color version of this figure, see w...
Figure 7.7. Position of the local optimum. For a color version of this figure, s...
Figure 7.8. Graphs of the functions f and g. For a color version of this figure,...
Figure 7.9. Contours of the functions f and g. For a color version of this figur...
Appendix 3
Figure A3.1. Window that opens when calling optimtool. For a color version of th...
Figure A3.2. Applications in the Optimization Toolbox
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
Appendices
Appendix 1
Appendix 2
Appendix 3
Appendix 4
References
Index
End User License Agreement
Pages
v
iii
iv
xi
xii
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
127
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
229
231
232
233
234
235
236
237
238
239
240
241
242
243
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
261
262
263
264
265
266
267
268
269
270
271
Digital Sciences Set
coordinated byAbdelkhalak El Hami
Volume 1
Optimizations and Programming
Linear, Nonlinear, Dynamic, Stochastic and Applications with Matlab
Abdelkhalak El Hami
Bouchaib Radi
First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
27-37 St George’s RoadLondon SW19 4EU UK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2021
The rights of Abdelkhalak El Hami and Bouchaib Radi to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2020948478
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-84821-953-3
Preface
Optimization is the domain of mathematics that studies how to minimize (or maximize) a certain objective, for example, an economic parameter or some type of energy. This is both an ancient topic, with the earliest optimization problems going back to Euclid, and a relatively new topic, with the recent development of numerical methods such as linear programming, which only truly began to flourish in the second half of the 20th century. As an illustration, imagine the problem of searching for a path that joins two points on a map in the shortest time. Some parameters of the problem might be uncertain; for example, we might encounter a traffic jam on the road. Optimization seeks to find the best compromise between the various possible risks.
In the presence of uncertainty, the optimizer (or decider) will often take advantage of information about the system that becomes available dynamically, i.e. gradually over time. For example, we will gradually discover which roads are most susceptible to traffic jams over time, as we try them out. The difficulty of an optimization problem is closely linked to the amount of information needed to make an optimal decision. A problem is said to be large if this quantity of information is too big for classical solving techniques to be applied by brute force.
This book is divided into two parts: programming (Part 1) and optimization (Part 2). In the programming part, we present a collection of tools for operations research, including linear programming, integer programming, binary programming, dynamic programming and stochastic programming. Operations research first arose in the United Kingdom during the Second World War, when scientific methods were used to study various aspects of military operations. Since then, it has become a key element of decision-making processes in various commercial, industrial and governmental contexts, offering a systematic way to apprehend the ever increasing complexity of the management problems faced by both the private and public sectors.
Following its success in military matters during the Second World War, operations research was applied to operational problems in the industry and private sector for many years. In the last decade or so, its applications have been extended to other domains, such as economics, finance, marketing and corporate planning. More recently, operations research has been used to manage healthcare and education systems, solve environmental problems and in other areas of public interest. Its principal users are manufacturing, distribution and retail companies in the mining, energy, transportation and construction sectors, as well as service companies such as banks, and various government bodies. Noteworthy examples of recent applications of operations research include logistical studies, railway safety, packaging design, strategic workforce planning, aerial transportation, forestry operations, nuclear fuel optimization, production planning, and so on.
The optimization part of this book is divided into three chapters: combinatorial optimization, nonlinear optimization without constraints and nonlinear optimization with constraints. It is entirely dedicated to numerical optimization algorithms, their theoretical foundations and convergence properties, their implementation and application, and other practical aspects. The objective is to familiarize readers with these numerical algorithms in order to understand how they behave in practice, how to properly take advantage of Matlab as a tool, how to design and adequately implement such algorithms and how to correctly diagnose any difficulties that might arise.
Each chapter starts with a few reminders of key results, but readers should not hesitate to consult the references listed at the end of the book. This book is organized according to a strictly linear approach. As a general rule, the concepts are illustrated with examples. Each chapter ends with an example in Matlab.
Acknowledgments
We would like to thank everyone who contributed, directly or indirectly, to the writing of this book and especially, the engineering and PhD students of INSA Rouen whom we have had the pleasure of supervising over the past few years.
Bouchaib RADIAbdelkhalak EL HAMINovember 2020
