A Set of Examples of Global and Discrete Optimization: Applications of Bayesian Heuristic Approach

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Springer Science & Business Media, Jul 31, 2000 - Business & Economics - 321 pages
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This book shows how the Bayesian Approach (BA) improves well known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of dis crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribu tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. Dif ferent examples illustrate different points of the general subject. How ever, one can consider each example separately, too.
 

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Contents

GENERAL IDEAS OF BAYESIAN HEURISTIC APPROACH
3
2 DIRECT BAYESIAN APPROACH DBA
4
3 BAYESIAN HEURISTIC APPROACH BHA
5
4 ILLUSTRATIVE EXAMPLES
6
5 HEURISTICS
7
EXPLAINING BAYESIAN HEURISTIC APPROACH BY EXAMPLE OF KNAPSACK PROBLEM
11
1 EXACT ALGORITHMS
12
2 APPROXIMATE ALGORITHMS
13
42 MATRIX GAME ALGORITHM
157
5 ONEDIMENSIONAL EXAMPLE
158
6 ECONOMIC DUEL NASH MODEL
159
62 DYNAMIC NASH MODEL
161
7 SOFTWARE EXAMPLE
163
71 OPERATING DUEL
165
FUTURE DEVELOPMENTS
169
PORTFOLIO PROBLEM OPTIMAL INVESTMENT OF RESOURCES
173

22 GREEDY HEURISTICS
14
24 PERMUTATION
16
3 SOFTWARE EXAMPLES OF KNAPSACK PROBLEM
21
31 C++
22
32 JAVA
23
SOFTWARE FOR GLOBAL OPTIMIZATION
31
INTRODUCTION TO SOFTWARE
33
12 DESCRIPTION OF METHODS
34
13 APPLICATION AREAS
36
15 COMPUTING ENVIRONMENT
37
3 DIFFERENT VERSIONS
39
33 UNIX C++ INTERACTIVE
40
4 WEBSITES
41
PORTABLE FORTRAN VERSION GMF
45
2 GENERAL DISCUSSION
47
22 LIST OF METHODS
48
3 PROGRAM DESCRIPTION
49
33 MAIN PROGRAM
50
34 EXAMPLE OF THE MAIN PROGRAM
51
TURBO C VERSION TCGM
55
2 USERS REFERENCE
56
24 MINIMIZATION
57
26 NAVIGATION
60
27 MOVING
61
C++ VERSION GMC
63
2 USERS REFERENCE
64
24 MENU SYSTEM
65
JAVA JDK10 VERSION GMJO
75
2 RUNNING GMJO
76
23 GRAPHICAL INTERFACE
77
24 IMPLEMENTING NEW METHOD
80
JAVA JDK11 AND JDK12 VERSIONS GMJ1 AND GMJ2
85
2 STARTING GMJ
86
22 CONFIGURING STANDALONE APPLICATION
88
32 TASK SELECTION
90
33 OPERATION CONTROL
92
4 UPDATING GMJ
93
41 NEW TASKS
95
42 NEW METHODS
97
43 CONFIGURING PROPERTY MANAGER
98
44 NEW ANALYSIS OBJECTS
100
45 PROGRAMMING TIPS
103
46 SECURITY RESTRICTIONS
104
5 FEATURES OF GMJ2
105
52 DOMAIN CONSTRAINT FUNCTION
106
53 RUNNING GMJ2
107
EXAMPLES OF MODELS
113
COMPETITION MODEL WITH FIXED RESOURCE PRICES NASH EQUILIBRIUM
115
2 NASH MODEL
116
3 SEARCH FOR NASH EQUILIBRIUM
118
31 EXISTENCE OF NASH EQUILIBRIUM
119
41 EXAMPLE OF SERVER COALITION
120
COMPETITION MODEL WITH FREE RESOURCE PRICES WALRAS EQUILIBRIUM
123
2 SEARCH FOR WALRAS EQUILIBRIUM
126
3 MONTECARLO SIMULATION
128
32 TESTING EQUILIBRIUM CONDITIONS
131
4 SOFTWARE EXAMPLE
136
INSPECTION MODEL
143
2 SEARCH FOR EQUILIBRIUM
144
21 DIRECT SEARCH ALGORITHM DSA
145
22 NECESSARY AND SUFFICIENT CONDITIONS
146
24 STRATEGY ELIMINATION ALGORITHM SEA
148
DUEL PROBLEM DIFFERENTIAL GAME MODEL
151
2 CONVEX VERSION
152
3 MIXED STRATEGIES
153
4 SEARCH FOR EQUILIBRIUM
155
2 EXPECTED UTILITY
174
3 OPTIMAL PORTFOLIO SPECIAL CASES
175
4 UTILITY FUNCTIONS
176
5 SOFTWARE EXAMPLE
178
52 A SET OF UTILITY FUNCTIONS
179
53 PREDICTING INVESTMENT RESULTS
180
54 DATA
182
55 RESULTS
183
56 FUTURE DEVELOPMENTS
184
EXCHANGE RATE PREDICTION TIME SERIES MODEL
187
2 AUTO REGRESSIVE MOVINGAVERAGE MODELS ARMA
189
31 OPTIMIZATION OF AR PARAMETERS
190
32 OPTIMIZATION OF MA PARAMETERS
191
34 EVALUATION OF ARMA PREDICTION ERRORS
192
4 EXTERNAL FACTORS
193
41 MISSING DATA
196
6 ARTIFICIAL NEURAL NETWORKS MODELS ANN
197
7 BILINEAR MODELS BL
199
82 MINIMIZATION OF RESIDUALS
200
83 DISCUSSIONS
202
9 MULTISTEP PREDICTIONS
204
10 STRUCTURAL STABILIZATION
205
102 SIMPLE EXAMPLE
208
103 EXAMPLES OF STRUCTURAL OPTIMIZATION WITH EXTERNAL FACTORS
209
11 EXAMPLES OF SQUARED RESIDUALS MINIMIZATION
210
112 OPTIMIZATION RESULTS
215
12 SOFTWARE EXAMPLES
221
122 JAVA VERSION OF ARMA SOFTWARE ARMAJ
238
123 ANN SOFTWARE
243
CALL CENTER MODEL
245
12 ASSUMPTIONS NOTATIONS AND OBJECTIVES
246
2 CALCULATION OF STATIONARY PROBABILITIES
247
3 ASYMPTOTIC EXPRESSIONS
248
5 CALL RATE ESTIMATE
249
7 MONTE CARLO SIMULATION MCS
250
72 MONTE CARLO ERRORS
252
73 STOPPING MONTE CARLO
253
MONTE CARLO MODEL
254
9 TIMEDEPENDANT CASES
255
91 SIMPLE EXAMPLE
256
10 CALL RATE PREDICTIONS
257
102 CALL RATE PREDICTION BY SCALE MODELS
259
103 EXPERT MODEL EVENT SCALE VERSION
261
104 TIME SCALE VERSION VECTOR PREDICTION
269
105 TIME SERIES MODEL ARMA
272
106 APPLICATION EXAMPLES
273
OPTIMAL SCHEDULING
275
2 FLOWSHOP PROBLEM
276
22 HEURISTICS
277
24 GMC SOFTWARE EXAMPLE
278
3 SCHOOL SCHEDULING
282
31 CONSTRAINTS
283
33 PERMUTATION AND EVALUATION ALGORITHM
284
34 SOFTWARE EXAMPLE
285
SEQUENTIAL STATISTICAL DECISIONS MODEL BRIDE PROBLEM
291
2 AVERAGE UTILITY
292
3 SINGLEMARRIAGE CASE
293
32 DISCRETE APPROXIMATION
294
33 INCLUDING THE WAITING COST
295
4 MULTIMARRIAGE CASE
296
42 BELLMANS EQUATIONS
297
5 SOFTWARE EXAMPLES
299
References
307
Index
317
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