(eBook PDF) Optimization in Operations Research
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,
,vi Contents
chaPter 2 determiniStic oPtimization modelS
in oPerationS reSearch 23
2.1 Decision Variables, Constraints, and Objective
Functions 23
Decision Variables 24
Variable-Type Constraints 24
Main Constraints 25
Objective Functions 25
Standard Model 26
2.2 Graphic Solution and Optimization Outcomes 27
Graphic Solution 27
Feasible Sets 27
Graphing Constraints and Feasible Sets 27
Graphing Objective Functions 30
Optimal Solutions 33
Optimal Values 34
Unique versus Alternative Optimal Solutions 35
Infeasible Models 36
Unbounded Models 38
2.3 Large-Scale Optimization Models and Indexing 40
Indexing 40
Indexed Decision Variables 41
Indexed Symbolic Parameters 42
Objective Functions 43
Indexed Families of Constraints 43
Pi Hybrids Application Model 45
How Models Become Large 46
2.4 Linear and Nonlinear Programs 46
General Mathematical Programming Format 46
Right-Hand Sides 47
Linear Functions 48
Linear and Nonlinear Programs Defined 50
Two Crude and Pi Hybrids Models are LPs 51
Indexing, Parameters, and Decision Variables for E-mart 51
Nonlinear Response 51
E-mart Application Model 52
2.5 Discrete or Integer Programs 53
Indexes and Parameters of the Bethlehem Application 53
Discrete versus Continuous Decision Variables 53
Constraints with Discrete Variables 55
Bethlehem Ingot Mold Application Model 56
Integer and Mixed-Integer Programs 56
Integer Linear versus Integer Nonlinear Programs 57
Indexing, Parameters, and Decision Variables for Purdue Finals
Application 59
, Contents vii
Nonlinear Objective Function 59
Purdue Final Exam Scheduling Application Model 60
2.6 Multiobjective Optimization Models 60
Multiple Objectives 61
Constraints of the DuPage Land Use Application 62
DuPage Land Use Application Model 63
Conflict among Objectives 64
2.7 Classification Summary 65
2.8 Computer Solution and AMPL 65
Solvers versus Modeling Languages 66
Indexing, Summations, and Symbolic Parameters 67
Nonlinear and Integer Models 70
Exercises 73
References 86
chaPter 3 imProving Search 87
3.1 Improving Search, Local, and Global Optima 87
Solutions 88
Solutions as Vectors 88
Example of an Improving Search 93
Neighborhood Perspective 94
Local Optima 95
Local Optima and Improving Search 95
Local versus Global Optima 95
Dealing with Local Optima 97
3.2 Search with Improving and Feasible Directions 98
Direction-Step Paradigm 98
Improving Directions 100
Feasible Directions 102
Step Size: How Far? 104
Search of the DClub Example 105
When Improving Search Stops 107
Detecting Unboundedness 108
3.3 Algebraic Conditions for Improving and Feasible
Directions 109
Gradients 109
Gradient Conditions for Improving Directions 112
Objective Function Gradients as Move Directions 114
Active Constraints and Feasible Directions 115
Linear Constraints 117
Conditions for Feasible Directions with Linear
Constraints 118
2nd Edition install download
https://ebookluna.com/product/ebook-pdf-optimization-in-
operations-research-2nd-edition/
Download more ebook instantly today - Get yours now at ebookluna.com
,
,vi Contents
chaPter 2 determiniStic oPtimization modelS
in oPerationS reSearch 23
2.1 Decision Variables, Constraints, and Objective
Functions 23
Decision Variables 24
Variable-Type Constraints 24
Main Constraints 25
Objective Functions 25
Standard Model 26
2.2 Graphic Solution and Optimization Outcomes 27
Graphic Solution 27
Feasible Sets 27
Graphing Constraints and Feasible Sets 27
Graphing Objective Functions 30
Optimal Solutions 33
Optimal Values 34
Unique versus Alternative Optimal Solutions 35
Infeasible Models 36
Unbounded Models 38
2.3 Large-Scale Optimization Models and Indexing 40
Indexing 40
Indexed Decision Variables 41
Indexed Symbolic Parameters 42
Objective Functions 43
Indexed Families of Constraints 43
Pi Hybrids Application Model 45
How Models Become Large 46
2.4 Linear and Nonlinear Programs 46
General Mathematical Programming Format 46
Right-Hand Sides 47
Linear Functions 48
Linear and Nonlinear Programs Defined 50
Two Crude and Pi Hybrids Models are LPs 51
Indexing, Parameters, and Decision Variables for E-mart 51
Nonlinear Response 51
E-mart Application Model 52
2.5 Discrete or Integer Programs 53
Indexes and Parameters of the Bethlehem Application 53
Discrete versus Continuous Decision Variables 53
Constraints with Discrete Variables 55
Bethlehem Ingot Mold Application Model 56
Integer and Mixed-Integer Programs 56
Integer Linear versus Integer Nonlinear Programs 57
Indexing, Parameters, and Decision Variables for Purdue Finals
Application 59
, Contents vii
Nonlinear Objective Function 59
Purdue Final Exam Scheduling Application Model 60
2.6 Multiobjective Optimization Models 60
Multiple Objectives 61
Constraints of the DuPage Land Use Application 62
DuPage Land Use Application Model 63
Conflict among Objectives 64
2.7 Classification Summary 65
2.8 Computer Solution and AMPL 65
Solvers versus Modeling Languages 66
Indexing, Summations, and Symbolic Parameters 67
Nonlinear and Integer Models 70
Exercises 73
References 86
chaPter 3 imProving Search 87
3.1 Improving Search, Local, and Global Optima 87
Solutions 88
Solutions as Vectors 88
Example of an Improving Search 93
Neighborhood Perspective 94
Local Optima 95
Local Optima and Improving Search 95
Local versus Global Optima 95
Dealing with Local Optima 97
3.2 Search with Improving and Feasible Directions 98
Direction-Step Paradigm 98
Improving Directions 100
Feasible Directions 102
Step Size: How Far? 104
Search of the DClub Example 105
When Improving Search Stops 107
Detecting Unboundedness 108
3.3 Algebraic Conditions for Improving and Feasible
Directions 109
Gradients 109
Gradient Conditions for Improving Directions 112
Objective Function Gradients as Move Directions 114
Active Constraints and Feasible Directions 115
Linear Constraints 117
Conditions for Feasible Directions with Linear
Constraints 118
