Advanced Optimization and Decision-Making Techniques in Textile Manufacturing PDF by Anindya Ghosh, Prithwiraj Mal, Abhijit Majumdar

Preface………………………………………………………………………………………………………..xi
About the Authors…………………………………………………………………………………..xiii
1. Introduction to Decision-Making and Optimization Techniques……..1
1.1 Introduction………………………………………………………………………………..1
1.2 Decision-Making Process and Classification……………………………….1
1.2.1 Decision-Making Under Certainty, Risk, and Uncertainty……………………………………………………………………..3
1.2.2 Multicriteria Decision-Making………………………………………..6
1.3 Optimization………………………………………………………………………………8
1.3.1 Linear Programming……………………………………………………….9
1.3.2 Multiobjective Optimization and Goal Programming…….9
1.3.3 Nontraditional Optimization Algorithms……………………..11
1.3.3.1 Genetic Algorithm…………………………………………..11
1.3.3.2 Particle Swarm Optimization…………………………..13
1.3.3.3 Simulated Annealing……………………………………….13
1.4 Summary…………………………………………………………………………………..14
References…………………………………………………………………………………………..14

2. Analytic Hierarchy Process……………………………………………………………….15
2.1 Introduction………………………………………………………………………………15
2.2 Analytic Hierarchy Process Methodology…………………………………16
2.2.1 Importance of Hierarchical Structure…………………………….22
2.2.2 Rank Reversal in Analytic Hierarchy Process………………..22
2.2.3 Multiplicative Analytic Hierarchy Process…………………….26
2.3 Fuzzy Analytic Hierarchy Process…………………………………………….26
2.3.1 Fuzzy Numbers and Their Operations………………………….26
2.3.2 Developing Decision Hierarchy and Constructing Fuzzy Comparison Matrix…………………………………………….27
2.3.3 Computing Criteria Weights………………………………………….28
2.3.4 Example of Fuzzy Analytic Hierarchy Process Application…………………………………………………………………….30
2.4 Summary…………………………………………………………………………………..32
References…………………………………………………………………………………………..32

3. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)……………………………………………………………………………..35
3.1 Introduction………………………………………………………………………………35
3.2 TOPSIS Methodology………………………………………………………………..35
3.3 Step-by-Step Working Principles of TOPSIS………………………………39
3.4 Application of TOPSIS in Textiles………………………………………………43
3.4.1 Selection of Handloom Fabrics for Summer Clothing Using TOPSIS………………………………………………………………..44
3.5 Fuzzy-TOPSIS Method………………………………………………………………50
3.6 Step-by-Step Working Principles of Fuzzy-TOPSIS……………………54
3.7 MATLAB® Coding…………………………………………………………………….58
3.8 Summary…………………………………………………………………………………..62
References…………………………………………………………………………………………..62

4. Elimination and Choice Translating Reality (ELECTRE)…………………65
4.1 Introduction………………………………………………………………………………65
4.2 ELECTRE Methodology…………………………………………………………….65
4.3 Step-by-Step Working Principles of ELECTRE Method……………..70
4.4 Application of ELECTRE Method in Textiles…………………………….75
4.4.1 Selection of Bulletproof Body Armors Using ELECTRE Method………………………………………………………….76
4.5 MATLAB® Coding…………………………………………………………………….80
4.6 Summary…………………………………………………………………………………..83
References…………………………………………………………………………………………..83 

5. Graph Theory and Matrix Approach of Decision-Making……………….85
5.1 Introduction………………………………………………………………………………85
5.2 Graph Theory and Matrix Approach…………………………………………85
5.3 Step-by-Step Working Principles of Graph Theory and Matrix Approach……………………………………………………………………….90
5.4 Application of Graph Theory and Matrix Approach of Decision-Making in Textiles………………………………………………….92
5.4.1 Cotton Fiber Selection Using Graph Theory and Matrix Approach…………………………………………………….92
5.5 MATLAB® Coding…………………………………………………………………….95
5.6 Summary…………………………………………………………………………………..96
References…………………………………………………………………………………………..96
6. Linear Programming………………………………………………………………………….99
6.1 Introduction………………………………………………………………………………99
6.2 Linear Programming Problem Formulation………………………………99
6.2.1 General Form of a Linear Programming Problem………..102
6.3 Graphical Method……………………………………………………………………103
6.4 Simplex Method………………………………………………………………………108
6.4.1 Big M Method………………………………………………………………112
6.4.2 Two-Phase Method………………………………………………………117
6.5 Applications…………………………………………………………………………….122
6.6 MATLAB® Coding…………………………………………………………………..122
6.7 Summary…………………………………………………………………………………124
References…………………………………………………………………………………………124
7. Fuzzy Linear Programming…………………………………………………………….127
7.1 Introduction…………………………………………………………………………….127
7.2 Crisp Set, Fuzzy Set, and Membership Function……………………..127
7.2.1 Fuzzy Set Operations…………………………………………………..129
7.3 Fuzzy Linear Programming Algorithm…………………………………..131
7.4 Applications…………………………………………………………………………….140
7.5 MATLAB® Coding…………………………………………………………………..140
7.6 Summary…………………………………………………………………………………141
References…………………………………………………………………………………………141
8. Quadratic Programming………………………………………………………………….143
8.1 Introduction…………………………………………………………………………….143
8.2 Quadratic Programming Algorithm………………………………………..143
8.2.1 Lagrangian Function……………………………………………………144
8.2.2 Kuhn-Tucker Conditions………………………………………………145
8.2.3 Wolfe’s Method to Solve Quadratic Programming Problem……………………………………………………………………….147
8.3 Application of Wolfe’s Method for Solving Quadratic Programming Problem in Textile Field……………………………………154
8.4 MATLAB® Coding…………………………………………………………………..157
8.5 Summary…………………………………………………………………………………160
References…………………………………………………………………………………………160
9. Genetic Algorithm……………………………………………………………………………163
9.1 Introduction…………………………………………………………………………….163
9.2 Genetic Algorithm…………………………………………………………………..164
9.2.1 Representation……………………………………………………………..164
9.2.2 Fitness Evaluation………………………………………………………..165
9.2.3 Reproduction……………………………………………………………….165
9.2.4 Crossover…………………………………………………………………….167
9.2.5 Mutation………………………………………………………………………171
9.2.6 Flowchart of a Genetic Algorithm………………………………..172
9.3 Step-by-Step Working Principle of Genetic Algorithm…………….173
9.4 Application of Genetic Algorithm in Textiles…………………………..184
9.4.1 Application of Genetic Algorithm in Fitting Stress–Strain Curve of Fibers……………………………………….185
9.5 MATLAB® Coding…………………………………………………………………..190
9.6 Summary…………………………………………………………………………………193
References…………………………………………………………………………………………193
10. Particle Swarm Optimization………………………………………………………….195
10.1 Introduction…………………………………………………………………………….195
10.2 Particle Swarm Optimization…………………………………………………..195
10.2.1 Flowchart of Particle Swarm Optimization………………….198
10.3 Step-by-Step Working Principle of Particle Swarm Optimization…………………………………………………………………………..199
10.4 Application of Particle Swarm Optimization in Textiles………….208
10.4.1 Application of Particle Swarm Optimization in Fabric Engineering……………………………………………………….208
10.5 MATLAB® Coding…………………………………………………………………..215
10.6 Summary…………………………………………………………………………………218
References…………………………………………………………………………………………218
11. Simulated Annealing……………………………………………………………………….221
11.1 Introduction…………………………………………………………………………….221
11.2 Simulated Annealing……………………………………………………………….221
11.2.1 Flowchart of Simulated Annealing………………………………225
11.3 Step-by-Step Working Principle of Simulated Annealing………..225
11.4 Application of Simulated Annealing in Textiles………………………235
11.4.1 Application of Simulated Annealing in Yarn Engineering…………………………………………………………………235
11.5 MATLAB® Coding…………………………………………………………………..239
11.6 Summary…………………………………………………………………………………242
References…………………………………………………………………………………………242
12. Multiobjective Optimization…………………………………………………………..245
12.1 Introduction…………………………………………………………………………….245
12.2 Goal Programming………………………………………………………………….245
12.2.1 Goal Programming with One Goal………………………………246
12.2.2 Goal Programming with Multiple Goals……………………..247
12.2.2.1 Non-Preemptive Goal Programming……………..248
12.2.2.2 Goal Programming with Differential Weighting………………………………………………………249
12.2.2.3 Preemptive Goal Programming……………………..250
12.3 Multiobjective Optimization Using Desirability Function……….252
12.3.1 Application of Desirability Function Approach for Multiobjective Optimization………………………………………..254
12.3.2 Multiobjective Optimization of Air Permeability, Thermal Conductivity, and Ultraviolet Protection Factor of Knitted Fabrics Using Desirability Function…………………………………………254
12.4 Multiobjective Optimization Using Evolutionary Algorithm………………………………………………………………………………..257
12.4.1 Application of Evolutionary Algorithm Approach for Multiobjective Optimization………………………………………..273
12.4.1.1 Using Two Objective Functions: Spinning Consistency Index and Yarn Strength…………………………………………………274
12.4.1.2 Using Three Objective Functions: Air Permeability, Thermal Conductivity, and Ultraviolet Protection Factor of Knitted Fabrics……………………………………………………………275
12.5 MATLAB® Coding…………………………………………………………………..276
12.6 Summary…………………………………………………………………………………291
References…………………………………………………………………………………………291
Index……………………………………………………………………………………………………….293