Multi-Objective Optimization (eBook)

Dr. Mandal received his M.Tech. in Computer Science from the University of Calcutta and his Ph.D. from Jadavpur University in the field of Data Compression and Error Correction Techniques. Currently he is a Professor of Computer Science and Engineering and Director of the IQAC at the University of Kalyani, West Bengal, India. He is a former Dean of Engineering, Technology & Management (2008–2012). He has 29 years of teaching and research experience. He has served as a Professor of Computer Applications, Kalyani Govt. Engineering College for two years and as an Associate and Assistant Professor at the University of North Bengal for sixteen years. He has been a Life Member of the Computer Society of India since 1992. Further, he is a fellow of the IETE and a member of the AIRCC. He has produced 146 publications in various international journals, has edited twenty volumes as a volume editor for Science Direct, Springer, CSI etc., and has successfully executed five Research Projects funded by the AICTE, Ministry of IT Government of West Bengal. In addition, he is a guest editor of Microsystem Technology Journal and Chief Editor of the CSI Journal of Computing. Somnath Mukhopadhyay is currently an Assistant Professor at Department of Computer Science and Engineering, Assam University, Silchar, India. He completed his M.Tech. and Ph.D. degrees in Computer Science and Engineering at the University of Kalyani, India, in 2011 and 2015, respectively. He has co-authored one book and has five edited books to his credit. He has published over 20 papers in various international journals and conference proceedings, as well as three chapters in edited volumes. His research interests include digital image processing, computational intelligence and pattern recognition. He is a member of IEEE and IEEE Computational Intelligence Society, Kolkata Section; life member of the Computer Society of India; and currently the regional student coordinator (RSC) of Region II, Computer Society of India.Dr. Paramartha Dutta completed his Bachelor’s and Master’s degrees in Statistics at the Indian Statistical Institute, Calcutta in 1988 and 1990, respectively. He received a Master’s of Technology in Computer Science from the latter institute in 1993 and a Doctor of Philosophy in Engineering from Bengal Engineering and Science University, Shibpur in 2005. Dr. Dutta is currently a Professor at the Department of Computer and System Sciences, Visva Bharati University, West Bengal, India. Prior to this, he served Kalyani Government Engineering College and College of Engineering in West Bengal as a full-time faculty member. He has coauthored eight books, and has five edited books to his credit. He has published over 180 papers in various journals and conference proceedings, both international and national, as well as several book chapters in books from respected international publishing house like Elsevier, Springer-Verlag, CRC Press, and John Wiley. He has also served as an editor of special volumes of several prominent international journals.

Foreword 5
Editorial Preface 6
Contents 11
About the Editors 13
Non-dominated Sorting Based Multi/Many-Objective Optimization: Two Decades of Research and Application 15
1 Introduction 15
2 Across Different Scenarios 19
2.1 Multi/Many-Objective Optimization 19
2.2 Single-objective Optimization 21
3 Recent Non-dominated Sorting Based Algorithms 21
3.1 ?0???????????????? 21
3.2 Other Successful Algorithms 25
4 State-of-the-Art Combinations 26
4.1 Alternating Phases 28
4.2 Two Local Search Operators 32
4.3 B-NSGA-III Results 34
5 Conclusions 35
References 35
Mean-Entropy Model of Uncertain Portfolio Selection Problem 39
1 Introduction 39
2 Literature Study 41
3 Preliminaries 43
4 Uncertain Multi-Objective Programming 47
4.1 Weighted Sum Method 49
4.2 Weighted Metric Method 50
5 Multi-Objective Genetic Algorithm 51
5.1 Nondominated Sorting Genetic Algorithm II (NSGA-II) 52
5.2 Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) 53
6 Performance Metrics 56
7 Proposed Uncertain Bi-Objective Portfolio Selection Model 58
8 Results and Discussion 60
9 Conclusion 64
References 65
Incorporating Gene Ontology Information in Gene Expression Data Clustering Using Multiobjective Evolutionary Optimization: Application in Yeast Cell Cycle Data 69
1 Introduction 69
2 Gene Ontology and Similarity Measures 70
2.1 Resnik's Measure 71
2.2 Lin's Measure 72
2.3 Weighted Jaccard Measure 72
2.4 Combining Expression-Based and GO-Based Distances 73
3 Multiobjective Optimization and Clustering 73
3.1 Formal Definitions 73
3.2 Multiobjective Clustering 75
4 Incorporating GO Knowledge in Multiobjective Clustering 75
4.1 Chromosome Representation and Initialization of Population 75
4.2 Computation of Fitness Functions 76
4.3 Genetic Operators 77
4.4 Final Solution from the Non-dominated Front 77
5 Experimental Results and Discussion 78
5.1 Dataset and Preprocessing 78
5.2 Experimental Setup 78
5.3 Study of GO Enrichment 79
5.4 Study of KEGG Pathway Enrichment 85
6 Conclusion 91
References 91
Interval-Valued Goal Programming Method to Solve Patrol Manpower Planning Problem for Road Traffic Management Using Genetic Algorithm 93
1 Introduction 93
2 IVGP Formulation 97
2.1 Deterministic Flexible Goals 99
2.2 IVGP Model 100
2.3 The IVGP Algorithm 101
2.4 GA Computational Scheme for IVGP Model 103
3 Definitions of Variables and Parameters 105
4 Descriptions of Goals and Constraints 106
4.1 Performance Measure Goals 106
4.2 System Constraints 114
5 An Illustrative Example 114
5.1 Construction of Model Goals 117
5.2 Description of Constraints 120
5.3 Performance Comparison 124
6 Conclusions and Future Scope 125
References 126
Multi-objective Optimization to Improve Robustness in Networks 128
1 Introduction 128
1.1 Robustness Measures Based on the Eigenvalues of the Adjacency Matrix 128
1.2 Measures Based on the Eigenvalues of the Laplacian Matrix 129
1.3 Measures Based on Other Properties 130
2 Properties of Network Robustness Measures 131
2.1 Robustness of Elementary Networks 132
2.2 Correlation of Robustness Measures 133
3 Multi-objective Definition of Robustness 135
3.1 Fast Calculation of Robustness Measures 136
4 Selecting Solutions from Multi-objective Optimization 137
4.1 Ranking Methods 138
4.2 Pruning Methods 139
4.3 Subset Optimality 140
5 Leave-k-out Approach for Multi-objective Optimization 141
6 Experimental Results 142
6.1 Improving Robustness by Edge Addition 142
6.2 Network Robustness After Node Attacks 147
7 Conclusion 147
References 150
On Joint Maximization in Energy and Spectral Efficiency in Cooperative Cognitive Radio Networks 153
1 Introduction 153
1.1 Machine Learning in CR 155
1.2 Scope and Contributions 156
2 System Model 157
2.1 Signal Model 158
3 Problem Formulation and Proposed Solution 161
4 Numerical Results 164
5 Conclusions 167
References 168
Multi-Objective Optimization Approaches in Biological Learning System on Microarray Data 170
1 Introduction 170
2 Fundamental Terms and Preliminaries 171
2.1 Microarray 172
2.2 Statistical Tests 172
2.3 Epigenetic Biomarker 174
2.4 Multi-Objective Optimization 174
2.5 Pareto-Optimal 175
3 Method Hierarchy 175
4 Description of Methods 176
4.1 Integrated Learning Approach to Classify Multi-class Cancer Data 176
4.2 Multi-Objective Optimization Method on Gene Regularity Networks 176
4.3 Multi-Objective Genetic Algorithm in Fuzzy Clustering of Categorical Attributes 178
4.4 Multi-Objective Differential Evolution for Automatic Clustering of Microarray Datasets 181
4.5 Multi-Objective Particle Swarm Optimization to Identify Gene Marker 182
4.6 Multi-Objective Binary Particle Swarm Optimization Algorithm for Cancer Data Feature Selection 183
4.7 Multi-Objective Approach for Identifying Coexpressed Module During HIV Disease Progression 185
4.8 Other Methods 186
5 Discussion 187
6 Conclusion 189
References 189
Application of Multiobjective Optimization Techniques in Biomedical Image Segmentation—A Study 192
1 Introduction 192
2 Multiobjective Optimization 196
3 Application of Multiobjective Optimization in Biomedical Images 197
4 Conclusion 200
References 202
Feature Selection Using Multi-Objective Optimization Technique for Supervised Cancer Classification 206
1 Introduction 206
2 Experimental Datasets 208
3 Objectives 210
4 Proposed Methodology 210
4.1 Multi-Objective Blended Particle Swarm Optimization (MOBPSO) 211
4.2 Other Comparative Methods for the Selection of Genes 216
5 Experimental Results 217
5.1 Classification Results 218
5.2 Comparative Analysis 219
5.3 Biological Relevance 222
6 Conclusion 223
References 223
Extended Nondominated Sorting Genetic Algorithm (ENSGA-II) for Multi-Objective Optimization Problem in Interval Environment 225
1 Introduction 225
2 Interval Mathematics and Order Relations Between Intervals 227
2.1 Interval Mathematics 227
2.2 Order Relations of Interval Numbers 230
3 Multi-Objective Optimization Problem with Interval Objectives 235
4 Nondominated Sorting Genetic Algorithm for Interval Objectives 235
4.1 Constraint Handling Techniques 236
4.2 Nondominated Sorting 236
4.3 Interval Crowding Distance 237
4.4 Crowded Tournament Selection 239
4.5 Crossover 240
4.6 Mutation 240
4.7 Algorithm 241
5 Numerical Simulation 242
6 Concluding Remarks 248
Appendix 248
References 251
A Comparative Study on Different Versions of Multi-Objective Genetic Algorithm for Simultaneous Gene Selection and Sample Categorization 252
1 Introduction 252
2 Brief Overview of State-of-the-Art Methods 253
3 Proposed Methodology 256
3.1 Initial Population and External Population 257
3.2 Fitness Function 259
3.3 Tournament Selection 263
3.4 Crossover Operation 263
3.5 Mutation Operation 264
3.6 Multi-Objective Genetic Algorithm for Gene Selection and Sample Clustering 264
4 Experimental Results 271
4.1 Microarray Dataset Description 271
4.2 Parameter Setup and Preprocessing 272
4.3 Performance Measurement 272
5 Summary 274
References 274
A Survey on the Application of Multi-Objective Optimization Methods in Image Segmentation 277
1 Introduction 277
2 Image Segmentation and MOO 278
3 Image Segmentation Design Issue 279
4 Image Segmentation Classification Using Multi-Objective Perspective 280
5 Survey on Image Application Including MOO 282
6 Conclusion 284
References 284
Bi-objective Genetic Algorithm with Rough Set Theory for Important Gene Selection in Disease Diagnosis 287
1 Introduction 287
2 Bi-objective Gene Selection 289
2.1 Initial Population Generation 289
2.2 Bi-objective Objective Function 290
2.3 Multipoint Crossover 294
2.4 Jumping Gene Mutation 294
2.5 Replacement Strategy 295
2.6 The GSBOGA Algorithm 296
3 Experimental Results of GSBOGA Method 298
3.1 Microarray Dataset Description 298
3.2 Parameter Setup and Preprocessing 299
3.3 Performance Measurement 299
3.4 Comparative Study 301
4 Summary 304
References 304
Multi-Objective Optimization and Cluster-Wise Regression Analysis to Establish Input–Output Relationships of a Process 307
1 Introduction 307
2 Literature Survey 309
3 Developed Approach 310
4 Experimental Data Collection 312
4.1 Experimental Setup and Procedure 313
4.2 Data Collection 313
5 Results and Discussion 314
5.1 Obtaining Nonlinear Input–Output Relationships from the Experimental Data 314
5.2 Formulation of the Optimization Problem 315
5.3 Obtaining Initial Pareto-Front 315
5.4 Training of an NFS 317
5.5 Obtaining Modified Pareto-Front 318
5.6 Clustering of the Modified Pareto-Front Data Set 318
6 Conclusion 322
Appendices 323
References 324