Multi-Objective Optimization : Evolutionary to Hybrid Framework

This book brings together the latest findings on efficient solutions of multi/many-objective optimization problems from the leading researchers in the field. The focus is on solving real-world optimization problems using strategies ranging from evolutionary to hybrid frameworks, and involving various computation platforms. The topics covered include solution frameworks using evolutionary to hybrid models in application areas like Analytics, Cancer Research, Traffic Management, Networks and Communications, E-Governance, Quantum Technology, Image Processing, etc. As such, the book offers a valuable resource for all postgraduate students and researchers interested in exploring solution frameworks for multi/many-objective optimization problems. Foreword......Page 5 Editorial Preface......Page 6 Contents......Page 11 About the Editors......Page 13 1 Introduction......Page 15 2.1 Multi/Many-Objective Optimization......Page 19 3.1 NSGA-III and Its Variants......Page 21 3.2 Other Successful Algorithms......Page 25 4 State-of-the-Art Combinations......Page 26 4.1 Alternating Phases......Page 28 4.2 Two Local Search Operators......Page 32 4.3 B-NSGA-III Results......Page 34 References......Page 35 1 Introduction......Page 39 2 Literature Study......Page 41 3 Preliminaries......Page 43 4 Uncertain Multi-Objective Programming......Page 47 4.1 Weighted Sum Method......Page 49 4.2 Weighted Metric Method......Page 50 5 Multi-Objective Genetic Algorithm......Page 51 5.1 Nondominated Sorting Genetic Algorithm II (NSGA-II)......Page 52 5.2 Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D)......Page 53 6 Performance Metrics......Page 56 7 Proposed Uncertain Bi-Objective Portfolio Selection Model......Page 58 8 Results and Discussion......Page 60 9 Conclusion......Page 64 References......Page 65 1 Introduction......Page 69 2 Gene Ontology and Similarity Measures......Page 70 2.1 Resnik's Measure......Page 71 2.3 Weighted Jaccard Measure......Page 72 3.1 Formal Definitions......Page 73 4.1 Chromosome Representation and Initialization of Population......Page 75 4.2 Computation of Fitness Functions......Page 76 4.4 Final Solution from the Non-dominated Front......Page 77 5.2 Experimental Setup......Page 78 5.3 Study of GO Enrichment......Page 79 5.4 Study of KEGG Pathway Enrichment......Page 85 References......Page 91 1 Introduction......Page 93 2 IVGP Formulation......Page 97 2.1 Deterministic Flexible Goals......Page 99 2.2 IVGP Model......Page 100 2.3 The IVGP Algorithm......Page 101 2.4 GA Computational Scheme for IVGP Model......Page 103 3 Definitions of Variables and Parameters......Page 105 4.1 Performance Measure Goals......Page 106 5 An Illustrative Example......Page 114 5.1 Construction of Model Goals......Page 117 5.2 Description of Constraints......Page 120 5.3 Performance Comparison......Page 124 6 Conclusions and Future Scope......Page 125 References......Page 126 1.1 Robustness Measures Based on the Eigenvalues of the Adjacency Matrix......Page 128 1.2 Measures Based on the Eigenvalues of the Laplacian Matrix......Page 129 1.3 Measures Based on Other Properties......Page 130 2 Properties of Network Robustness Measures......Page 131 2.1 Robustness of Elementary Networks......Page 132 2.2 Correlation of Robustness Measures......Page 133 3 Multi-objective Definition of Robustness......Page 135 3.1 Fast Calculation of Robustness Measures......Page 136 4 Selecting Solutions from Multi-objective Optimization......Page 137 4.1 Ranking Methods......Page 138 4.2 Pruning Methods......Page 139 4.3 Subset Optimality......Page 140 5 Leave-k-out Approach for Multi-objective Optimization......Page 141 6.1 Improving Robustness by Edge Addition......Page 142 7 Conclusion......Page 147 References......Page 150 1 Introduction......Page 153 1.1 Machine Learning in CR......Page 155 1.2 Scope and Contributions......Page 156 2 System Model......Page 157 2.1 Signal Model......Page 158 3 Problem Formulation and Proposed Solution......Page 161 4 Numerical Results......Page 164 5 Conclusions......Page 167 References......Page 168 1 Introduction......Page 170 2 Fundamental Terms and Preliminaries......Page 171 2.2 Statistical Tests......Page 172 2.4 Multi-Objective Optimization......Page 174 3 Method Hierarchy......Page 175 4.2 Multi-Objective Optimization Method on Gene Regularity Networks......Page 176 4.3 Multi-Objective Genetic Algorithm in Fuzzy Clustering of Categorical Attributes......Page 178 4.4 Multi-Objective Differential Evolution for Automatic Clustering of Microarray Datasets......Page 181 4.5 Multi-Objective Particle Swarm Optimization to Identify Gene Marker......Page 182 4.6 Multi-Objective Binary Particle Swarm Optimization Algorithm for Cancer Data Feature Selection......Page 183 4.7 Multi-Objective Approach for Identifying Coexpressed Module During HIV Disease Progression......Page 185 4.8 Other Methods......Page 186 5 Discussion......Page 187 References......Page 189 1 Introduction......Page 192 2 Multiobjective Optimization......Page 196 3 Application of Multiobjective Optimization in Biomedical Images......Page 197 4 Conclusion......Page 200 References......Page 202 1 Introduction......Page 206 2 Experimental Datasets......Page 208 4 Proposed Methodology......Page 210 4.1 Multi-Objective Blended Particle Swarm Optimization (MOBPSO)......Page 211 4.2 Other Comparative Methods for the Selection of Genes......Page 216 5 Experimental Results......Page 217 5.1 Classification Results......Page 218 5.2 Comparative Analysis......Page 219 5.3 Biological Relevance......Page 222 References......Page 223 1 Introduction......Page 225 2.1 Interval Mathematics......Page 227 2.2 Order Relations of Interval Numbers......Page 230 4 Nondominated Sorting Genetic Algorithm for Interval Objectives......Page 235 4.2 Nondominated Sorting......Page 236 4.3 Interval Crowding Distance......Page 237 4.4 Crowded Tournament Selection......Page 239 4.6 Mutation......Page 240 4.7 Algorithm......Page 241 5 Numerical Simulation......Page 242 Appendix......Page 248 References......Page 251 1 Introduction......Page 252 2 Brief Overview of State-of-the-Art Methods......Page 253 3 Proposed Methodology......Page 256 3.1 Initial Population and External Population......Page 257 3.2 Fitness Function......Page 259 3.4 Crossover Operation......Page 263 3.6 Multi-Objective Genetic Algorithm for Gene Selection and Sample Clustering......Page 264 4.1 Microarray Dataset Description......Page 271 4.3 Performance Measurement......Page 272 References......Page 274 1 Introduction......Page 277 2 Image Segmentation and MOO......Page 278 3 Image Segmentation Design Issue......Page 279 4 Image Segmentation Classification Using Multi-Objective Perspective......Page 280 5 Survey on Image Application Including MOO......Page 282 References......Page 284 1 Introduction......Page 287 2.1 Initial Population Generation......Page 289 2.2 Bi-objective Objective Function......Page 290 2.4 Jumping Gene Mutation......Page 294 2.5 Replacement Strategy......Page 295 2.6 The GSBOGA Algorithm......Page 296 3.1 Microarray Dataset Description......Page 298 3.3 Performance Measurement......Page 299 3.4 Comparative Study......Page 301 References......Page 304 1 Introduction......Page 307 2 Literature Survey......Page 309 3 Developed Approach......Page 310 4 Experimental Data Collection......Page 312 4.2 Data Collection......Page 313 5.1 Obtaining Nonlinear Input–Output Relationships from the Experimental Data......Page 314 5.3 Obtaining Initial Pareto-Front......Page 315 5.4 Training of an NFS......Page 317 5.6 Clustering of the Modified Pareto-Front Data Set......Page 318 6 Conclusion......Page 322 Appendices......Page 323 References......Page 324