Multi-Objective Optimization - Evolutionary to Hybrid Framework

Foreword

Editorial Preface

Contents

About the Editors

Non-dominated Sorting Based Multi/Many-Objective Optimization: Two Decades of Research and Application

1 Introduction

2 Across Different Scenarios

2.1 Multi/Many-Objective Optimization

2.2 Single-objective Optimization

3 Recent Non-dominated Sorting Based Algorithms

3.1 ?0????????????????

3.2 Other Successful Algorithms

4 State-of-the-Art Combinations

4.1 Alternating Phases

4.2 Two Local Search Operators

4.3 B-NSGA-III Results

5 Conclusions

References

Mean-Entropy Model of Uncertain Portfolio Selection Problem

1 Introduction

2 Literature Study

3 Preliminaries

4 Uncertain Multi-Objective Programming

4.1 Weighted Sum Method

4.2 Weighted Metric Method

5 Multi-Objective Genetic Algorithm

5.1 Nondominated Sorting Genetic Algorithm II (NSGA-II)

5.2 Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D)

6 Performance Metrics

7 Proposed Uncertain Bi-Objective Portfolio Selection Model

8 Results and Discussion

9 Conclusion

References

Incorporating Gene Ontology Information in Gene Expression Data Clustering Using Multiobjective Evolutionary Optimization: Application in Yeast Cell Cycle Data

1 Introduction

2 Gene Ontology and Similarity Measures

2.1 Resnik's Measure

2.2 Lin's Measure

2.3 Weighted Jaccard Measure

2.4 Combining Expression-Based and GO-Based Distances

3 Multiobjective Optimization and Clustering

3.1 Formal Definitions

3.2 Multiobjective Clustering

4 Incorporating GO Knowledge in Multiobjective Clustering

4.1 Chromosome Representation and Initialization of Population

4.2 Computation of Fitness Functions

4.3 Genetic Operators

4.4 Final Solution from the Non-dominated Front

5 Experimental Results and Discussion

5.1 Dataset and Preprocessing

5.2 Experimental Setup

5.3 Study of GO Enrichment

5.4 Study of KEGG Pathway Enrichment

6 Conclusion

References

Interval-Valued Goal Programming Method to Solve Patrol Manpower Planning Problem for Road Traffic Management Using Genetic Algorithm

1 Introduction

2 IVGP Formulation

2.1 Deterministic Flexible Goals

2.2 IVGP Model

2.3 The IVGP Algorithm

2.4 GA Computational Scheme for IVGP Model

3 Definitions of Variables and Parameters

4 Descriptions of Goals and Constraints

4.1 Performance Measure Goals

4.2 System Constraints

5 An Illustrative Example

5.1 Construction of Model Goals

5.2 Description of Constraints

5.3 Performance Comparison

6 Conclusions and Future Scope

References

Multi-objective Optimization to Improve Robustness in Networks

1 Introduction

1.1 Robustness Measures Based on the Eigenvalues of the Adjacency Matrix

1.2 Measures Based on the Eigenvalues of the Laplacian Matrix

1.3 Measures Based on Other Properties

2 Properties of Network Robustness Measures

2.1 Robustness of Elementary Networks

2.2 Correlation of Robustness Measures

3 Multi-objective Definition of Robustness

3.1 Fast Calculation of Robustness Measures

4 Selecting Solutions from Multi-objective Optimization

4.1 Ranking Methods

4.2 Pruning Methods

4.3 Subset Optimality

5 Leave-k-out Approach for Multi-objective Optimization

6 Experimental Results

6.1 Improving Robustness by Edge Addition

6.2 Network Robustness After Node Attacks

7 Conclusion

References

On Joint Maximization in Energy and Spectral Efficiency in Cooperative Cognitive Radio Networks

1 Introduction

1.1 Machine Learning in CR

1.2 Scope and Contributions

2 System Model

2.1 Signal Model

3 Problem Formulation and Proposed Solution

4 Numerical Results

5 Conclusions

References

Multi-Objective Optimization Approaches in Biological Learning System on Microarray Data

1 Introduction

2 Fundamental Terms and Preliminaries

2.1 Microarray

2.2 Statistical Tests

2.3 Epigenetic Biomarker

2.4 Multi-Objective Optimization

2.5 Pareto-Optimal

3 Method Hierarchy

4 Description of Methods

4.1 Integrated Learning Approach to Classify Multi-class Cancer Data

4.2 Multi-Objective Optimization Method on Gene Regularity Networks

4.3 Multi-Objective Genetic Algorithm in Fuzzy Clustering of Categorical Attributes

4.4 Multi-Objective Differential Evolution for Automatic Clustering of Microarray Datasets

4.5 Multi-Objective Particle Swarm Optimization to Identify Gene Marker

4.6 Multi-Objective Binary Particle Swarm Optimization Algorithm for Cancer Data Feature Selection

4.7 Multi-Objective Approach for Identifying Coexpressed Module During HIV Disease Progression

4.8 Other Methods

5 Discussion

6 Conclusion

References

Application of Multiobjective Optimization Techniques in Biomedical Image Segmentation—A Study

1 Introduction

2 Multiobjective Optimization

3 Application of Multiobjective Optimization in Biomedical Images

4 Conclusion

References

Feature Selection Using Multi-Objective Optimization Technique for Supervised Cancer Classification

1 Introduction

2 Experimental Datasets

3 Objectives

4 Proposed Methodology

4.1 Multi-Objective Blended Particle Swarm Optimization (MOBPSO)

4.2 Other Comparative Methods for the Selection of Genes

5 Experimental Results

5.1 Classification Results

5.2 Comparative Analysis

5.3 Biological Relevance

6 Conclusion

References

Extended Nondominated Sorting Genetic Algorithm (ENSGA-II) for Multi-Objective Optimization Problem in Interval Environment

1 Introduction

2 Interval Mathematics and Order Relations Between Intervals

2.1 Interval Mathematics

2.2 Order Relations of Interval Numbers

3 Multi-Objective Optimization Problem with Interval Objectives

4 Nondominated Sorting Genetic Algorithm for Interval Objectives

4.1 Constraint Handling Techniques

4.2 Nondominated Sorting

4.3 Interval Crowding Distance

4.4 Crowded Tournament Selection

4.5 Crossover

4.6 Mutation

4.7 Algorithm

5 Numerical Simulation

6 Concluding Remarks

Appendix

References

A Comparative Study on Different Versions of Multi-Objective Genetic Algorithm for Simultaneous Gene Selection and Sample Categorization

1 Introduction

2 Brief Overview of State-of-the-Art Methods

3 Proposed Methodology

3.1 Initial Population and External Population

3.2 Fitness Function

3.3 Tournament Selection

3.4 Crossover Operation

3.5 Mutation Operation

3.6 Multi-Objective Genetic Algorithm for Gene Selection and Sample Clustering

4 Experimental Results

4.1 Microarray Dataset Description

4.2 Parameter Setup and Preprocessing

4.3 Performance Measurement

5 Summary

References

A Survey on the Application of Multi-Objective Optimization Methods in Image Segmentation

1 Introduction

2 Image Segmentation and MOO

3 Image Segmentation Design Issue

4 Image Segmentation Classification Using Multi-Objective Perspective

5 Survey on Image Application Including MOO

6 Conclusion

References

Bi-objective Genetic Algorithm with Rough Set Theory for Important Gene Selection in Disease Diagnosis

1 Introduction

2 Bi-objective Gene Selection

2.1 Initial Population Generation

2.2 Bi-objective Objective Function

2.3 Multipoint Crossover

2.4 Jumping Gene Mutation

2.5 Replacement Strategy

2.6 The GSBOGA Algorithm

3 Experimental Results of GSBOGA Method

3.1 Microarray Dataset Description

3.2 Parameter Setup and Preprocessing

3.3 Performance Measurement

3.4 Comparative Study

4 Summary

References

Multi-Objective Optimization and Cluster-Wise Regression Analysis to Establish Input–Output Relationships of a Process

1 Introduction

2 Literature Survey

3 Developed Approach

4 Experimental Data Collection

4.1 Experimental Setup and Procedure

4.2 Data Collection

5 Results and Discussion

5.1 Obtaining Nonlinear Input–Output Relationships from the Experimental Data

5.2 Formulation of the Optimization Problem

5.3 Obtaining Initial Pareto-Front

5.4 Training of an NFS

5.5 Obtaining Modified Pareto-Front

5.6 Clustering of the Modified Pareto-Front Data Set

6 Conclusion

Appendices

References