Multi-Objective Optimization in Theory and Practice II · Metaheuristic Algorithms by Keller, Andre A. -- Read -- Imperial Library of Trantor

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PREFACE ACKNOWLEDGEMENTS

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Pareto-Optimal Front Determination

Abstract 1.1. Introduction

1.1.1. Heuristic and Metaheuristic Algorithm 1.1.2. History of Metaheuristics 1.1.3. Metaheuristic Algorithms and Applications 1.1.4. Optimum Design of Framed Structures: A Review of Literature

1.2. ELEMENT OF STATIC MULTI-OBJECTIVE PROGRAMMING

1.2.1. Problem Formulation 1.2.2. Concept of Dominance 1.2.3. Pareto-Optimality

1.3. Pareto-Optimal Front

1.3.1. Non-Dominated Solution 1.3.2. Analytical Pareto-Optimal Front 1.3.3. Near Pareto-Optimal Front

1.3.3.1. Pareto Ranking 1.3.3.2. Extended Pareto Ranking Application 1.3.3.3. Application to an Engineering Problem 1.3.3.4. Near Pareto-Optimal Front Approximation

1.3.4. Shape of a Pareto-Optimal Front

1.3.4.1. The Impact of Minimizing or Maximizing each Objective 1.3.4.2. The Impact Conflicting or Non-conflicting Objectives

1.4. Selection Procedures of Algorithms

1.4.1. Elitist Pareto Criteria 1.4.2. Non-Pareto Criteria 1.4.3. Bi-criterion Evolution 1.4.4. Other Concepts of Dominance

REFERENCES

Metaheuristic Optimization Algorithms

Abstract 2.1. Introduction 2.2. Simulated Annealing Algorithm

2.2.1. Annealing Principle and Description 2.2.2. Problem Formulation 2.2.3. Algorithm Description

2.2.3.1. Acceptance Probability 2.2.3.2. Algorithm 2.2.3.3. Different Cooling Schedules 2.2.3.4. Penalty Function Approach

2.3. Multi-Objective Simulated Annealing

2.3.1. MOSA Algorithm 2.3.2. Test Problems

REFERENCES

Evolutionary Strategy Algorithms

Abstract 3.1. Introduction 3.2. Principles and Operators

3.2.1. Algorithm for Solving Optimization Problems 3.2.2. Binary and Real-Number Encoding 3.2.3. Genetic Operators

3.3. GA-Based Mathematica® Notebook 3.4. Single-Objective Optimization

3.4.1. SciLab Package for Genetic Algorithm 3.4.2. GA-Based Software Package: GENOCOP III

REFERENCES

Genetic Search Algorithms

Abstract 4.1. Introduction 4.2. Niched Pareto Genetic Algorithms (NPGA) 4.3. Non-Dominated Sorting Genetic Algorithm 4.4. Multi-Objective Optimization Test Problems

4.4.1. Unconstrained Optimization Problems

4.4.1.1. Kursawe's Test Function using SciLab 4.4.1.2. UF1 Test Function using MOEA Framework 4.4.1.3. Viennet’s Test Function with SciLab

4.4.2. Constrained Optimization Problem

REFERENCES

Evolution Strategy Algorithms

Abstract 5.1. Introduction 5.2. Differential Evolution Strategy

5.2.1. Principles and Algorithm 5.2.2. DE Operators

5.2.2.1. Mutation Operators 5.2.2.2. Crossover Operators 5.2.2.3. Selection Operators

5.3. DE Algorithm for Single-Objective Optimization Problems 5.4. Multi-Objective DE Algorithm

5.4.1. Diversity-Promoting 5.4.2. Performing Elitism

REFERENCES

Swarm Intelligence and Co-Evolutionary Algorithms

Abstract 6.1. Introduction 6.2. Particle Swarm Optimization 6.3. Cooperative Co-Evolutionary Genetic Algorithm 6.4. Competitive Predator-Prey Optimization Model

6.4.1. Principle of PP Algorithm 6.4.2. PP Algorithm 6.4.3. Illustrative Problems

REFERENCES

Decomposition-Based and Hybrid Evolutionary Algorithms

Abstract 7.1. Introduction 7.2. Decomposition-Based Algorithm

7.2.1. Scalar Decomposition Principle

7.2.1.1. Weighted Sum Approach 7.2.1.2. Tchebycheff Approach 7.2.1.3. Weighted Vector Generation Techniques

7.2.2. Decomposition-Based MOEA Algorithm 7.2.3. MOEA Framework Software Package

7.3. Hybrid Evolutionary Algorithms

7.3.1. Hybridization under Lamarckian Strategy 7.3.2. Two-Stage Hybrid Search Method 7.3.3. Multi-Objective Genetic Local Search Algorithm 7.3.4. Archive-Based Hybrid Scatter Search (AbYSS)

7.3.4.1. Description and Main Features 7.3.4.2. Scatter Search Template 7.3.4.3. jMetal Implementation

REFERENCES

Many-Objective Optimization and Parallel Computation

Abstract 8.1. Introduction 8.2. Many-Objective Optimization

8.2.1. Dominance Extensions for MaOPs 8.2.2. Efficient Optimizers for MaOPs

8.2.2.1. Hypervolume-Based Algorithm 8.2.2.2. Vector Angle-Based Algorithm 8.2.2.3. Reference Point-Based Evolutionary Algorithm 8.2.2.4. Preference-Based Evolutionary Algorithm

8.2.3. Test Problem Suites for MaOPs 8.2.4. A Matlab Platform for MaOPs 8.2.5. Test Problem DTLZ#2 with Many Objectives

8.2.5.1. Formulation of Test Problem DTLZ#2 8.2.5.2. Implementation of a Pseudo NSGA-III Algorithm 8.2.5.3. Parallel Coordinate Plots for DTLZ#2

8.3. Parallel Computation of Metaheuristic Algorithms

8.3.1. Parallelization Strategies 8.3.2. Parallel Designs 8.3.3. Parallel Metaheuristic Algorithms and Applications

REFERENCES

Design of Test Problems

Abstract 9.1. Introduction 9.2. Key Characteristics of Test Functions

9.2.1. Major Complexities 9.2.2. Generating Methods 9.2.3. Test Suites

9.3. Analytical Pareto-Optimal Fronts 9.4. Multi-Objective Optimization with Mathematica®

9.4.1. Interactive Mathematica® Demonstration 9.4.2. Pareto-Optimal Solution 9.4.3. Resolution Process

REFERENCES

Fifty Collected Test Functions

Abstract 10.1. Introduction 10.2. All Fifty Test Problems

10.2.1. Problem Description 10.2.2. Approximated Pareto Fronts Using NSGA-II 10.2.3. Mathematical Problem Formulation

10.3. Selected Test Problems REFERENCES

List of Abbreviations List of Journal Abbreviations in the References List of Symbols

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