Archiving Strategies for Evolutionary Multi-objective Optimization Algorithms (Studies in Computational Intelligence, 938)

✍ Scribed by Oliver Schütze, Carlos Hernández

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 242
• Edition: 1st ed. 2021
• Category: Library

✦ Synopsis

This book presents an overview of archiving strategies developed over the last years by the authors that deal with suitable approximations of the sets of optimal and nearly optimal solutions of multi-objective optimization problems by means of stochastic search algorithms. All presented archivers are analyzed with respect to the approximation qualities of the limit archives that they generate and the upper bounds of the archive sizes. The convergence analysis will be done using a very broad framework that involves all existing stochastic search algorithms and that will only use minimal assumptions on the process to generate new candidate solutions. All of the presented archivers can effortlessly be coupled with any set-based multi-objective search algorithm such as multi-objective evolutionary algorithms, and the resulting hybrid method takes over the convergence properties of the chosen archiver. This book hence targets at all algorithm designers and practitioners in the field of multi-objective optimization.

✦ Table of Contents

Foreword
Preface
Contents
Acronyms
1 Introduction
2 Multi-objective Optimization
3 Archiving in Evolutionary Multi-objective Optimization: A Short Overview
4 The Framework
5 Computing the Entire Pareto Front
5.1 The Set of Interest
5.2 ArchiveUpdatePQ
5.3 Numerical Examples
6 Computing ε-(approximate) Pareto Fronts
6.1 The Sets of Interest
6.2 ArchiveUpdateEps1
6.3 ArchiveUpdateEps2
6.4 Numerical Results
7 Computing Gap Free Pareto Fronts
7.1 The Sets of Interest
7.2 ArchiveUpdateTight1
7.3 ArchiveUpdateTight2
7.4 Numerical Results
8 Computing the Set of Approximate Solutions
8.1 The Set of Interest
8.2 ArchiveUpdatePQ,ε
8.3 ArchiveUpdatePQ,εDy
8.4 ArchiveUpdatePQ,εDx
8.5 ArchiveUpdatePQ,εDxy
8.6 Numerical Results
9 A Short Excursion to Scalar Optimization: Computing the Set of Approximate Solutions for SOPs
9.1 The Set of Interest
9.2 ArchiveUpdateMQ,ε
9.3 ArchiveUpdateMQ,εDx
9.4 Numerical Results
9.4.1 Sphere Function
9.4.2 Himmelblau's Function
9.4.3 Eggholder Function
10 Using Archivers Within MOEAs
10.1 NSGA-II-A, MOEA/D-A, and SMS-EMOA-A
10.2 NεSGA
10.3 Numerical Results
Appendix A Test Problems
A.1 CONV2
A.2 DENT
A.3 SSW
A.4 CONV3
A.5 DTLZ 7
A.6 DEB99
A.7 TWO-ON-ONE
A.8 SYM-PART
A.9 OMNI-TEST
A.10 LSS
A.11 OKA1
Appendix B Archivers
B.1 ArchiveUpdatePQ
B.2 ArchiveUpdateEps1
B.3 ArchiveUpdateEps2
B.4 ArchiveUpdateTight1
B.5 ArchiveUpdateTight2
B.6 ArchiveUpdatePQ,ε
B.7 ArchiveUpdatePQ,εDx
B.8 ArchiveUpdatePQ,εDy
B.9 ArchiveUpdatePQ,εDxy
B.10 ArchiveUpdateMQ,ε
B.11 ArchiveUpdateMQ,εDx
Appendix References