Many-Criteria Optimization and Decision Analysis: State-of-the-Art, Present Challenges, and Future Perspectives (Natural Computing Series)

Preface
Contents
Contributors
Part I Key Research Topics
1 Introduction to Many-Criteria Optimization and Decision Analysis
	1.1 Motivation
	1.2 What is Many-Criteria Optimization?
		1.2.1 Salient Challenges in Many-Criteria Optimization
		1.2.2 History of Many-Criteria Optimization
	1.3 Where are We Now? MACODA by the Time of the 2019 Lorentz Center Workshop
		1.3.1 Algorithmic Aspects
		1.3.2 Salient Topics
	1.4 What Remains to be Done? A Vision for MACODA in 2030
	1.5 Synopsis
		1.5.1 Key Topics
		1.5.2 Emerging Topics
		1.5.3 Coda
	References
2 Key Issues in Real-World Applications  of Many-Objective Optimisation  and Decision Analysis
	2.1 Introduction
	2.2 Problem Formulation
	2.3 Developing a Decision-Making Framework
	2.4 Algorithm Selection
	2.5 Interactive Methods, Preference Articulation  and the Use of Surrogates
	2.6 Uncertainty Handling
	2.7 Machine Learning Techniques
		2.7.1 Problem Formulation and Decomposition
		2.7.2 Model-Based Solution Generation
		2.7.3 Data-Driven Surrogate-Assisted Optimisation
		2.7.4 Transfer Optimisation
	2.8 More Advanced Topics
		2.8.1 Multidisciplinary Considerations
		2.8.2 Dynamic Environments
		2.8.3 Mixed and Metameric Nature of Variables
	2.9 Conclusions
	References
3 Identifying Properties of Real-World Optimisation Problems Through  a Questionnaire
	3.1 Introduction
	3.2 Related Work
	3.3 Questionnaire
		3.3.1 Background
		3.3.2 Questionnaire Outline
	3.4 Results
	3.5 Conclusions
		3.5.1 Discussion
		3.5.2 Highlights for Many-Objective Optimisation
		3.5.3 Future Work
	References
4 Many-Criteria Dominance Relations
	4.1 Motivation
	4.2 Formal Definition and Properties of Order Relations
		4.2.1 Cone Orders
	4.3 Order Extensions
	4.4 Order Relations Used in Many-Objective Optimization
		4.4.1 Counting-Based Orders
		4.4.2 Cone-Based Orders
		4.4.3 Volume- and Area-Based Order Relations
		4.4.4 Preference-Information and Utility Functions
	4.5 Discussion and Comparison
	4.6 Open Questions
	References
5 Many-Objective Quality Measures
	5.1 Introduction
	5.2 Currently Used Measures in Many-Objective Optimisation and Their Scalability, Complexity and Properties
		5.2.1 Most Commonly Used Indicators
		5.2.2 Indicator-Based Algorithms
	5.3 Quality Indicators for a Priori Methods
		5.3.1 User-Preference Metric Based on a Composite Front
		5.3.2 R-metric
		5.3.3 Other Indicators for a Priori Evolutionary Methods
	5.4 Under-Explored Areas for Quality Indicators
		5.4.1 Noisy Multi- and Many-Objective Optimisation
		5.4.2 Robust Many-Objective Optimisation
		5.4.3 Quality Measures for Interactive Methods
		5.4.4 Summary
	5.5 Open Issues and Considerations
	5.6 Conclusions
	References
6 Benchmarking
	6.1 Introduction
		6.1.1 Definition
		6.1.2 Historical and Current Context
		6.1.3 Motivation and Overview
	6.2 Existing Benchmarks
		6.2.1 Artificial Benchmarks
		6.2.2 Real-World Benchmarks
		6.2.3 Shortcomings in Existing Benchmarks
	6.3 (Avoiding) Pitfalls
		6.3.1 Problem Choice (PC)
		6.3.2 Analysis and Performance Evaluation (AP)
		6.3.3 Benchmark Usage
		6.3.4 Checklist to Avoid Pitfalls
	6.4 Summary and Open Issues
	References
7 Visualisation for Decision Support in Many-Objective Optimisation: State-of-the-art, Guidance and Future Directions
	7.1 Introduction
	7.2 Different Ways of Using Visualisations to facilitate many-objective decision making
	7.3 State-of-the-Art
		7.3.1 Overview of Individual Visualisation Techniques  for Solution Sets
		7.3.2 Integrating Visualisation into Many-Objective Decision Support
	7.4 Illustrative Example of Visualisation in Real-World Decision Making
	7.5 Future Research Directions
	7.6 Conclusions
	References
8 Theoretical Aspects of Subset Selection in Multi-Objective Optimisation
	8.1 Introduction
	8.2 Background
		8.2.1 Preference Articulation
		8.2.2 Decision-Making Problems
		8.2.3 Remarks
	8.3 Notation and Definitions
	8.4 Scalarisations
		8.4.1 Weighted Sum Scalarisation
		8.4.2 epsilonε-Constraint Scalarisation
		8.4.3 Methods of Weighted Distance and Reference Point Methods
		8.4.4 Remarks
	8.5 Quality Indicators
		8.5.1 Monotonicity
		8.5.2 Optimal muµ-Distributions
		8.5.3 Remarks
	8.6 Concluding Remarks
	References
9 Identifying Correlations in Understanding and Solving Many-Objective Optimisation Problems
	9.1 Introduction
	9.2 Identifying Correlations From Data
		9.2.1 Pearson\'s Correlation Measure
		9.2.2 Spearman\'s Correlation Measure
		9.2.3 Kendall\'s Correlation Measure
		9.2.4 Goodman and Kruskal\'s Correlation Measure
		9.2.5 Cramér\'s Correlation Measure
		9.2.6 Nonlinear Correlation Information Entropy (NCIE)
	9.3 Conflict and Harmony Between Objectives
		9.3.1 Definitions and Metrics of Conflict and Harmony
		9.3.2 Comparing Conflict and Harmony with Correlation Measures
	9.4 Exploiting Correlations
		9.4.1 Data Mining
		9.4.2 Innovization
		9.4.3 Objective Reduction
	9.5 Benchmarking and Case Studies
		9.5.1 Explicit Correlation
		9.5.2 Implicit Correlation
	9.6 Summary
	References
Part II Emerging Topics
10 Bayesian Optimization
	10.1 Introduction
		10.1.1 Definitions and Notations
	10.2 Bayesian Optimization
	10.3 Surrogate-Assisted Modeling
		10.3.1 Gaussian Process Regression
		10.3.2 GP for Multi-objective Problems
		10.3.3 Other Surrogate Models
	10.4 Acquisition Functions
		10.4.1 Single-Objective Acquisition Function
		10.4.2 Multi-objective Acquisition Functions
		10.4.3 Parallelization
		10.4.4 Constraint Handling
	10.5 Applications
	References
11 A Game Theoretic Perspective on Bayesian Many-Objective Optimization
	11.1 Introduction
	11.2 Game Equilibria to Solution Elicitation
		11.2.1 Nash Games and Equilibria
		11.2.2 The Kalai–Smorodinsky Solution
		11.2.3 Disagreement Point Choice
	11.3 Bayesian Optimization Algorithms for Games
		11.3.1 Fixed Point Approaches for the Nash Equilibrium
		11.3.2 Stepwise Uncertainty Reduction
		11.3.3 Thompson Sampling
	11.4 Application Example: Engineering Test Case
	11.5 What Is Done and What Remains
	References
12 Heterogeneous Objectives: State-of-the-Art and Future Research
	12.1 Motivation and Overview
	12.2 Fundamental Concepts and Types of Heterogeneity
		12.2.1 Fixed Evaluation Budget Definitions
		12.2.2 Types of Heterogeneity
	12.3 Algorithms and Benchmarking
		12.3.1 Algorithms
		12.3.2 Empirical Study: Towards Many-Objective Heterogeneous Latencies
		12.3.3 Benchmarking
	12.4 Related Research
	12.5 Conclusions and Future Work
	References
13 Many-Criteria Optimisation  and Decision Analysis Ontology  and Knowledge Management
	13.1 Introduction
	13.2 MACODA Ontology
		13.2.1 Ontology Overview
		13.2.2 Ontologies in Knowledge Management
		13.2.3 Semantic Web
		13.2.4 Related Work
	13.3 MyCODA Platform
		13.3.1 Conceptual Model
		13.3.2 Ontology Design Best Practices
	13.4 Conclusions and Future Work
	References
Appendix  Glossary