Evolutionary Multi-Criterion Optimization: 4th International Conference, EMO 2007, Matsushima, Japan, March 5-8, 2007, Proceedings (Lecture Notes in Computer Science, 4403)

Title Page
Preface
Organization
Acknowledgements
Table of Contents
Aspiration Level Methods in Interactive Multi-objective Programming and Their Engineering Applications (Abstract of Invited Talk)
Improving the Efficacy of Multi-objective Evolutionary Algorithms for Real-World Applications (Abstract of Invited Talk)
Decision Making in Evolutionary Optimization(Abstract of Invited Talk)
MOEAs in the Design of Network Centric Systems (Abstract of Invited Talk)
Controlling Dominance Area of Solutions and ItsImpact on the Performance of MOEAs
	Introduction
	Multiobjective Optimization Concepts and Definitions
	Related Works
	Proposed Method
		Contraction and Expansion of Dominance Area
		Effects of Controlling Dominance Area
	Benchmark Problems, Metrics, and Parameters
	Experimental Results and Discussion
		Performance Varying the Number of Objectives
		Performance Varying the Size of the Search Space
		Performance Varying the Search Space Feasibility Ratio $\\phi$
		Results on Complementary Metrics and Obtained Solutions
	Conclusions
Designing Multi-objective Variation Operators Using a Predator-Prey Approach
	Introduction
	Background
		Laumanns\' Predator-Prey Model
		Extensions to the Original Model
	A Model for Variation Operator Design
		Adaptation of the Predator-Prey Model
		A Building Block Approach for Variation Operator Design
	Standard Recombination Operators on Multi-objective Problems
	An Operator Design Case Study
		Operator Design for Two Objectives
		Operator Design for Three Objectives
		Discussion
	Conclusion and Future Work
Capabilities of EMOA to Detect and Preserve Equivalent Pareto Subsets
	Introduction
	Aims and Methods
	A Test-Problem Class: SYM-PART
		Construction of the Test Problems
		Experimental Investigation of Problem Hardness
	Evaluation of Standard EMOA on SYM-PART
	A Multistart Approach for Pareto Subset Detection
	Conclusions and Future Work
Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization
	Introduction
	Optimization of Scalarizing Functions by EMO Algorithms
		Scalarizing Functions
		NSGA-II and Its Single-Objective Version
		Computational Experiments
	Handling of Weighted Sum Fitness Functions
		Weighted Sum Fitness Function of Two Objectives
		Weighted Sum Fitness Function of Many Objectives
	Application of a Hybrid EMO Algorithm
	Handling of Other Scalarizing Fitness Functions
	Conclusions
	References
Reliability-Based Multi-objective Optimization Using Evolutionary Algorithms
	Introduction
	Existing Reliability-Based Methodologies
		Simulation Methods
		Double-Loop Methods
		Single-Loop Methods
		Decoupled Methods
	Optimization for Seeking Multiple Solutions for Different Reliability Values
		Reliability-Based Evolutionary Approach
		Simulation Results
	Multi-objective Reliability-Based Optimization
		Reliability-Based Evolutionary Procedure
		Simulation Results
	Conclusions
	Functions for Car Side Impact Problem
Multiobjective Evolutionary Algorithms on Complex Networks
	Introduction
	Multiobjective Optimization
	Spatial Evolutionary Models
		Single Objective Models
		Multiobjective Models
	Complex Networks
		Definitions
		Network Models
	The Model
	Experiments and Results
		Model Parameters
		Results
	Discussion and Conclusion
On Gradient Based Local Search Methods in Unconstrained Evolutionary Multi-objective Optimization
	Introduction
	Classical Generating Methods
		Gradient Estimation Methods
		Schäffler\'s Stochastic Method (SSM)
		Timmel\'s Population Based Method (TPM)
	Simulation Results
	Conclusions
Symbolic Archive Representation for a Fast Nondominance Test
	Introduction
	Related Work
	Problem Formulation
	Using BDDs for a Fast Nondominance Test
	Experimental Results
	Conclusions
Design Issues in a Multiobjective Cellular Genetic Algorithm
	Introduction
	Related Work
	The Algorithm
		Canonical cGA Model
		A Multiobjective cGA: MOCell
		MOCell Configurations
	Computational Results
		Test Problems
		Performance Metrics
		Comparison of the MOCell Variants
		Comparison Against NSGA-II and SPEA2
	Conclusions and Future Work
FastPGA: A Dynamic Population Sizing Approach for Solving Expensive Multiobjective Optimization Problems
	Introduction
		Evolutionary Algorithms for Multiobjective Optimization
		Purpose of Research
	Proposed Methodology – Fast Pareto Genetic Algorithm (FastPGA)
		FastPGA Initialization and Solution Evaluation
		Solution Ranking and Fitness Assignment
		Elitism and Population Regulation
		Search Stopping Criterion
	Experimental Study
		Test Problems
		Algorithm Parameter Settings
		Performance Metrics
	Computational Results
	Conclusions and Future Work
	References
Constraint-Handling Method for Multi-objective Function Optimization: Pareto Descent Repair Operator
	Introduction
	Constraint Handling in Multi-objective Function Optimization
		Constrained Multi-objective Function Optimization
		Existing Constraint-Handling Methods
			Penalty Methods.
			Objectivization of Constraint Violations.
			Repair Operators.
	Pareto Descent Repair Operator
		Guidelines for Effective Constraint Handling
		Strategies for Meeting the Guidelines
		Search Direction Calculation
			When No Active Constraints Exist.
			When Active Constraints Exist.
			Inactivation.
		Linear Search over Active Constraint Boundaries
			Moving Solutions back onto Active Constraint Boundaries.
			Linear Search.
		Proposal of Pareto Descent Repair Operator
		Use of PDR in GA
	Experiments
		Experiment Setup
		Results
	Conclusions
Steady-State Selection and Efficient Covariance Matrix Update in the Multi-objective CMA-ES
	Introduction
	Covariance Matrix Adaptation
	Generational and Steady-State Multi-objective Selection
	MO-CMA-ES
		Cholesky Update
		Steady-State Selection
	Experiments
		Evaluating the Performance of MOO Algorithms
		Benchmark Functions
		Experiments
	Results and Discussion
A Multi-tiered Memetic Multiobjective Evolutionary Algorithm for the Design of Quantum Cascade Lasers
	Introduction
	Quantum Cascade Laser Overview
	Memetic MOEAs
		Lamarckian vs. Baldwinian
		Application of Local Search Approaches
		Type of Local Search
		How Local Search Is Applied
		Method of Selecting Individuals from Local Search
	Algorithm Selection
		GENMOP Description
		Local Search Description
		Multi-tiered Local Search Description
	Results and Analysis
	Conclusion
Local Search in Two-Fold EMO Algorithm to Enhance Solution Similarity for Multi-objective Vehicle Routing Problems
	Introduction
	Multi-objective Vehicle Routing Problems
	Similarity Between Sets of Non-dominated Solutions
	Two-Fold EMO Algorithm for Multi-objective VRPs
		Genetic Operators
		Two-Fold EMO Algorithm
	Two-Fold Memetic EMO Algorithm
	Simulation Results by Two-Fold Memetic EMO Algorithm
		Effect of Similarity
		Effect of Local Search to Enhance the Similarity in HDP
	Conclusion
	References
Mechanism of Multi-Objective Genetic Algorithm for Maintaining the Solution Diversity Using Neural Network
	Introduction
	Problem of Multi-Objective Genetic Algorithms with a Small Population
	Maintaining the Solution Diversity Mechanism Using Neural Network
	Effectiveness of Diversity Maintenance Mechanism Using ANN
		Examination Environment
		Assessment of Approximation Ability of ANN
		Examination of Diversity Improvement Using ANN
		Examination of Number of Times ANN Is Applied
		Comparison of a Search with Small and Large Numbers of Individuals
	Conclusions
Pareto Evolution and Co-evolution in Cognitive Game AI Synthesis
	Introduction
		Tic-Tac-Toe
	Methods
		Pareto Differential Evolution (PDE)
			Pseudocode of PDE
			Evaluation of individuals (in PDE).
		Pareto Co-evolutionary Differential Evolution (PCDE)
		Pareto Co-evolutionary Differential Evolution with an Archive (PCDE-A)
		Adaptive Evolution
		Cognitive Game AI Representation
	Experimental Setup
	Experimental Results and Discussion
		Overall Performance of All Experiments
		The Introduction of Co-evolution
		Co-evolution with an Archive
		Performance With/Without the Additional Archive
		Performance Without Co-evolution
	Conclusion
The Development of a Multi-threaded Multi-objective Tabu Search Algorithm
	Introduction
	Background
		Multi-objective Optimization
		Tabu Search
	Multi-threaded Multi-objective TS Implementation
		The Memories
		The Hooke and Jeeves Move and Pattern Move
		Intensification, Diversification and Step-Size Reduction
		Parallelisation Strategy
		Constraint Handling
	Test Procedures
		Test Functions
		Performance Assessment Using Unary Indicators
		Details of the Procedure
	Results and Discussion
	Conclusions
Differential Evolution Versus Genetic Algorithms in Multiobjective Optimization
	Introduction
	Multiobjective Optimization with the Basic GA
	Multiobjective Optimization with DE
		Related Work
		DEMONS-II, DEMOSP2 and DEMOIB
	Experimental Setup
		Test Problems
		Parameters of the Algorithms
		Performance Assessment
	Results and Discussion
		DEMONS-II vs. NSGA-II
		DEMOSP2 vs. SPEA2
		DEMOIB vs. IBEA
	Conclusion
EMOPSO: A Multi-Objective Particle Swarm Optimizer with Emphasis on Efficiency
	Introduction
	Towards an Efficient MOPSO
		Handling Well-Distributed Solutions
			A First Comparative Study.
		Avoiding Premature Convergence
		Maximizing the Spread
		A Constraint-Handling Mechanism
		Analyzing the Impact of the PSO\'s Parameters
			Conclusions from the Second Series of Experiments.
		Self-adaptive Mechanism
	Test Problems
	Comparison of Results
	Conclusions and Future Work
A Novel Differential Evolution Algorithm Based on $epsilon$-Domination and Orthogonal Design Method for Multiobjective Optimization
	Introduction
	Background of $epsilon$-MOEA
	Function Optimization by Conventional DE
	Our Approach: -ODEMO
		Orthogonal Initial Population
		Producing New Solutions with DE/rand/1/exp Strategy
		Procedure of -ODEMO
	Simulation Results
		Performance Measures
		Experimental Setup
		Experimental Results
	Results Analysis
		Two-Objective Test Problems
		Three-Objective Test Problems
	Conclusion
Molecular Dynamics Optimizer
	Introduction
	The Etiology of Molecular Dynamics Optimizer
		Molecular Dynamics
		Applying Molecular Dynamics for Multi Objective Optimization
	Molecular Dynamics Optimizer
		Implementation of MDO
		Comparison of MDO with Conventional Evolutionary Optimizers
	Experimental Study
		Performance Metrics
		Experimental Results
	Conclusion
	References
Sequential Approximation Method in Multi-objective Optimization Using Aspiration Level Approach
	Introduction
	Support Vector Regression
	Multi-objective Optimization
	Generation of Pareto Frontier by the Proposed Method
	Numerical Examples
	Concluding Remarks
Multi-objective Optimisation of a HybridElectric Vehicle: Drive Train and DrivingStrategy
	Introduction
	The Model of the Hybrid Vehicle
		Vehicle Dynamics
		Hybrid Power Train and Driving Control Strategy
	Multi-objective Optimisation of the Parallel Hybrid Power Train
		Optimisation Results: Drive Train
	Multi-objective Optimisation of the Drive Train and Driving Control Strategy
		The Introduction of Control Strategy Variables
		Optimisation Results: Drive Train and Driving Strategy
	Conclusions
Multiobjective Evolutionary Neural Networks for TimeSeries Forecasting
	Introduction
	Time Series Forecasting
	Multiobjective Evolutionary Neural Networks
	Preliminary Investigation
	Algorithm Description
	Experimental Results
	Conclusion
	References
Heatmap Visualization of Population Based MultiObjective Algorithms
	Introduction
		Multi-objective Optimization Problems (MOPs)
		Visualization of MOPs
	An Example Multi-objective Optimization Problem
	Heatmaps
	Multi-component Chemical Systems in Mineralogy
	Application in Multi-objective Calibration of Hydrologic Models
	Conclusion and Future Work
	References
Multiplex PCR Assay Design by HybridMultiobjective Evolutionary Algorithm
	Introduction
	Multiplex PCR Assay Design
	Hybrid Multiobjective Evolutionary Algorithm for Multiplex PCR Assay Design
		The Preprocessing
		The Hybrid Multiobjective Evolutionary Algorithm
		Local Search
	Experimental Results
	Conclusions
ParadisEO-MOEO: A Framework forEvolutionary Multi-objective Optimization
	Introduction
	Multi-objective Optimization
	ParadisEO-MOEO Motivations
		Goals
		Existing Multi-objective Optimization Frameworks
	ParadisEO-MOEO Implementation and Deployment
		A General Eolutionary Algorithm Implementation
		Archive-Related Features
		Implemented Multi-objective Fitness Assignment Strategies
	Parallelism and Hybridization Design for Multi-objective Problems Using the ParadisEO Framework
		Parallel Distributed Evolutionary Algorithms
		Hybridization
	Applications
		Preliminaries: GUIMOO
		Examples
	Conclusion and Perspectives
Multi-objective Evolutionary Algorithms forResource Allocation Problems
	Introduction
	Related Works
	Class Timetabling and Land-Use Management Problems as Multi-objective Optimization Problems
		Objective Functions in University Class Timetabling Problem
		Objective Functions in Land-Use Management Problem
		Constraints in University Class Timetabling Problem
		Constraints in Land-Use Management Problem
	NSGA-II-UCTO and NSGA-II-LUM
		Chromosome Representations
		Crossover Operators
		Mutation Operators
		Guidance to Speed Up the Search for Optimum Solutions
		Salient Features of NSGA-II-UCTO and NSGA-II-LUM
	Two Case Studies (IITK2 and LBAP)
		NSGA-II-UCTO to IITK2
		NSGA-II-LUM to LBAP
	Similarity Among RAPs
	Conclusions
Multi-objective Pole Placement withEvolutionary Algorithms
	Introduction
	Problem Formulation
		Preliminaries
		Control Topology
		The Control Problem
	MOPPEA: A Linear Controller Design Method
		The Pole Placement Method
		Problem Reformulation
		Representation of Individuals
		Variation Operators
		Multi-Objective Genetic Algorithm (MOGA)
	Design Example: A Mixed H2/H Control Problem
		Experimental Results
	Conclusions and Future Work
A Multi-objective Evolutionary Approach forPhylogenetic Inference
	Introduction
	Phylogenetic Inference Problem
		Maximum Parsimony
		Maximum Likelihood
	Genetic Algorithms in Phylogenetic Inference
	Multi-objective Optimization
	A Multi-objective Approach to Phylogenetic Inference
		Internal Encoding
		Initial Solutions
		Fitness Evaluation
		Crossover Operator
		Mutation Operator
	Experiments
	Conclusions and Future Works
	References
On Convergence of Multi-objective ParetoFront: Perturbation Method
	Introduction
	Perturbation Method
	Test Cases
		New York Tunnels (NYT) Problem
		The Hanoi Network
	Solutions and Analysis
		Performance in Finding Pareto Front
		Comparison of Results
	Conclusion
Combinatorial Optimization of StochasticMulti-objective Problems: An Application to theFlow-Shop Scheduling Problem
	Introduction
	A Bi-objective Flow-Shop Scheduling Problem with Stochastic Processing Times
		Deterministic Model
		Sources of Uncertainty
		Stochastic Models
	Indicator-Based Evolutionary Methods
		Indicator-Based Multi-objective Optimization
		Handling Stochasticity
		Proposed Methods
		Implementation
	Simulation Results
		Benchmarks
		Optimization Runs
		Performance Assessment
		Computational Results and Discussion
	Conclusion and Perspectives
Evolutionary Algorithm Based Corrective ProcessControl System in Glass Melting Process
	Introduction
	Data Collection
	Corrective Process Control System
		Basic Pick-Up Logic (BPL)
		Evolutionary Algorithm Based Search Logic (EASL)
	Implementation and Case Study
		System Implementation
		Case Study
	Conclusions
	References
Bi-objective Combined Facility Location andNetwork Design
	Introduction
	The Structure of Pareto-Sets in MJFLND
		Multiobjective Optimization
		MJFLND Problem
		Expected Characteristics of a MJFLND Pareto-Front
	Conceptual Algorithm for Finding Pareto-Sets in MJFLND
	Problem Description
		Problem Statement
		Multiobjective Design of Power Distribution Systems
	The Multiobjective GA-BFGS Algorithm for Power Distribution Systems
		Modules Description
	Numerical Results
	Conclusions
Local Search Guided by Path Relinking andHeuristic Bounds
	Introduction
	Path Relinking for BPFSP
		Initial Solutions for the Path Relinking
		Path Relinking
		Local Search Within PR
	Numerical Results
		Evaluation Metrics
		Analysis
	Conclusion
Rule Induction for Classification UsingMulti-objective Genetic Programming
	Introduction
	Rule Representation and Manipulation
		Attribute Tests
		Attribute Test Representation
		Rule Trees
		Genetic Operators
		Bloat and Rule Simplification
	Rule Evaluation
		Misclassification Costs
		Measuring Rule Complexity
	Experimentation and Results
		Data
		Algorithm and Parameter Tuning
		Training, Validation, Selection and Testing
		Results
	Conclusions
	Further Research
Combining Linear Programming andMultiobjective Evolutionary Computation forSolving a Type of Stochastic Knapsack Problem
	Introduction
	Problem Statement and Mathematical Modelling
		Problem Statement
		Modelling Using Stochastic Multi-objective Nonlinear Integer Programming
		Modelling Using Stochastic Multi-objective Linear Integer Programming
		Modelling Using Linear Programming and Evolutionary Computation
	Hybrid Algorithm Based on Integer Linear Programming and Multi-objective Evolutionary Computation
		Stage A: Efficiency Evaluation. An Integer Linear Programming Approach
		Stage B. Population Evolution. A Multi-criteria Evolutionary Algorithm
	Industrial Application
		Origin of the Problem
		Experimental Framework of the Multi-criteria Problem
		Experimental Results
	Conclusions and Future Work
Hybridizing Cellular Automata Principles and NSGAIIfor Multi-objective Design of Urban Water Networks
	Introduction
	Multi-objective Water Systems Design
		Water Systems Design
		Multi-objective Optimization
	Cellular Automata Based Optimization
		Cellular Automata
		Cellular Automata Based Water Network Design
	Methodology
		Principles
		Execution Process
	Experiments
		Networks
		Performance Evaluation Measures
		Results and Discussions
	Conclusions
	References
Using Multiobjective Evolutionary Algorithmsto Assess Biological Simulation Models
	Introduction
		The Pareto Frontier in Model Assessment
		Model Assessment Objective Functions
	MOEA Algorithm for Model Assessment
		Elitism
	Assessing a Model of Shoot Growth
		Ecological Phenomenon and Observations
		Process Model
		Assessment Objective Functions
	Results
		Model Assessment for Days 179--181
		Model Assessment for Days 182--184
		Model Revision
	Discussion
Improving Computational MechanicsOptimum Design Using Helper Objectives:An Application in Frame Bar Structures
	Introduction
	Frame Structural Optimum Design
	Helper Objective: A New Proposal
	Evolutionary Multiobjective Algorithms
	Test Cases
	Results and Discussion
	Conclusions
	References
A Multi-objective Approach to the Design ofConducting Polymer Composites forElectromagnetic Shielding
	Introduction
	Background
		Electromagnetic Properties
		Multi-objective Optimization
	The Design Problem
	Approximation of the Pareto Fronts
	Selecting the Preferred Material
	Conclusions and Future Work
Evolutionary Multiobjective Optimization of SteelStructural Systems in Tall Buildings
	Introduction
	Background
		Evolutionary Computation in Structural Design
		Steel Structural Systems in Tall Buildings
	Multiobjective Optimization of Tall Buildings
		Topological Optimum Design of Steel Structures in Tall Buildings
		Representations of Steel Structural Systems in Tall Buildings
	Experimental Design
	Experimental Results
		Sensitivity Analysis
		Shape of the Pareto Front
		Impact of the Aspect Ratio on the Pareto Front
		Optimal Structural Topologies Along the Pareto Front
	Conclusions
	References
Multi Criteria Decision Aiding Techniques to SelectDesigns After Robust Design Optimization
	Introduction
	The Idea of Robust Design in Aeronautics
		Why We Need a Multi Objective Approach
	Game Theory on Robust Design
	Exhaustive Example: Multi Objective Robust Design Optimization of an AIRFOIL
	Results
	Multi Criteria Decision Making
	Conclusion
	References
MOGA-II for an Automotive Cooling DuctOptimization on Distributed Resources
	Problem Description
	Summary of Flow Modeling with OpenFOAM
	Optimization Phase
	MOGA-II
		MOGA-II Results
	Multi-criteria Decision Making
	Robustness of Solutions
	Concluding Remarks
Individual Evaluation Scheduling forExperiment-Based Evolutionary Multi-objectiveOptimization
	Introduction
	Current Studies
		Experiment-Based Optimization Under Hardware in the Loop Simulation Environment
		Multi-objective Genetic Algorithm for Noisy Fitness Functions
		Crossover Operator for Periodic Functions
	Individual Evaluation Scheduling for Dynamical Systems
		Evaluation Order Scheduling
		Evaluation Time Scheduling
	Numerical Experiment
		Experiment Settings and Measures
		Discussion of Results
	Real Engine Experiment
		Experiment Settings
		Discussion of Results
	Conclusions
A Multiobjectivization Approachfor Vehicle Routing Problems
	Introduction
	Vehicle Routing Problem
	The Multiobjectivization of Vehicle Routing Problem
		The Purpose of the Proposed Multiobjectivization Approach
		The Evaluation Method Related to Assignment of Customers
	Implementation of GA
		Gene Expression (String Representation)
		Population Initialization
		Crossover
		Mutation
		The Decision of Start and End Point in a Route
		Treatment of a Solution with Constraint Violation
	Numerical Examples
		VRPs Instances
		Results and Analysis
	Conclusions
Designing Traffic-Sensitive Controllers forMulti-Car Elevators Through EvolutionaryMulti-objective Optimization
	Introduction
	MCE System and Controllers
		Multi-Car Elevator Systems
		MCE Controller
		Linear-Sum Policy Controller
		Exemplar-Based Policy Controller
	Simulation-Based Policy Optimization
		Evaluation Using MCE Simulation
		Obtaining Traffic Sensitive Controller Through Single and Multi Objective Optimization
		GA for Single Objective Optimization
		GA for Multi Objective Optimization
	Experiments
		Evolution Process
		Performance Comparison of Policies Obtained
	Conclusion
On the Interactive Resolution of Multi-objectiveVehicle Routing Problems
	Introduction
	A Framework for Interactive Multi-objective Vehicle Routing
	Implementation and Experimental Investigation
		Configuration of the System
		Experiments
	Summary and Conclusions
Radar Waveform Optimisation as a Many-ObjectiveApplication Benchmark
	Introduction
	Radar Waveform Design
		Introduction
		PRF Selection
		The Radar Model
	Software Structure
	Initial Objective Surface Analysis
	Algorithm Comparison
	Conclusions
Robust Multi-Objective Optimization in HighDimensional Spaces
	Introduction
	Preliminaries
		Relations
		Methods
	Application of Models
		Utilization Planing Problem
		Implementation
		Experimental Evaluation
		Discussion
	Robust MOO
		Overall Idea
		Relation -Preferred
		Experimental Evaluation
	Conclusions and Future Work
Substitute Distance Assignments in NSGA-II forHandling Many-Objective OptimizationProblems
	Introduction
	Substitute Distance Assignments in NSGA-II
		Structure of NSGA-II Algorithm
		NSGA-II and Many Objectives
		Secondary Ranking Assignment by Pareto Dominance Degrees
		Using the Substitute Distance Assignments
	Results
		Convergence Metric
		Pareto Front Coverage
	Conclusions
Pareto-, Aggregation-, and Indicator-BasedMethods in Many-Objective Optimization
	Introduction
	Benchmark Settings
		Test Functions
		Performance Assessment
	Pareto-based EMOA
		Experimental Results
	Aggregation-Based EMOA
		Experimental Results
	Indicator-Based EMOA
		Experimental Results
	Summary and Outlook
Quantifying the Effects of Objective SpaceDimension in Evolutionary MultiobjectiveOptimization
	Introduction
	Definitions and Methods
		Quality Indicators for Performance Assessment
		Ranking
		Data Suite
	Empirical Distributions
		Nondominated Ranking Distributions
		Empirical Distributions of Coverage of the PF
	Analytical Methods and Results
		Analytical Expression for Expected Value of Coverage
	Case Study Using NK Landscapes
	Conclusion
Non-linear Dimensionality Reduction Procedures forCertain Large-Dimensional Multi-objectiveOptimization Problems: Employing Correntropy and aNovel Maximum Variance Unfolding
	Introduction
	Difficulties with PCA
	Non-linear Dimensionality Reduction
	Methods Based on Non-linear Mappings
		Main Ingredients of Kernel Methods
		From PCA to Kernel-PCA (K-PCA): Difficulties in Generalization
		Correntropy PCA (C-PCA)
	Methods Based on Proximity Matrices
		Maximum Variance Unfolding: The Concept
		Maximum Variance Unfolding: A Novel Implementation
	Proposal: C-PCA-NSGA-II or MVU-PCA-NSGA-II
		Algorithmic Details
		Overall C-PCA-NSGA-II or MVU-PCA-NSGA-II Procedure
	Simulation Results
		C-PCA-NSGA-II
		MVU-PCA-NSGA-II
	Conclusions
I-MODE: An Interactive Multi-objectiveOptimization and Decision-Making UsingEvolutionary Methods
	Introduction
	Existing Methodologies for Hybrid Multi-objective Optimization and Decision-Making
	Interactive Multi-objective Optimization and Decision-Making Using Evolutionary Methods (I-MODE)
		Description of the I-MODE Procedure
		I-MODE Software Implementation
	Case Study: A Welded Beam Design Problem
		Step 1: Find an Approximate Front
		Step 2: Improve the Trade-Off Frontier
		Step 3: Verify Obtained Front
		Step 4: Make Decisions and Choose Regions of Interest
		Step 5: Termination Criterion
		Step 1: Find More Solutions in Preferred Region by NSGA-II
		Step 2: Improve the Front
		Step 3: Verify Obtained Front
		Step 4: Make Decisions and Choose Subregions of Interest
		Step 5: Select the Most Preferred Solution
	Conclusions
Dynamic Multi-objective Optimization andDecision-Making Using Modified NSGA-II:A Case Study on Hydro-thermal PowerScheduling
	Introduction
	Dynamic Problems as On-Line Optimization Problems
	Proposed Modifications to NSGA-II
	Simulation Results on a Test Problem
	A Case Study: Hydro-thermal Power Scheduling
		Optimization Problem Formulation
		Simulation Results on the Stationary Problem
	Dynamic Hydro-thermal Power Scheduling Problem
		Simulation Results
	Decision Making in Dynamic EMO
	Conclusions
	Parameters for Hydro-thermal Problem
Acceleration of Experiment-Based EvolutionaryMulti-objective Optimization Using FitnessEstimation
	Introduction
	Background of Locally Weighted Regression
	Pre-selection for MOEAs
	Numerical Experiments
		Problems, Parameter Settings and Measures
		Performance Analysis Under Noise-Free Environments
		Performance Analysis Under Observation Noise Environments
	Conclusion
Prediction-Based Population Re-initialization forEvolutionary Dynamic Multi-objective Optimization
	Introduction
	Re-initialization Strategies for Dynamic Multi-objective Optimization
		The Algorithm Framework
		Prediction-Based Population Re-initialization
	Experimental Setup
		Benchmark Problems
		Performance Indicators
	Experimental Results
		Parameter Settings
		Results and Discussions
	Conclusions
multi-Multi-Objective Optimization Problem and ItsSolution by a MOEA
	Introduction
	Methodology
		Problem Definition
		A Sequential EMO Approach
		Assessment Measures
	Test-Cases
		Academic Example – 1
		Academic Example - 2
		Real World Example
	Summary Conclusions and Future Work
	Bibliography
The Hypervolume Indicator Revisited: On theDesign of Pareto-compliant Indicators ViaWeighted Integration
	Motivation
	Mathematical Framework
		Preliminaries
		The Hypervolume Indicator
	Introductory Example and Outline of the Proposed Approach
	Methodology: The Weighted-Integration Approach
	Proof-of-Principle Results
		Simple Indicator-Based Optimization Algorithm
		Experiments
	Discussion
The Multiple Multi Objective Problem –Definition, Solution and Evaluation
	Introduction
	Definition of the M-MOP
	Solving a M-MOP
	Evaluating M-MOP Optimizers
		Average Pareto Rank Difference
		Performance of the E-NSGA-II for M-MOP
	Conclusion
Adequacy of Empirical Performance Assessment forMultiobjective Evolutionary Optimizer
	Introduction
	Algorithm Development of MOEO
		Algorithm Formulation
		Experimental Specification
		Experimental Design
		Experimental Execution
	Ideality of Empirical Assessment
	Adequacy of Empirical Assessment
		Adequacy Criterion
		Axiomatization of Empirical Analysis Adequacy
		Discussion of Adequacy Test Criterion
		Summary
	Conclusion
	References
A Comparative Study of Progressive PreferenceArticulation Techniques for Multiobjective Optimisation
	Introduction
	Requirements of Multiobjective Optimisers
	The Investigated Preference Articulation Techniques
		Guided Dominance for Evolutionary Multi-objective Optimisation
		Biased Crowding Distance
		ε –MOEA: Manipulating the ε-Dominance
		FF-PPA Technique
	PPA Techniques in Practice
		Demonstration of ε –Dominance as a PPA Technique in the ε –MOEA Context
		Demonstration of the Biased Crowding as PPA Technique
		Demonstration of the Guided Dominance Principle as a PPA Technique
		Demonstration of FF-PPA Technique
	Discussion and Concluding Remarks
	References
Test Problems Based on Lam´e Superspheres
	Introduction
	Mathematical Preliminaries
	Efficient Set and Pareto Front for the Generalized Schaffer Problem
	N-Dimensional Pareto Fronts with Superspherical Geometry
		Convexity and Concavity of Superspheres
		Resolvability/Intractability of Conflict Versus
	Construction of Test Problems
		Parametrizations of Hyperspheres and Superspheres
		Test Problems
		Uni- and Multimodal Test Problems and Their Mirror Problems
	Implementation of Performance Metrics
		Dominated Hypervolume of Pareto Fronts
		Distance to the Pareto Front
		A Note on Knee-Points
	Case Study
	Conclusions
Overview of Artificial Immune Systems forMulti-objective Optimization
	Introduction
	Multiobjective Optimization and the Immune System
		The Immune System
		Terminology in AIS Optimization
	Multiobjective AIS Algorithms
		Yoo and Hajela\'s Algorithm
		I-PAES
		Luh and Chueh\'s MOIA
		MISA
		MOCSA
		VAIS
		IDCMA
		IFMOA
		ACSAMO
	A Common Framework for MO-AIS Algorithms
	Other Immune Principles
		Negative Selection
		Danger Theory
	Discussion
Author Index