Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization
Proceedings of the 5th International Conference on Genetic Algorithms
Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function
EMO '01 Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations
ISDA '05 Proceedings of the 5th International Conference on Intelligent Systems Design and Applications
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
The measure of Pareto optima applications to multi-objective metaheuristics
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
Pareto-, aggregation-, and indicator-based methods in many-objective optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
A new analysis of the lebmeasure algorithm for calculating hypervolume
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
A faster algorithm for calculating hypervolume
IEEE Transactions on Evolutionary Computation
Dominance-Based Multiobjective Simulated Annealing
IEEE Transactions on Evolutionary Computation
Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems
Computers and Operations Research
Preference-driven co-evolutionary algorithms show promise for many-objective optimisation
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Focussing multi-objective software architecture optimization using quality of service bounds
MODELS'10 Proceedings of the 2010 international conference on Models in software engineering
Computers and Operations Research
On the properties of the R2 indicator
Proceedings of the 14th annual conference on Genetic and evolutionary computation
The relationship between the covered fraction, completeness and hypervolume indicators
EA'11 Proceedings of the 10th international conference on Artificial Evolution
Computational Mathematics and Mathematical Physics
Computers and Operations Research
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This chapter reviews methods for the assessment and comparison of Pareto set approximations. Existing set quality measures from the literature are critically evaluated based on a number of orthogonal criteria, including invariance to scaling, monotonicity and computational effort. Statistical aspects of quality assessment are also considered in the chapter. Three main methods for the statistical treatment of Pareto set approximations deriving from stochastic generating methods are reviewed. The dominance ranking method is a generalization to partially-ordered sets of a standard non-parametric statistical test, allowing collections of Pareto set approximations from two or more stochastic optimizers to be directly compared statistically. The quality indicator method -- the dominant method in the literature -- maps each Pareto set approximation to a number, and performs statistics on the resulting distribution(s) of numbers. The attainment function method estimates the probability of attaining each goal in the objective space, and looks for significant differences between these probability density functions for different optimizers. All three methods are valid approaches to quality assessment, but give different information. We explain the scope and drawbacks of each approach and also consider some more advanced topics, including multiple testing issues, and using combinations of indicators. The chapter should be of interest to anyone concerned with generating and analysing Pareto set approximations.