Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art
Evolutionary Computation
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
Towards a quick computation of well-spread pareto-optimal solutions
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
The measure of Pareto optima applications to multi-objective metaheuristics
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th 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
Properties of an adaptive archiving algorithm for storing nondominated vectors
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
RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm
IEEE Transactions on Evolutionary Computation
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Convergence, uniformity and spread are three basic issues in comparing the performance of multi-objective evolutionary algorithms. However, most of metrics pay more attention on former two performance indices. In this paper, we introduce a metric for evaluating the spread of non-dominated solutions. Unlike existed metrics only calculating the extreme solutions in objective space, this metric defines boundary concept of non-dominated set. And it evaluates the extent of boundary solutions by projecting them on low-dimensional spaces. Moreover, the centroid of solutions set is introduced to avoid the impact of different convergence result of algorithms. From a comparative study on several test problems, the metric is examined to assess spread of non-dominated solutions set in objective space.