Dimension reduction by local principal component analysis
Neural Computation
GTM: the generative topographic mapping
Neural Computation
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
Covering pareto sets by multilevel evolutionary subdivision techniques
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
The naive MIDEA: a baseline multi-objective EA
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
On the convergence of a class of estimation of distribution algorithms
IEEE Transactions on Evolutionary Computation
Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
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Under mild conditions, the Pareto set of a continuous multi-objective optimization problem exhibits certain regularity. We have recently advocated taking into consideration such regularity in designing multi-objective evolutionary algorithms. Following our previous work on using Local Principal Component Analysis for capturing the regularity, this paper presents a new approach for acquiring and using the regularity of the Pareto set in evolutionary algorithms. The approach is based on the Generative Topographic Mapping and can be regarded as an Estimation of Distribution Algorithm. It builds models of the distribution of promising solutions based on regularity patterns extracted from the previous search, and samples new solutions from the models thus built. The proposed algorithm has been compared with two other state-of-the-art algorithms, NSGA-II and SPEA2 on a set of test problems.