Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Techniques for highly multiobjective optimisation: some nondominated points are better than others
Proceedings of the 9th annual conference on Genetic and evolutionary computation
An introduction to nonlinear dimensionality reduction by maximum variance unfolding
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Controlling dominance area of solutions and its impact on the performance of MOEAs
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Substitute distance assignments in NSGA-II for handling many-objective optimization problems
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
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
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Many objective optimization is a natural extension to multi-objective optimization where the number of objectives are significantly more than five. The performance of current state of the art algorithms (e.g. NSGA-II, SPEA2) is known to deteriorate significantly with increasing number of objectives due to the lack of adequate convergence pressure. It is of no surprise that the performance of NSGA-II on some constrained many-objective optimization problems [7] (e.g., DTLZ5-(5,M), M = 10, 20) in an earlier study [18] was far from satisfactory. Till date, research in many-objective optimization has focussed on two major areas (a) dimensionality reduction in the objective space and (b) preference ordering based approaches. This paper introduces a novel evolutionary algorithm powered by epsilon dominance (implemented within the framework of NSGA-II) and controlled infeasibility for improved convergence while the critical set of objectives is identified through a nonlinear dimensionality reduction scheme. Since approaching the Pareto-optimal front from within the feasible search space will need to overcome the problems associated with low selection pressure, the mechanism to approach the front from within the infeasible search space is promising as illustrated in this paper. The performance of the proposed algorithm is compared with NSGA-II (original, with crowding distance measure) and NSGA-II (epsilon dominance) on the above set of constrained multiobjective problems to highlight the benefits.