Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
SIAM Journal on Optimization
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
On gradient based local search methods in unconstrained evolutionary multi-objective optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Many-objective directed evolutionary line search
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Advances in evolutionary multi-objective optimization
SSBSE'12 Proceedings of the 4th international conference on Search Based Software Engineering
Comprehensive Survey of the Hybrid Evolutionary Algorithms
International Journal of Applied Evolutionary Computation
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The hybridization of multi-objective evolutionary algorithms (MOEAs) with mathematical programming techniques has gained increasing popularity in the specialized literature in the last few years. However, such hybrids normally rely on the use of gradients and, therefore, normally consume a high number of extra objective function evaluations in order to estimate the gradient information required. The use of direct (nonlinear) optimization techniques has been, however, less common in the specialized literature, although several hybrids of this sort have been proposed for single-objective evolutionary algorithms. This paper proposes a hybridization between a well-known MOEA (the NSGA-II) and two direct search methods (Nelder and Mead's method and the golden section algorithm). The aim of the proposed approach is to combine the global search mechanisms of the evolutionary algorithm with the local search mechanisms provided by the aforementioned mathematical programming techniques, such that a more efficient (i.e., with a lower number of objective function evaluations) approach can be produced.