Computers and Operations Research
`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
Data Structures and Algorithms
Data Structures and Algorithms
Gilding the Lily: A Variant of the Nelder-Mead Algorithm Based on Golden-Section Search
Computational Optimization and Applications
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
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
SIAM Journal on Optimization
Fortified-Descent Simplicial Search Method: A General Approach
SIAM Journal on Optimization
A convergent variant of the Nelder-Mead algorithm
Journal of Optimization Theory and Applications
A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization
INFORMS Journal on Computing
An interactive approach for solving multi-objective optimization problems (interactive computer, nelder-mead simplex algorithm, graphics)
Multidirectional search: a direct search algorithm for parallel machines
Multidirectional search: a direct search algorithm for parallel machines
Continuous interacting ant colony algorithm based on dense heterarchy
Future Generation Computer Systems - Special issue: Computational chemistry and molecular dynamics
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Grid Restrained Nelder-Mead Algorithm
Computational Optimization and Applications
A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search
Computers and Industrial Engineering - Special issue: Sustainability and globalization: Selected papers from the 32 nd ICC&IE
Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search
Journal of Global Optimization
Gaussian variable neighborhood search for continuous optimization
Computers and Operations Research
Global optimization using a genetic algorithm with hierarchically structured population
Journal of Computational and Applied Mathematics
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In this paper we propose a simple but efficient modification of the well-known Nelder-Mead (NM) simplex search method for unconstrained optimization. Instead of moving all n simplex vertices at once in the direction of the best vertex, our ''shrink'' step moves them in the same direction but one by one until an improvement is obtained. In addition, for solving non-convex problems, we simply restart the so-modified NM (MNM) method by constructing an initial simplex around the solution obtained in the previous phase. We repeat restarts until there is no improvement in the objective function value. Thus, our restarted modified NM (RMNM) is a descent and deterministic method and may be seen as an extended local search for continuous optimization. In order to improve computational complexity and efficiency, we use the heap data structure for storing and updating simplex vertices. Extensive empirical analysis shows that: our modified method outperforms in average the original version as well as some other recent successful modifications; in solving global optimization problems, it is comparable with the state-of-the-art heuristics.