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Restarted local search algorithms for continuous black box optimization.

Petr Pošík¹, Waltraud Huyer

¹Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic. posik@labe.felk.cvut.cz

Evolutionary Computation

|July 12, 2012

Summary

This summary is machine-generated.

This study compares local search algorithms for real-valued domains. For low dimensions, Nelder-Mead simplex search is best, while higher dimensions benefit from quadratic modeling methods like NEWUOA or quasi-Newton.

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Area of Science:

Optimization algorithms
Computational mathematics

Background:

Local search algorithms are crucial for solving complex optimization problems.
Choosing appropriate baseline algorithms is essential for benchmarking evolutionary computation methods.

Purpose of the Study:

To compare several local search algorithms in real-valued domains.
To guide evolutionary algorithm researchers in selecting effective baseline opponents.
To inspire hybridization strategies between evolutionary and local search methods.

Main Methods:

Comparison of axis parallel line search, Nelder-Mead simplex search, Rosenbrock's algorithm, quasi-Newton method, NEWUOA, and VXQR.
Implementation within a multi-start framework.
Adoption of the Comparing Continuous Optimizers (COCO) methodology.

Main Results:

The Nelder-Mead simplex search algorithm remains highly successful in low-dimensional spaces.
For higher-dimensional problems, algorithms utilizing quadratic modeling, such as NEWUOA and quasi-Newton methods, demonstrate superior performance.

Conclusions:

Algorithm performance is highly dependent on problem dimensionality.
Quadratic modeling approaches offer a robust baseline for high-dimensional continuous optimization.
The findings provide valuable insights for selecting and hybridizing optimization algorithms.