Global Minimum of a Surface

This Demonstration applies a simple evolutionary algorithm to find the global minimum for a closed and bounded surface in 3D space.


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1. For the initial generation, 10 or more points are randomly selected in the plane below the surface.
2. Two pairs of points are selected randomly from the initial population. Each pair produces a new point halfway between them.
3. From those two new points, the one below the surface at a lower height is selected.
4. Steps 2 and 3 are repeated until there are enough points for the next generation.
Rastrigin surface:
sinc surface:
exp surface:
Rosenbrock surface:
[1] K. A. De Jong, Evolutionary Computation: A Unified Approach, Cambridge, MA: MIT Press, 2006.
[2] C. Jacob, Illustrating Evolutionary Computation with Mathematica, San Francisco: Morgan Kaufmann, 2001.
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