Evolutionary multimodal optimization

Knowledge of multiple solutions to an optimization task is especially helpful in engineering, when due to physical (and/or cost) constraints, the best results may not always be realizable.

Multiple solutions could also be analyzed to discover hidden properties (or relationships) of the underlying optimization problem, which makes them important for obtaining domain knowledge.

Evolutionary algorithms (EAs) due to their population based approach, provide a natural advantage over classical optimization techniques.

The underpinning of that framework was the selection of a peak individual per subpopulation in each generation, followed by its sampling to produce the consecutive dispersion of search-points.

The biological analogy of this machinery is an alpha-male winning all the imposed competitions and dominating thereafter its ecological niche, which then obtains all the sexual resources therein to generate its offspring.

Finding multiple optima using genetic algorithms in a multi-modal optimization task. (The algorithm demonstrated in this demo is the one proposed by Deb, Saha in the multi-objective approach to multimodal optimization.)
Graph of a strictly concave quadratic function with unique maximum.
Optimization computes maxima and minima.