Optimization is the art of finding the best value of a problem possibly with the most quick strategy. (see wiki page: https://en.wikipedia.org/wiki/Optimization_(disambiguation))
People are everyday sourrounded by problems (engineering, database analysis, financial, etc…) whose nature is intrisecaly complex: the elements composing the problem have very strict and dependent relationship, and a slight change of a single element can rapidily affect the state of the others, often in a non-proportional way. With modern times, also the number of elements composing the problem is growing significantly, and researchers often needs to deal with tens or hundreds of variables simultaneously.
Under these conditions it is extremely hard – if not impossible – for people to manage this complexity, controlling and directing the result where they need to go, that often appears as a black-box problem.
Optimization and regression analysis come to help in this: their sophisticated algorithms are able to identify the relationship and unkown functions behind a given problem and, once this is done, to direct the solution toward the goal given by the user, maximizing the performance of the system.
A wide choiche of algorithms
The way that this relationship between quantities is found, and the optimal solution identified, is a very complex science. Along the years hundreds of algorithms (and as many modifications) have been developed by mathematicians. Common strategies are: radial basis functions, krigging, gradient methods, neural networks, genetic algorithms, evolutionary algorithms, stochastics, and any hybrid form. Each of them suites at the best particular kind of problems, that are often classified from their mathematical point of view: number of dimension, noise/uncertainetais, constrains, analytical, differentiable, etc… .
For the R&D needs of engineering companies or research centers (medical, farmaceutical, financial) are particularly interesting those problems classified as: black-box and costly.
Black-box and costly problems
A black-box problem is a problem which the mathematical relationship between input data and results is unkown, like for medical database analysis, or known but for which the complexity of resolution is so high to be considered as unknown, like for any engineering problem envolving systems of differential equations.
For engineering problems, in particular, the time needed to obtain the solution of the problem once that the input data are provided is often very long (hours or days), as it is the case for CFD or FEM or weather forecast calculations. In these cases the problem is said to be “costly”, because getting the solution costs a large time. With costly functions is not possible to take advantage on a large number of samples to discover the underlying relationship, and algorithms needs to be particularly smart to find the optimal solution within a very few trials. (theoretically, with an infinite number of trials the optimal solution is always found)
Our optimization algorithms are particularly optimized for black-box and costly functions and offer the most modern solution for engineers and scientist.