GOT-It_Quick_start_en

Optimization software for electrical devices and systems
by CEDRAT
GOT-It 2.0
Quick Start
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1. Basics of optimization
a. Optimization problem (mono-objective)
Variables space
Obj ectives space
In this case the point P, is not an optimum, it is dominated. In fact, with P, it is possible to succeed on F1 without failing on F2 and on F2 without losing on F1. While benefitting in a direction we are arriving on point A where it is not possible to gain anymore on one objective without losing on another. The point A is an optimum in the sense of Pareto (i.e. a non dominated solution). The set of the Pareto’s optima constitute a frontier called front of Pareto which is formed by all non dominated solutions.
Xopt
x
b. Optimum and modality
An optimization problem can have one or several minima; this is called uni-modal or multimodal, respectively. An optimum can be a local minimum (i.e. a minimum in a neighborhood) or a global optimum (i.e. a minimum in the entire domain of the definition of a function).
Optimization algorithm x Sf(x) cheap calls
Numerous
Response surface (Xopt) f(x) Few costly
calls
Objective function
Interpolation principle
x
Optimization of response surface (or indirect optimization)
ቤተ መጻሕፍቲ ባይዱ

The SSO is well adapted for a mono-objective problem by converging within a unique solution whereas the HLHRBF by conserving the entire domain is better adapted for the multi-objective case where we are searching the best set of compromises between the objectives. In conclusion, these algorithms make accessible optimization of numerical models by reducing the computation costs and stream lining the operation of the optimization process.
e. Computation cost and optimization strategy
There are two major methods of optimization: Deterministic methods: that use all possible local information of the function to determine a searching direction or trend (for instance: gradients, derivative….): - Conjugate gradients, SQP, BFSG…. Stochastic methods: that are based on a wide number of, more or less, random trials in order to explore the domain and to find an optimum: - Genetic Algorithms (the trial is based on evolutionist principles), Niching, SA, PSO, GMGA….
These functions could also help to determine the more influential parameters in order to reduce the variation parameter number, thereby saving computation time. However it may be necessary to increase the density of the number of experiment points in order to get a response surface well adapted to the optimization process. In GOT-It, two types of algorithms for automating this process are included: The SSO (or Sequential Surrogate Optimizer) builds a response surface (characteristics are editable in the options), and then applies a costly algorithm (internal algorithm is also editable) to it. We then compare the value of the surrogate to the real one. If the results are too different, the SSO automatically reiterates the process by refining the response surface by reducing the research domain with a constant number of trials around the considered point. The HLHRBF uses the same methods of sequential building of a surrogate if necessary. But the HLHRBF refines the response surface by increasing the number of trials in the entire domain.
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Deterministic methods are economical (in terms of computation cost) but are not appropriate to erratic functions and are likely to become trapped in a local optimum not being sensitive to the starting point of search. On the other hand Stochastic methods are efficient for the search of global optimum on multi-modal function but are very costly (in relation to the required number of trials). In order to save on computation time, when do not know the explicit function behavior (as is widely the case in finite element modeling and simulation), it is possible to rely on approximation functions or response surfaces methods. These simple analytical functions, in which we know all the characteristics, are built by interpolation of the original function based on well selected experiments points. Therefore plans of experimental methods are important in order to get a maximum of data on the functions' behavior from a minimum of experimental points on the original function. For example they are built by considering a quadratic model of approximation (with or without interaction): F’(x) = a0 +a1.x1+a2.x2+a12.x1²+a22.x2²+a3.x1.x2 F