Classical and Evolutionary Algorithms in the Optimization fo by Darko Vasiljevic

By Darko Vasiljevic

The optimization of optical structures is a really outdated challenge. once lens designers came upon the potential of designing optical platforms, the need to enhance these platforms via the technique of optimization all started. for a very long time the optimization of optical platforms was once attached with famous mathematical theories of optimization which gave stable effects, yet required lens designers to have a robust wisdom approximately optimized optical structures. in recent times sleek optimization tools were built that aren't based mostly at the identified mathematical theories of optimization, yet quite on analogies with nature. whereas trying to find winning optimization tools, scientists spotted that the strategy of natural evolution (well-known Darwinian conception of evolution) represented an optimum technique of variation of dwelling organisms to their altering atmosphere. If the strategy of natural evolution used to be very winning in nature, the rules of the organic evolution can be utilized to the matter of optimization of complicated technical platforms.

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If the value for the scaling factor ~ is small, escape from local minima is easy but convergence is even less efficient. Hearn, discussing the positive and the negative features of the simulated annealing, concludes that the major practical strength of simulated annealing is ability to escape from local minima and eventually locate a global minimum. He in [22] proposes to combine two optimization methods: simulated annealing and damped least squares. Then the simulated annealing will overcome the major weakness of DLS, getting stuck in a nearest local minimum, while the rapid convergence of DLS will overcome the two weaknesses of the simulated annealing, the poor convergence and the sensitivity to an ALl",(SO) value selection.

54) with this condition is sometimes called the minimal solution: dX=A T . 55) The solution obtained by Eq. 55) ought to be kept within the linear approximation. This can be done with two methods. The first method is to reduce the length of the vector of constructional parameter changes II~II by multiplying the right side of Eq. 55) by a scalar q ~ 1 : dX=q·A T . 56) Glatzel in [23] calculates the scalar q in such way that the largest constructional parameter change maxlaxjl is not lager than the step length, a small predefined quantity.

This is accomplished by expanding the approximating neighbourhood over which optimization can progress during each optimization iteration. With the ELS method the neighbourhood is defined by a quadratic approximation to the problem. It is well known that classical least squares used linear approximation. It is important to note that within the ELS quadratic neighbourhood linear least squares optimization steps must be taken. However, within this ELS neighbourhood the sequence of least squares steps is made without recalculating the Jacobian matrix.

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