Classical and Evolutionary Algorithms in the Optimization fo by Darko Vasiljevic

By Darko Vasiljevic

The optimization of optical platforms is a truly previous challenge. once lens designers found the opportunity of designing optical platforms, the need to enhance these platforms through the technique of optimization started. for a very long time the optimization of optical structures used to be hooked up with recognized mathematical theories of optimization which gave solid effects, yet required lens designers to have a powerful wisdom approximately optimized optical platforms. in recent times sleek optimization equipment were built that aren't based at the identified mathematical theories of optimization, yet relatively on analogies with nature. whereas looking for winning optimization tools, scientists spotted that the tactic of natural evolution (well-known Darwinian thought of evolution) represented an optimum technique of model of dwelling organisms to their altering surroundings. If the strategy of natural evolution was once very profitable in nature, the foundations of the organic evolution may be utilized to the matter of optimization of complicated technical structures.

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One sided penalty function called the barrier function have been proposed but can lead to constraints violently oscillating between feasibility and violation on successive iterations. Reliable algorithms for weighted inequality constraints are complex and unwieldy compared to the Lagrange multipliers. 2 Algorithms for the constrained optimization can be developed from the consideration of the necessary and sufficient conditions for a constrained optimum point. In the solution, a linear combination of the active constraint gradients is equal and oposite to the merit function gradient.

6 49 Linear normalization Davis in [34] describes the scaling method that can be used in both the minimization problems and the maximization problems. The algorithm for the linear normalization consists of the following steps: Step 1: Order the individuals of the population so that the best individual is the first and the worst individual is the last one. If the optimization problem is the minimization problem then the best individual has the smallest merit function value. Step 2: The individual with the best merit function is assigned a constant predefined value (the staring value for the linear normalization).

Most GA applications use fixed length, fixed order bit strings to encode individuals. Some people in the genetic algorithms field have come to believe that the bit strings should be used as encoding technique whenever they apply a genetic algorithm. However, in recent years, there have been experiments with other kinds of representation of individuals in the genetic algorithms like the floating point numbers. 1 Representation of individuals with the binary numbers The representation of individuals with the binary numbers use the bit strings (string of binary digits 1 or 0) for encoding of possible solutions to the problem.

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