Click here to learn more. By continuing to use this site, you agree to our use of cookies. We've also updated our Privacy Notice. Click here to see what's new. This study proposes a newly developed optimization method for an aspherical lens system employed in a refractive laser beam shaping system, which performs transformations on laser spots such that they are transformed into flat-tops of any size.

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In this paper, a genetic algorithm GA with multipoint search is proposed as the optimization method, together with macro language in optical simulation software, in order to search for ideal and optimized parameters. In comparison to a traditional two-dimensional 2D computational method, using the one-dimensional 1D computation for laser beam shaping can search for the optimal solution approximately twice as fast after experiments.

The optimal results show that when the laser spot shrinks from 3 mm to 1. The distances between the lenses for both systems described above are even smaller than the thickness for the first lens, enabling us to conclude that our design objectives of extra light and slimness in the system are achieved. A 18 4 Neal C.

Evans and David L. Shealy Appl. A 29 12 Fang, C. Yen, and J. Sun, Y. Fang, B. Hsueh, and W. Laser Technol. Fang, T.

Liu, B. Wu, J. Chou, and J.

## List of genetic algorithm applications

Serkan and H. Liu and S. Shealy and J. Zhang, G. Neil, and M. Hoffnagle and C. Scott and W. Citing articles from OSA journals and other participating publishers are listed here. Alert me when this article is cited. Click here to see a list of articles that cite this paper. Equations on this page are rendered with MathJax. Learn more. Login or Create Account. Allow All Cookies. Each job is processed by one machine in each stage and it must go through one or more stages. Machines in each stage can be identical, uniform or unrelated Linn and Zhang, We assume that all jobs and machines are always available during the scheduled period and the preemption is not allowed.

The objective is. A hybrid flow shop scheduling problem's mathematical model is described as a mix integer programming. The model is given as follows Hong Wang :. Constraint 2.

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These constraints do not allow more than one job to be processed on a machine at any time. Constraints 2. Ramamurthy They developed a branch and one machine on the first stage and two machines on. Gupta the second stage. The other studies on the hybrid. Wang et al. In the HGA, not only multiple genetic operators based on evolutionary mechanism are used simultaneously in hybrid sense, but also a neighborhood structure based on graph model is employed to enhance the local search, so that the exploration and exploitation abilities can be well balanced.

They investigated the effects of buffer size and decision probability on optimization performances using simulation. Oguz and Ercan proposed a GA for hybrid flow-shop scheduling with multiprocessor task problems and described its implementation.

They also employed a preliminary test to establish the best combination of the control parameters to be used along with different genetic operators. Li-Xin et al. Randomly generated instances were tested by simulation program. Computational experiments show that for small size HFSS scheduling problems, the average deviation of GDA from the optimal solution is 0. Xia et al. The algorithm is based on the list scheduling principle by developing job sequences for the first stage and queuing the remaining stages in a FIFO manner. The effectiveness of the proposed method is tested with Carlier and Neron's.

The computational results indicate that the proposed approach is effective in terms of reduced makespan for the attempted problems. To the best of our knowledge, there are no genetic algorithms applied to Hybrid flow shop including Carlier and Neron's scheduling problems in the literature.

The rest of the paper is organized as follows. The proposed effective algorithm is explained in Section 2. In Section 3, an extensive computational study using the proposed algorithm and experiments are presented.

- References.
- Application of the genetic algorithm to residual statics estimation!
- OSA | Application of genetic algorithm on optimization of laser beam shaping?

In Section 4, the paper is concluded with some comments. GAs were invented by John Holland Goldberg, and they were stochastic search methods designed to search large and complex spaces by exploitation of currently known solutions and a robust exploration of the entire search space Yoon and Ventura, GAs use a collection of solutions called population. Each individual in the population is called a chromosome a string of symbols and a chromosome represents a solution to the problem.

The chromosomes can be produced through successive iterations, called generations and the population size the number of individuals in a population remains fixed from generation to generation. The chromosomes are evaluated using the value of the fitness function during each generation. A set of genetic operators such as reproduction selection and recombination crossover and mutation is applied to create new and better solutions off springs from the individuals of the current population and the solutions are steadily improved from generation to generation.

The structure of GAs is given in Fig. The proposed GA is based on a permutation representation of the n jobs. The details of our implementation for the GAs are given as follows. A direct coding approach is used. In this coding, a chromosome represents a schedule directly Yamada et al. The initial population is randomly generated.

The population size is determined by the help of a full factorial experimental design using our GA program. Selection schemes allow the algorithm to take biased decisions favoring good strings when generations change. For this aim, some of the good strings are replicated while some of bad strings are removed. As a consequence, after the selection mechanism is determined, the population is likely to be "dominated" by good strings. Various selection schemes in the literature have been used. We focus on roulette wheel selection and tournament selection without replacement.

Crossover is used as the main genetic operator and the performance of a GA is heavily dependent on it. During the past three decades, various crossover operators have been proposed for the scheduling problems. These six crossover operators are briefly explained in the following:.

First, it is generated a random mask and then exchanged relative genes between parents according to the mask. This operator is explained and detailed in section 3. The offspring inherits the elements between the two crossover points from the selected parent in the same order and position as they appear in the parent. The remaining elements are inherited from the alternate parent in the order in which they appear in that parent, beginning with the first position following the second crossover point and skipping over all elements already present in the off spring Kaya and Engin, ; Cheng et al.

A parent and two crossover sites are selected randomly and the elements between two string positions in one of the parents are directly inherited by the offspring.

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## List of genetic algorithm applications - Wikipedia

Each element between the two crossovers points in the alternate parent are mapped to the position held by this element in the first parent. Then the remaining elements are inherited from the alternate parent Kaya and Engin, ; Cheng et al. The cycle between strings is fined, the symbols in the cycle are coped to a new string, the remaining symbols are determined for the new string by deleting the symbols and the remaining symbols are fulfilled with the new string.

The two sublists are selected from strings randomly. Sublist2 is removed from string1, leaving some "holes" and then holes are slide from the extremities toward the center until they reach the cross section. Similarly, Sublist1 is removed from string2. At the end, Sublist1 is inserted into the holes of string2 to form offspring1 and sublist2 is inserted into the holes of string1 to form offspring2 Gen and Cheng, A set of positions is selected randomly; the order of symbols in the selected positions is imposed on the corresponding symbols in the other string.

Mutation operator plays a very important role in GAs and it helps maintain diversity in the population to prevent premature convergence.