GENETIC CODING APPLICATION TO SYNTHESIS OF PLANAR MECHANISMS

th 5 International Advanced Technologies Symposium (IATS’09), May 13-15, 2009, Karabuk, Turkey GENETIC CODING APPLICATION TO SYNTHESIS OF PLANAR MEC...
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5 International Advanced Technologies Symposium (IATS’09), May 13-15, 2009, Karabuk, Turkey

GENETIC CODING APPLICATION TO SYNTHESIS OF PLANAR MECHANISMS a, *

Aykut KENTLI a,*, A. Kerim KAR.b, Ertuğrul TAÇGIN c

Marmara Üniversitesi, Istanbul, Turkey, [email protected] Marmara Üniversitesi, Istanbul, Turkey, [email protected] c Marmara Üniversitesi, Istanbul, Turkey, [email protected] b

Abstract Genetic Algorithm is an optimization technique based on a genetic model comprising string representation of genes, mate and cross-over of strings, generation of new offsprings. Invention of GAs approach initially created great expectations in a broad variety of fields. As researches progress, it has been noticed that GAs have severe limitations and difficulty to be useful in real life applications, one of which is the requirement of extremely much computational time. Another limitation may be the length and the volume of population to be considered. Genetic Coding Approach is a genetic base alternative technique to overcome these limitations of conventional GAs. Genetic coding requires much less computation time due to the fact that the string length is only limited to three regardless of the sophistication of the application. Another significant improvement is that accuracy obtained in GCA is much larger than that of Conventional GAs. In the mean time, synthesis of mechanisms is a field requiring a high effort for optimization. There have been attempts to apply Artificial Intelligence techniques to mechanism synthesis like Expert Systems and GAs. In this study, fundamentals of Genetic Coding Algorithm (GCA) investigated together with an application to synthesizing planar mechanisms. Keywords: Genetic Coding, Mechanism Optimization

1. Introduction Different techniques have been used for synthesis of mechanisms. The great increase in computer power has permitted the development of routines that apply numerical methods to the minimization of a goal function. Han [1] studied these methods, whose work was later improved by Kramer et.al. [2] and Sohoni et.al.[3]. Moreover, multiobjective techniques are addressed by Rao et.al.[4] and Krishnamurty et.al.[5]. But, all these methods either restrict the number of precision points or take a lot of time to solve. This paper deals with application of an optimization approach to synthesis of planar mechanisms. An algorithm is defined which applies genetic coding based on evolutionary techniques and the type of aim function. Problem of synthesis of four-bar planar mechanism is used to test the method, showing that solutions are accurate and valid for all cases. The advantages of the method are implied. The approach presented in this paper to the synthesis of mechanisms deals with genetic coding. Genetic Coding is a variant of genetic algorithms. Genetic algorithms were firstly introduced by Holland [6, 7], whose work is included in [8], and they have been extensively and successfully applied to different optimization problems. Cabrerra et.al. [9] has summarized the studies on synthesis of

© IATS’09, Karabük Üniversitesi, Karabük, Türkiye

mechanisms with GAs. Interestingly, there is no study regarding the synthesis of mechanisms with GCA even its convenience. This study aims to cover in this space. The paper is organized as follows: Section 2 deals with the explanation of the algorithm. In Section 3 the main steps of mechanism synthesis will be mentioned. Section 4 analyzes the results found by the proposed method for the illustrative example and summarizes the conclusions of the paper.

2. Genetic Coding Fundamentals of GA and its benefits are mentioned in the literature [10]. However, on the contrary, GAs have many drawbacks originating from their random nature. There exist a couple of cases where GA fails to converge to the desired global optima: When the search space has more than one peak points, it is probable for GA to get stuck into one of the sub optimal points (After converging, the crossover and mutation operators can not generate so random individuals to diverse the uniformed population) When the search domain is not defined to include the whole domain where the function extends (Due to the fact that the length of the chromosome string is a parameter restricting the search domain in GA s and needs to be decided early in the lifecycle of the algorithm, all the search domain might not be represented) When the length of the chromosome string is not decided long enough to represent the optimal point, at the required precision. Even when the sought high precision can be represented well enough to satisfy the requirements, a noticeable decrease in performance of the algorithm is observed. In order to survive the ordinary GA from above troubles, a new approach to GAs named Genetic Coding Approach is developed as a new technique of adaptive optimization algorithms. It is inspired from the adaptiveness of biological systems like genetic algorithms and bases its theory on genetics science. This new technique is first developed by Kadir Celik in 1998 and first published in his MS Thesis in 1999 [11]. 2.1. Differences between GCA and GA Before mentioning any differences, it is better to state some of the similarities between these two algorithms. First of all, GCA, like GA, uses generations and an iterative formation and evaluation of these generations to reach the optima. Moreover, GCA operates the same way as the GA

algorithm. GCA uses crossover and mutation, two fundamental production operators of GA (Fig. 1), to produce a new generation.

Kentli, A., Kar, A.K. ve Taçgın, E.

does not require any decision on individual length, by operating on three-bit individuals and reaching any length precision, using those three-bit individuals. 2.3. Genetic Coding Algorithm In this method, the parents are generated by gathering different string (codon) which has 3 digits, x and f(x) values are calculated using these parents. First digit of string is called ‘sign parameter’ and represents if the value as positive or negative. The other two digits will be used in calculation. These two digits only can have 0,1,2,3 in 10 base. When its value is 3, this value will be used as 2. Crossover and mutation ratios are also defined at the beginning. Generally it works in order. Generation cells are written at the beginning. Family members which have 8 strings are defined randomly. n and inherited parameters are accepted as 0. Using string’s sign parameter and its value in 10 base, x and f(x) values are calculated.

START

Figure 1. General structure of a genetic algorithm

In contrast to above similarities, there are many differences between GA and GCA both in theory and implementation. On the theory side, due to, the fact that both algorithms base themselves on genetics science, the difference starts at how these two algorithms analogy the concepts of biological genetics. On the implementation side, the main differences come up in the way GCA reaches the solution and the way the individuals forming up a generation are represented. In GA the solution is searched by sending all individuals of a generation to objective function one by one and the best performing individual is ended up as the solution. However, in GCA directly the solution code is examined to get whether the solution is found or not. Furthermore on differences on the implementation side, GA bases its implementation on the evaluation of individuals constituted of genes or alleles. Any predefined arbitrary length of these genes, the length being greater than 0, form up an individual that is to exist with other individuals in a population. On the other hand, GCA bases its implementation on numeric representations of genetic codons known as Adenine, Guanine, Cytosine, Tomin rather than single genes.

REPRODUCTION Determine x and f(x) values Set the initial values ia=0 n=0 err=0.001 counter=0

f(x)

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