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Research Papers

Evolving Hidden Genes in Genetic Algorithms for Systems Architecture Optimization

[+] Author and Article Information
Ossama Abdelkhalik

Department of Mechanical Engineering
and Engineering,
Mechanics Michigan Tech Univesity,
Houghton, MI 49931
e-mail: ooabdelk@mtu.edu

Shadi Darani

Department of Mechanical Engineering
and Engineering,
Mechanics Michigan Tech Univesity,
Houghton, MI 49931

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 24, 2017; final manuscript received April 21, 2018; published online June 4, 2018. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(10), 101015 (Jun 04, 2018) (11 pages) Paper No: DS-17-1273; doi: 10.1115/1.4040207 History: Received May 24, 2017; Revised April 21, 2018

The concept of hidden genes was recently introduced in genetic algorithms (GAs) to handle systems architecture optimization problems, where the number of design variables is variable. Selecting the hidden genes in a chromosome determines the architecture of the solution. This paper presents two categories of mechanisms for selecting (assigning) the hidden genes in the chromosomes of GAs. These mechanisms dictate how the chromosome evolves in the presence of hidden genes. In the proposed mechanisms, a tag is assigned for each gene; this tag determines whether the gene is hidden or not. In the first category of mechanisms, the tags evolve using stochastic operations. Eight different variations in this category are proposed and compared through numerical testing. The second category introduces logical operations for tags evolution. Both categories are tested on the problem of interplanetary trajectory optimization for a space mission to Jupiter, as well as on mathematical optimization problems. Several numerical experiments were designed and conducted to optimize the selection of the hidden genes algorithm parameters. The numerical results presented in this paper demonstrate that the proposed concept of tags and the assignment mechanisms enable the hidden genes genetic algorithms (HGGA) to find better solutions.

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Figures

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Fig. 1

Interplanetary trajectory optimization problem topology

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Fig. 2

Chemical tags (diamonds) and the “tails” of histone proteins (triangles) mark DNA to determine which genes will be transcribed. (picture is modified from Ref. [26]).

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Fig. 3

Hidden genes and effective genes in two different chromosomes

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Fig. 4

Crossover operation in HGGA

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Fig. 5

Hidden genes genetic algorithms and the tags concept

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Fig. 6

Tags of children as computed using the logic A

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Fig. 7

Comparison of three HGGA tags mechanisms—using Schwefel 2.26 function

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Fig. 8

Comparison of three HGGA tags mechanisms—using Egg holder function

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Fig. 9

Success rate versus number of runs for the Earth–Jupiter trajectory optimization problem using mechanism A and logic A

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Fig. 10

Mechanism A: EVEJ trajectory for MGADSM model

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Fig. 11

Evolution of tags using logic C in the Earth–Jupiter problem

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Fig. 12

Success rate versus number of runs for Schwefel 2.26 function using three different logics for tags evolution

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Fig. 13

Success rate versus number of runs for Egg holder function using three different logics for tags evolution

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Fig. 14

Success rate of the Schwefel 2.26 function for different stochastic mechanisms

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