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<HTML><HEAD><!-- This HTML file has been created by texi2html 1.51 from gpkernel.texi on 3 July 1997 --><TITLE>Genetic Programming Kernel Version 0.5.2 - 2 Parameter Study</TITLE></HEAD><BODY>Go to the <A HREF="gpkernel_1.html">first</A>, <A HREF="gpkernel_1.html">previous</A>, <A HREF="gpkernel_3.html">next</A>, <A HREF="gpkernel_3.html">last</A> section, <A HREF="gpkernel_toc.html">table of contents</A>.<P><HR><P><H1><A NAME="SEC28" HREF="gpkernel_toc.html#TOC28">2 Parameter Study</A></H1><H2><A NAME="SEC29" HREF="gpkernel_toc.html#TOC29">2.1 Initial Configuration</A></H2><P>To investigate the influence of some important configuration parametersof the Genetic Programming kernel, a problem which can be quicklycalculated was selected: the lawn-mower problem (See Koza's book).</P><P>The lawn-mower problem can be described as follows. Consider anautonomous mower which must evolve the ability to mow the lawn it isplaced upon. The lawn in question is a ten times ten grid toriodalworld. Toriodal means that if the mower moves outside the lawn, itautomatically comes in again on the opposite side. The mower has nosensors. It can move forward, turn left, and jump.</P><P>Starting from a reasonably good configuration, some parameters weremodified. The starting configuration was:</P><BLOCKQUOTE><PRE>PopulationSize = 100NumberOfGenerations = (depends on parameter)CreationType = 2CreationProbability = 2.0CrossoverProbability = 98.0MaximumDepthForCreation = 6MaximumDepthForCrossover = 17SelectionType = 1TournamentSize = 10DemeticGrouping = 0DemeSize = 20DemeticMigProbability = 100.0SwapMutationProbability = 3.0ShrinkMutationProbability = 3.0SteadyState = 0LengthFactor = 0.001</PRE></BLOCKQUOTE><P>As many as 50 runs were made for each parameter value. The averagefitness values of the best performing genetic programs were recorded foreach generation.</P><P>This study was done to determine the influence of the GeneticProgramming control parameters. The conclusions that can be drawn fromthe study are, however, not generally applicable to all problems.</P><H2><A NAME="SEC30" HREF="gpkernel_toc.html#TOC30">2.2 Results</A></H2><IMG SRC="images/popsize.gif" ALT="Picture (Parameter study: population size)"ALIGN="CENTER"> <BR> Parameter study: population size </A> <P><IMG SRC="images/popsize.gif" ALT="Picture (Parameter study: large population size versus large number of generations)"ALIGN="CENTER"> <BR> Parameter study: large population size versus large number of generations </A> <P><IMG SRC="images/steady.gif" ALT="Picture (Parameter study: steady state)"ALIGN="CENTER"> <BR> Parameter study: steady state </A> <P><IMG SRC="images/maxdepth.gif" ALT="Picture (Parameter study: maximum depth for creation)"ALIGN="CENTER"> <BR> Parameter study: maximum depth for creation </A> <P><IMG SRC="images/select.gif" ALT="Picture (Parameter study: selection method)"ALIGN="CENTER"> <BR> Parameter study: selection method </A> <P><IMG SRC="images/crossove.gif" ALT="Picture (Parameter study: crossover probability)"ALIGN="CENTER"> <BR> Parameter study: crossover probability </A> <P><IMG SRC="images/demgroup.gif" ALT="Picture (Parameter study: demetic grouping)"ALIGN="CENTER"> <BR> Parameter study: demetic grouping </A> <P><IMG SRC="images/demesize.gif" ALT="Picture (Parameter study: deme size)"ALIGN="CENTER"> <BR> Parameter study: deme size. Demetic grouping=1 </A> <P><IMG SRC="images/dememig.gif" ALT="Picture (Parameter study: demetic migration probability)"ALIGN="CENTER"> <BR> Parameter study: demetic migration probability. Demetic grouping=1 </A> <P><IMG SRC="images/swapmut.gif" ALT="Picture (Parameter study: swap mutation)"ALIGN="CENTER"> <BR> Parameter study: swap mutation </A> <P><IMG SRC="images/shrnkmut.gif" ALT="Picture (Parameter study: shrink mutation)"ALIGN="CENTER"> <BR> Parameter study: shrink mutation </A> <P><IMG SRC="images/toursize.gif" ALT="Picture (Parameter study: tournament size)"ALIGN="CENTER"> <BR> Parameter study: tournament size </A> <P><IMG SRC="images/creation.gif" ALT="Picture (Parameter study: creation type)"ALIGN="CENTER"> <BR> Parameter study: creation type </A> <P><H2><A NAME="SEC31" HREF="gpkernel_toc.html#TOC31">2.3 Conclusions</A></H2><P>There are some conclusions that can be drawn from the parameter study:</P><UL><LI>In general: <STRONG>The faster the convergence in the first generations,the worse is the best achievable result, and vice versa.</STRONG><LI>The population size should not fall below a certain minimum value. Thisvalue depends on the problem. When extremely good results are needed,nothing is better than a large population size. A cross check was doneto underline this. A population size of 500 was run for 2000generations, but it did not yield an equally good result than thepopulation size 5000 running for 200 generations (this particular runtook 15 hours 35 minutes CPU time on an Ultra Sparc SUN workstation).By the way, the program consumed about 62MB memory with a populationsize of 5000. Using steady state can reduce this to approximately halfthe amount, of course.<LI>If the steady state Genetic Programming is used, the results of thefirst generations are better.<LI>Tournament selection performs better, except when running a lot ofgenerations.<LI>The higher the crossover probability, the faster the convergence. Thefirst conclusion does not appear to be applicable to this parameter.<LI>With the parameters from above, demetic grouping has no effect. Thischanges with the deme size and the demetic migration probability,reduction of which slows down convergence.<LI>The effect of swap mutation is marginal.<LI>Shrink mutation can yield better results. The reason for this is thatthe calculation of the standardised fitness takes the tree length intoaccount, and shrink mutation therefore helps improving the fitness.<LI>The tournament size has a big effect. The smaller it is, thebetter the best achievable result.<LI>The creation types <EM>Variable</EM> and <EM>RampedVariable</EM> should notbe used. The reason for their bad performance in the few firstgenerations may be that during creation, the chance of selecting afunction node or a terminal node is equal. This can lead to shorttrees.<LI>The parameter <EM>MaximumDepthForCreation</EM> should not be too low.</UL><P><HR><P>Go to the <A HREF="gpkernel_1.html">first</A>, <A HREF="gpkernel_1.html">previous</A>, <A HREF="gpkernel_3.html">next</A>, <A HREF="gpkernel_3.html">last</A> section, <A HREF="gpkernel_toc.html">table of contents</A>.</BODY></HTML>?? 快捷鍵說明
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