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From: mak-fu@fuku.shimane-u.ac.jp (fukusima makoto)
Subject: An idea of GA for school timetable
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Date: Mon, 31 Oct 1994 07:22:57 GMT
Organization: Shimane University
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I have an idea of GA for school timetable problem using unfitness
not fitness.
The summary  is as follows:
======================================================
Assumed conditions.
1) Every teacher has only one subject.
2) Number of lessons held at every period is equal to that of classes.
3) No preassignments of teachers.
4) Off-work periods required by teachers are available at any periods.
5) Numbers of teachers and classes are N(=10) and K(=5), respectively.
6) Number of lessons  in a week is M(=35)  and 7 lessons  in a day.
7) Half of teachers  work 20 hours in a week and others are 15 hours.
8) More than  5 hours of lessons are not  assigned  to  every teacher in a day.
9) Every class has 4   lessons for each subject  by every half of teachers 
   and 3 times by  rest  of  them in a week.
10)No mutations.   
------------------------------------------------------------- 
GA for generating teachers' timetable.

1) Create the infeasible teachers' schedule (NxM matrix T) using random numbers 
   according to above conditions except  2) and 8).
2) The matrix is a population and its column is a individual. 
   The elements tnm are genes with codes 0(not assigned), 1(assigned) and 9(off-work).
3) Calculate the unfitness(Um)  of the individual m (<= M) for crossover. Um is given by
                 Um=Sm-5 
   where Sm is the sum of the lessons held at same period.
4) Calculate the selection probability Pm for the individual m using Um.
          Pm=|Um| / sum ( |Um|) from m=1 to M
5) Select a pair of individuals from two subsets of the population.
   The individuals of one subset satisfy Um> 0 and those of the other one is Um< 0.
6) Select a gene for crossover  from each individual according to the unfitness Un 
   with cube scaling,
                     Un=cube(1/Vn*),      Vn*=Max(Vn,0.5) ,
   where Vn is the number of the modified genes of teacher n from the first state,
   through crossover. 
7) Assume a two-point crossover with one length (swap genes each other at same locus ),
   which generates one  time at one  generation. 
8) Create 10 child populations from  the first generated population.
9) Terminate the child populations when above condition 2) and 8) are satisfied.
10) Select the good populations which have the least sum of Vn.
----------------------------------------------------------------------------------
 GA for generating class timetables from the feasible teachers' timetables
 selected above 10) is omitted.

 If someone interested in this idea, please send E-mail to
 mak-fu@fuku.shimane-u.ac.jp  .

 
