Complete Mask Rules

 

1. :

   Case: Both children are good.

   Summary: Very encouraging behavior and as such is reflected in the mask settings below and in figure . The parents' masks are OR'd to produce the children's masks, ensuring preservation of the contributions from both parents.

     
   Figure: Mask rule : Example of mask propagation when both C1 and C2 are good
   

   Action:

   • CM1: OR the masks of PM1 and PM2. If there are any 0's left in CM1, toss a coin to decide their value.
   • CM2: Same as for CM1.
   • PM1: No changes except for those produced by mask mutation.
   • PM2: Same as for PM1.

2. :

   Case: Both children are bad.

   Summary: Discouraging behavior and must be guarded against in future. Each parent contributed bits that were detrimental to the children's fitness. MX has not set up the parents' masks correctly. Changes are given below and shown in figure .

     
   Figure: Mask rule : Example of mask propagation when both C1 and C2 are bad.
   

   Action:

   • CM1: This mask should reflect the undesirability of the current search direction. Contributions from P2 were detrimental, therefore CM1 should search in the area of P2's contribution which is specified by the loci where is 0 and is 1. Set these loci in to 0. If P2 > P1 in fitness, toss a coin to set the bits of CM1 at those locations where both and are 1.
   • CM2: A similar rule applies to CM2.
   • PM1: P2's contribution to C1 led to a bad child. The C1 positions copied from P2 need to be explored in P1. These loci are those for which was 0 and was 1. Therefore set these loci in by tossing a coin. In addition, PM1 specified loci that were detrimental to C2. Therefore when is 1 and is 0, set these locations by tossing a coin.
   • PM2: A similar rule applies for PM2.

3. :

   Case: One child is bad while the other is average. Assume that C1 is bad and C2 is average.

   Summary: There are two sub-cases. If C2's fitness is less than that of P2, it means that P1's contribution was deleterious, and that PM2 needs to be augmented with 1's at those positions that were copied from P1 to C2 (see figure ). If C2's fitness is less than that of P1, P1's contribution increased C2's fitness, so preserve P1's contribution in C2. The masks are shown in figure .

     
   Figure: Mask rule , Part 1: Example of mask propagation when C1 is bad and C2 is average. (C1 < P1 < C2 < P2)
   

   Action:

   • When C1 < P1 < C2 < P2:
     • CM1: Very similar to 's CM1. This mask should reflect the undesirability of the current search direction. Contributions from P2 were detrimental, therefore CM1 should search in the area of P2's contribution which is specified by the loci where is 0 and is 1. Set these loci in to 0. Since P2 > P1 in fitness, toss a coin to set the bits of CM1 at those locations where both and are 1.
     • CM2: As P1's contribution decreased C2's fitness, set by tossing a coin when is 1 and is 0, searching around P1's contribution.
     • PM1: P2's contribution to C1 led to a bad child. The C1 positions copied from P2 need to be explored in P1. These loci are those for which is 0 and is 1. Therefore set these loci in by tossing a coin. In addition, PM1 specified loci that were detrimental to C2. Therefore when is 1 and is 0, again set these locations by tossing a coin.
     • PM2: Since P1's contribution led to a decrease in fitness, set to 1 for those loci for which is 1 and is 0. To help fix positions currently 0, toss a coin to fix those loci in for which both and are 0.

   • When C1 < P2 < C2 < P1:

       
     Figure: Mask rule , Part 2: Example of mask propagation when C1 is bad and C2 is average. (C1 < P2 < C2 < P1)
     

     • CM1: Same as the action for CM1 when C1 < P1 < C2 < P2. Except that as P1 > P2, no action need be taken when both parent masks have a 1 at some position.
     • CM2: To preserve P1's contribution, when is 1 and is 0 set to 1.
     • PM1: Those bits that contributed to C1 but not those that helped C2 need to be modified. Therefore for those loci where is 1 and is 0, toss a coin to decide . P2's contribution was detrimental so when is 1 and is 0 set to 1.
     • PM2: Set by tossing a coin for those loci that contributed to C1.

4. :
   • Case: Both children are average.
   • Summary: Once again there are two sub-cases depending on whether a child is better or worse than its dominating parent. Assume that C1 is better than P1 implying that C2 is worse than P2. The complementary case when C1 is worse than P1 and C2 is better than P2 is treated the same way by substituting C1 for C2 and P1 for P2. The masks are given in figure .
   • Action:
     • CM1: This mask should reflect the desirability of the current search direction since P2 contributions lead to C1's increased fitness. OR the masks of PM1 and PM2, if there are any zeero's left in CM1 toss a coin to decide their value.
     • CM2: Contributions from P1 were detrimental. Set the loci that specify P1 contribution to C2 to 0.

         
       Figure: Mask rule , Example of mask propagation when both C1 and C2 are average.
       

     • PM1: P1's contributions to C2 were detrimental, set these loci by a coin toss.
     • PM2: The positions that P1 contributed to C2 decreased C2's fitness, set these loci to 1.
5. :
   • Case: One child is good and the other average.
   • Summary: There are two sub-cases depending on the relative ordering of the parents and children. If P1 < C1 < P2 < C2 is behavior to be encouraged. The other case stresses the importance of P1.
   • Action:
     • When P1 < C1 < P2 < C2: This is also encouraging behavior and is depicted in figure .
       • CM1: Same as for 's CM1.
       • CM2: Same as for CM1 above.

           
         Figure: Mask rule , Part 1: Example of Mask propagation when C1 is average and C2 is good. (P1 < C1 < P2 < C2)
         

       • PM1: Since both children are better than their prospective parents flip a coin to decide positions that are 0 in both PM1 and PM2
       • PM2: Same as for PM1 above .
     • P2 < C1 < P1 < C2 Clearly P1's contribution is vital to reproduction. The mask settings describe this below and in figure .

         
       Figure: Mask rule , Part 2: Example of Mask propagation when C1 is average and C2 is good. (P2 < C1 < P1 < C2)
       

       • CM1: P2's contribution decreased C1's fitness. To encourage search in this area, when is 1 and is 0 set to 0.
       • CM2: P1's contribution clearly contributed positively to C2's fitness. Set to 1 when is 1 and is 0.
       • PM1: Since P2's contribution decreased the fitness of C1, should be 1 at those loci where is 1 and is currently 0.
       • PM2: Since P2's contribution to C1 was negative, set to 0 at those loci where is 0 and is currently 1.
6. :
7. Case: One child is good and the other bad. Assume C1 is bad and C2 is good.
8. Summary: This should try to preserve C2's schemas, while the relative fitnesses of P1 and P2 drive the settings of PM1 and PM2.
9. Action:
   • CM1: Same as 's CM1.
   • CM2: When is 1 and is 0, set to 1. In addition, whenever both parent masks are 0 use a random coin toss to set the corresponding position in .

       
     Figure: Mask rule : Example of Mask propagation when C1 is bad and C2 is good
     

   • PM1: P2's contribution decreased C1's fitness. Set to 1 when is 0 and is 1. If P1 < P2 in fitness, to further improve PM1, flip a coin to set positions where both and are 1.
   • PM2: No changes except for mask mutation.