Combining Interval Branch and Bound and Stochastic Search

Algorithm 11

Integrated interval algorithm and GA for constrained problems.

(1) Set .

(2) Subdivide into boxes and put them in listx.

(3) Calculate fit using Algorithm 7 for every box in listx and set the value of ifit_box().

(4) fit where   listx.

(5) Randomly choose an integer idactive  . Denote the box in listxidactive by .

(6) Calculate nviol_box() and .

(7) repeat

(8)   Randomly choose an integer idnew  idactive}. Let be the box in listxidnew.

(9)   Calculate nviol_box() and .

(10)   Calculate funfun where fun is defined in (6).

(11)  Randomly select a number Unif.

(12)   If     then

(13)    idsearch  =  idactive

(14)  else

(15)    idsearch  =  idnew

(16)  end if

(17)  Perform GA by using Algorithm 12.

(18)  Let idbisect be an integer corresponding to the box with nviol_box(), nviol_box()}.

(19)  Bisect the box from listxidbisect as and .

(20)  Delete listxidbisect.

(21)  Check status of and . Discard the box with status 2.

(22)  Put and at the bottom of listx.

(23)  if (idsearch    idbisect) then

(24)   idactive  =  

(25)  else

(26)    idactive  =  idsearch

(27)  end if

(28)  Check deletion criteria to remove some boxes from listx.

(29)     Update using annealing schedule.

(30)     Update .

(31) until (stopping criteria are satisfied)