Combining Interval Branch and Bound and Stochastic Search

Algorithm 8

Integrated interval algorithm and GA for unconstrained problem.

(1) Subdivide the domain into boxes and calculate .

(2) Put the box along with its lower bound of in listx in nondecreasing order of

  that is, listx  = .

(3) Set .

(4) Let be a set of the first boxes on listx.

(5) Randomly select points from and put them in a set . Evaluate value for each point in .

(6) Set to be the minimum value of from .

(7) repeat

(8)   Generate a new set of points, , from using Algorithm 9.

(9)   Evaluate value of each point in . Update .

(10)  Let be a box with the maximum value of where .

(11)  Bisect in the direction of the maximum length of the edge such that .

(12)  Calculate and .

(13)  Remove from listx.

(14)  Enter the pairs and into listx in a way that do not decrease.

(15)  Let be a set of the first boxes on listx.

(16)  Prepare by choosing points with the lowest value of from

   the two sets and . The other points from .

(17)    Delete a pair from listx if .

(18)    Set .

(19) until (the stopping condition becomes true)