Research Article

A DE-Based Scatter Search for Global Optimization Problems

Algorithm 2

Hybrid scatter search with differential evolution (SSDE).
(1)    Begin
(2)  Set the selection probability of each crossover operator to be the same, that is, ,
   where is the sum of all mutation operators.
(3)  Set the iteration counter and the .
(4)  Use the Diversification method to generate a population , evaluate each solution in and then set the best solution
    found so far to be the best one in .
(5)   while (the termination criterion is not reached) do
(6)    Use the Reference update method to update reference set .
(7)    Set , and . Set the solution set to be empty.
(8)    if () do
(9)     while ()do // generate a new solution for each in
(10)    Set the successful count and failure count of the crossover operator to be zero.
(11)     (1) Mutation
(12)       Randomly select a mutation operator (namely ) using the Adaptive selection method.
(13)       Randomly select solutions from according to the requirement of mutation operator .
(14)       Perform mutation operator on the selected solutions to generate a new trial solution .
(15)     (2) Crossover
(16)        Apply crossover operation based on (5) to obtain new solution .
(17)     (3) Selection
(18)       Use (7) to select the new solution . If , set = ; otherwise, set = .
(19)     Add and of each crossover operator to the end of a list whose length is . If ,
      then remove the first node of this list so that only a maximum of nodes are stored in list .
(20)     Update the selection probability of each operator according to the method described in Section 3.4.
(21)      Set .
(22)   end while
(23)   if (the best solution in is better than ) do
(24)      Update and set .
(25)   else do
(26)      Set .
(27)   end if
(28)  else do
(29)    Sort the solutions in the in the ascending order of the objective value, and then randomly reinitialize
     the latter half of solutions in .
(30)    Set .
(31)  end if
(32) end while
(33)Report the best solution .
(34) End