Dichotomous Binary Differential Evolution for Knapsack Problems

Algorithm 2

DBDE for knapsack problem.

Input: Population size, NP; Crossover probability, CR1 and CR2; Maximum number of objective function evaluations, MaxFEs

  ()    Randomly initialize population with NP individuals

  ()    for    do

  ()     if   is an infeasible individual  then

  ()      Execute Algorithm 1 for ratio-greedy repair

  ()     end if

  ()     Evaluate the objective function value

  ()    end for

  ()    FEs = NP

  ()    while  FEs < MaxFEs  do

  ()  for    do

  ()   Randomly select two individuals and from population

  ()   Execute the dichotomous mutation to generate a mutate individual

  ()   Execute the dichotomous crossover to generate a trial individual

  ()   if   is an infeasible individual  then

  ()    Execute Algorithm 1 for ratio-greedy repair

  ()   end if

  ()   Evaluate the objective function value

  ()   if    then

  ()    

  ()   end if

  ()  end for

  ()  FEs = FEs + NP

  () end while

Output: Optimal individual with the maximum profit value