Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization

Algorithm 1

Framework of MOEA/D using MUP Method.

Input:

  MOP: the multiobjective optimization problem

  N: the size of population

  T: the size of neighborhood

  : probability of local mating

Output: a set of solutions

Initialize a set of solutions

Generate a set of uniformly distributed weight vectors

for do

 , where are T closest weight vectors to

end

Initialize the ideal point

Initialize the nadir point by corner points in population P

while stopping criterion is not satisfied do

   for do

    if then

    else

    end

    Randomly select two indexes , from E

    Produce a solution from by crossover operator

    Perform mutation operator on to produce a new solution

    Update the ideal reference point

    Update neighboring solutions by Algorithm 2

   end

   Reevaluate the nadir point by corner solutions in the updated population

end

return P