A Pareto-Based Adaptive Variable Neighborhood Search for Biobjective Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup Time

Algorithm 2

Overall procedure of the proposed PABOVNS.

()    Input: a set of candidate neighborhoods , the maximum iterations , the

    selection probability of each neighborhood to be , the iteration number , the

    external archive to be empty, and .

()    Initialization of external archive :

()       Generate an initial solution and set

()       while               //q is the sum of candidate neighborhoods

()              //perform multi-objective local search on in and

                         obtains a set of non-dominated solutions

()              //update the external archive with

()           

()        end while

()    while

()           //select a neighborhood based on selection probabilities

()     Multi-objective local search:  Phase I – neighborhood search:

()               //randomly select a solution from

()                //a random solution is generated in neighborhood

()               //perform multi-objective local search on in

()     Multi-objective local search:  Phase II – path relinking:

()              //randomly select a solution from

()              //randomly select another solution from

()            //perform multi-objective path relinking from to

()     Update external archive and selection probability of the selected neighborhood:

()         //update the external archive with and

()       UpdateProbability           //update the selection probability of neighborhood

()     

() end while