A Mutualism Quantum Genetic Algorithm to Optimize the Flow Shop Scheduling with Pickup and Delivery Considerations

Algorithm 1

MQGA (mutualism quantum genetic algorithm).

Begin

Step  1. Set parameters: crossover probability , mutation probability , iterative

   generation GN, two subpopulations sizes , .

Step  2. Initialize subpopulations in hybrid -bit representation.

While () do

Begin

Step 3. If (subpopulation is not empty)

     Apply mutualism strategy, rescale the size of subpopulations according to population growth model.

   End.

Step  4. Perform selection, crossover, mutation operations in each subpopulation;

Step  5. If (catastrophe condition is satisfied)

     Perform catastrophe operation.

   Else

     Apply quantum rotation operation.

   End

Step  6. Calculate objective value and fitness value of each individual in the current generation,

   and update the best solution if possible.

End

End

Output the global best result.