A Multiobjective Optimization Algorithm to Solve the Part Feeding Problem in Mixed-Model Assembly Lines

Algorithm 1

First stage: minimizing the number of tours.

While 𝑇0>1
For 𝑘=1 to NI
While (i) is not satisfied
^NT∑𝑡=1AB𝑖𝑡≥∑^NT𝑡=1𝑑𝑖𝑡∀𝑖=1,…,𝑛		(i)
Start a new tour, 𝑚=1, and create the FCL according to (ii).
𝑖∈FCL(𝑡)⟺IL𝑖𝑡<𝑑𝑖𝑡		(ii)
If FCL is not empty
While FCL is not empty
Select a part reference which is in the FCL and assign as many bins as necessary to
satisfy (iii). Remove the selected reference from FCL.
AB𝑖𝑡+IL𝑖𝑡≥𝑑𝑖𝑡		(iii)
End while
While Equation (iv) is satisfied
^𝑛∑𝑖=1AB𝑖𝑡<𝐴		(iv)
Create the SCL according to (v).
𝑖∈SCL(𝑡)⟺[AB𝑖𝑡+IL𝑖𝑡]^+<𝐶𝑖∩∑^𝑡𝑝=1AB𝑖𝑝<∑^NT𝑡=1𝑑𝑖𝑡		(v)
If SCL is not empty
Use the solution string, select a reference according to the given heuristic on the 𝑚th
element of the string and assign one bin of the selected reference to the tow train, 𝑚=𝑚+1.
Else
Update the stock level and capacity in the stations according to (vi) and (vii), respectively.
Terminate the assigning process in the current tour.
IL𝑖𝑡+1=IL𝑖𝑡+AB𝑖𝑡−𝑑𝑖𝑡∀𝑖=1,…,𝑛		(vi)
𝐶𝑖=𝐶𝑖−IL𝑖𝑡+1^−∀𝑖=1,…,𝑛		(vii)
End if
End while
Else
Leave the current tour without assigning any bins and update the stock level and capacity
in the stations according to (vi) and (vii), respectively.
End if
End while
Continue the solution process in the second part of the algorithm.
Calculate the objective function
If OB𝑁≤OB𝐶
𝐶𝑠=𝑁𝑠
Else
Calculate the 𝑃𝑠 according to (12) and generate the 𝑟
If 𝑟≤𝑃𝑠
𝐶𝑠=𝑁𝑠
End
End
Generate a neighbouring solution using the defined mutation operators.
Terminate the process in the current inner loop if 𝐶𝑠 is the same for 5 consecutive iterations
End if
End for
If 𝐶𝑠≤𝐵𝑠
𝐵𝑠=𝐶𝑠
End if
Reduce the temperature using the decrement function presented as (13).
Terminate the algorithm if 𝐵𝑠 is the same for 5 consecutive iteration
End while