Efficient Constraint Handling in Electromagnetism-Like Algorithm for Traveling Salesman Problem with Time Windows

Algorithm 4

General scheme of proposed EMA.

(1) Set  𝑃𝑜𝑝𝑆𝑖𝑧𝑒← Population Size

(2) Set  𝑀𝑎𝑥𝐼𝑡𝑒𝑟← Maximum iteration limit

(3) Set  𝑈← Upper Bound for time window normalization

(4) Set  𝐿← Lower bound for time window normalization

(5) Normalize time windows of customers

(6) Generate 𝑃𝑜𝑝𝑆𝑖𝑧𝑒 of points within normalized time windows by 𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑖𝑧𝑒 procedure

(7) Calculate the OFV of each point.

(8) Check feasibility of each point.

(9) Set best and worst solution points.

(10) While  𝐼𝑡𝑒𝑟<𝑀𝑎𝑥𝐼𝑡𝑒𝑟  do

(11)   For  𝑖=1  to  𝑃𝑜𝑝𝑆𝑖𝑧𝑒

(12)      For  𝑗=1  to  𝑃𝑜𝑝𝑆𝑖𝑧𝑒

(13)        Calculate 𝑞_𝑖𝑗

(14)        Calculate 𝐅_𝑖𝑗

(15)      End for

(16)     Calculate resultant force 𝐅_𝑖

(17)   End for

(18)   Move each solution point.    //Relocate particles by updating position vectors.

(19)   Calculate OFV of each solution point.

(20)  Check boundaries of each solution point by 𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦𝐶𝑜𝑛𝑡𝑟𝑜𝑙 procedure.

(21)   Set the best and worst points.

(22)   Set  𝐼𝑡𝑒𝑟←𝐼𝑡𝑒𝑟+1

(23) End while