| Step 1: Set the model and algorithm parameters , , , and initialize some transient variables | | for heuristics , , , , , . | | We let if customer i has not been visited by vehicles yet, otherwise, ; is defined as the remaining quantity | | of products loaded by a vehicle k when it departs from customer in its lth cycle; is the cost due to the time windows | | is violated, that is, the second term of the objective function, (1). | | Step 2: Initially, each vehicle starts from the central depot “” for delivery, and update and for simplicity | | where and ; | | Step 3: Vehicle k is assigned to service customer j in terms of Rule 1, and update and ; | | If | | Generate the potential demand of customer j, update , and go to Step 4; | | Else go to Step 4; | | End; | | Step 4: Calculate the decision variable in terms of Rule 2, that is, the demand of customer j met by a vehicle in its lth cycle, | | and the penalty cost induced by the time windows. | | (a) If | | If then and update | | , , ; | | Else and update , ; | | End; | | Else | | If then and update , ; | | Else and update , ; | | End; | | End; | | (b) It can be concluded that from assumption (5): | | If then ,; | | Elseif then ; | | Else , ; | | End; | | Step 5: Decision whether to continue to delivery or return to the central depot. | | If | | , , go to Step 6; | | Else | | If then , and update , ; | | Go to Step 3; | | Else go to Step 3; | | End; | | End; | | Step 6: Output the route of all vehicles according to , and the decision variable such that a solution for VRP is created. | | Step 7: Repeat Steps 1–6 and terminate until M individuals are generated. |
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