Research Article
A Simulation-Based Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Travel Times
Algorithm 2
The method of improving a solution generated by a CVRP heuristic.
1 Set the incumbent solution IS = CS, where CS is obtained from step 14 of Algorithm 1; | 2 Fabricate a solution IS′ whose expected total cost is set to an infinite value that cannot be | exceeded by the total cost of any solution; | 3 While the expected total cost of IS is less than that of IS′, do: | 4 Set IS′ = IS, Solutions = ; | 5 Fetch the vehicle that returns to depot at the earliest expected time from all vehicles in IS | and denote the vehicle’s route by er; | 6 Fetch the vehicle that returns to depot at the latest expected time from all vehicles in IS | and denote the vehicle’s route by lr; | 7 For each customer node cn of lr, do: | 8 For each position ep of er, into which a customer node can be inserted, do: | 9 Delete cn from lr and insert cn into er at its position ep; | 10 Insert the solution obtained from the above step into Solutions; | 11 Next ep; | 12 Next cn; | 13 Fetch a solution with the least expected travel cost from Solutions into IS; | 14 Use Monte Carlo simulation method like steps 6–11 in Algorithm 1 to calculate the expected | total cost of solution IS; | 15 Endwhile; | 16 Return the solution IS′. |
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