A Three-Stage Saving-Based Heuristic for Vehicle Routing Problem with Time Windows and Stochastic Travel Times

Algorithm 4

The procedure of improving a solution generated by the solution construction stage.

(1) Set the incumbent solution IS to the solution obtained from the solution construction stage;

(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 customer denoted by that has the minimum reserved time under the expected travel times;

(6)  For each route ro, do:

(7)   For each position ep of ro, into which a customer node can be inserted, do:

(8)    Delete customer from its original route and insert it into ro at the position ep;

(9)    Insert the solution obtained from the above step into Solutions;

(10)   Next ep;

(11)  Next ro;

(12)  Fetch a solution with the least expected total cost E(z) from Solutions into IS;

(13) Endwhile;

(14) Return the solution IS′.