An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We proposed an iterated local search algorithm for the vehicle routing problem with capacity and time window constraints in [1]. We conducted some computational experiments to evaluate the proposed algorithm. The algorithm was coded in C language and run on an IBM-compatible PC (Intel Pentium 4, 2.8 GHz, 1 GB memory). We used the following benchmark instances: (1) Solomon’s benchmark instances [2], and (2) Gehring and Homberger’s benchmark instances [3]. The time limit of our iterated local search algorithm for instances with 100, 200, 400, 600, 800 and 1000 customers are 1000, 2000, 4000, 6000, 8000 and 10000 seconds, respectively. As initial values of κp and κq (parameters), we conducted two types of experiments: (1) κp = 1/100000 and κq = 1/100000 (called ILS-1), and (2) κp = 1 and κq = 1 (called ILS-2). The detailed results for these instances are shown in Tables 1, 2, 3, 4, 5 and 6. We compare our computational results with the previous best known values as of June 7, 2006, presented in the web site (http://www.sintef.no/static/am/opti/projects/top/vrp/benchmarks.html). Each row of these tables represents a problem instance. “m” represents the number of vehicles, “distance” represents the total travel distance value, and “#LS in total” represents the total number of local search procedure called in our iterated local search algorithm. An asterisk “∗” in the row “m” means that our algorithm uses a smaller number of vehicles than the previous best known solution. An asterisk “∗” in the row “distance” means that our algorithm uses the same number of vehicles as the previous best known solution, and the total travel distance value is smaller than the best known value. A dagger “†” in the row “distance” means that our algorithm uses the same number of vehicles as the previous best known solution, and the total travel distance is also same as the best known value.