1

Hybrid Construction Heuristics for Vehicle

Routing Problem

Hok Lie School of Computer Science, The Australian National University,Canberra, Australia, Hok.Lie@anu.edu.au

Philip Kilby Optimization Research Group, Canberra Research Laboratory,National ICT Australia (NICTA) , Philip.Kilby@nicta.com.au

Keywords: Construction heuristics; Experimental design

Construction heuristic has played significant role to create an initial solution in localsearch method for solving vehicle routing problem (VRP) such as large neighbourhood search(LNS) [3]. An ordinary construction heuristic usually takes one feature, for example mini-mum insertion cost, into consideration. In this work, we propose an enhanced constructionheuristic to build a better initial solution. Our idea is to combine several features into asingle hybrid heuristic by assigning weight to each selected features.

The features can be used in either choosing where to insert a visit, or choosing the visitto insert. In our system, there are seventeen features for choosing where to insert a visitand six features for choosing the visit to insert. Each feature has different value and basevalue. For example, route domain is a feature that favour visits with few feasible routes tobe inserted first, value is the number of routes that can be feasibly inserted into, with totalnumber of routes as the base value. While time window width encourages visits with smallesttime window to be inserted first, value is the width of time window, with maximum of timewindow widths as the base value.

Therefore, these features need to be normalized before they assigned weights and usedas a hybrid heuristic. The weight to which a particular feature is presented is rated on ascore of 0 to 1, with 0 meaning not present, and 1, present. We have used a normalizationprocedure [1] for each heuristic feature which allow us to assign the weight set.

In order to determine which features should be used and an appropriate weight set forthem, we undertake a systematic statistical study to design the hybrid construction heuristicsused in ALNS. The objective is to develop the best combination of construction heuristicfeatures for the algorithm for a given instance set. Statistical analyses are performed byfollowing the approach of response surface methodology [2], using commercial statisticalpackage. A screening experiment by using a fractional factorial design of experiment is runto eliminate unimportant heuristics feature. The remaining task is to determine the weightset for each selected features which done by using central composite design and the steepestascent procedure. Our preliminary experiment shows that the appropriate weight set forconstruction process can bring improvement for the solution over the Solomon [4] instancesset which demonstrated in figure 1.

2

Figure 1: Results from construction heuristic for solomon instance set, left graphshow results from default weight set, right graph show results from tuned weight set,all solution measured by the distance to the best known solutions.

Bibliography

[1] Kilby, P., Verden, A.: Flexible routing combing constraint programming, large neigh-bourhood search, and feature-based insertion. Artificial Intelligence and Logistics(AILog) Workshop at IJCAI’11 p. 43 (2011)

[2] Myers, R., Montgomery, D., Anderson-Cook, C.: Response surface methodology: pro-cess and product optimization using designed experiments, New York: John Wiley andSons Inc (2009)

[3] Shaw, P.: A new local search algorithm providing high quality solutions to vehiclerouting problems. APES Group, Dept of Computer Science, University of Strathclyde,Glasgow, Scotland, UK (1997)

[4] Solomon, M., Desrosiers, J.: Survey paper: Time window constrained routing andscheduling problems. Transportation science 22(1), 1-13 (1988)

3