Variable neighbourhood search in commercial VRP packages: evolving towards self-adaptive methods

Transcription

1 Variable neighbourhood search in commercial VRP packages: evolving towards self-adaptive methods Kenneth Sörensen 1, Marc Sevaux 2, and Patrick Schittekat 1,3 1 University of Antwerp 2 University of South Brittany 3 ORTEC Belgium September 2006 All commercial packages for vehicle routing that the authors are aware of use some form of variable neighbourhood search. This paper attempts to answer the question why this is the case. As we will show, variable neighbourhood search can be considered to be a very adaptable metaheuristic, which makes it especially suitable for the practical problems encountered in real life. We also point out that there is a need for the VNS applications used in commercial packages to evolve towards more self-adapting systems. Key words: commercial vehicle routing packages, variable neighbourhood search, adaptive methods 1 Introduction Vehicle routing is arguably one of the most useful and successful fields of operations research. As the total cost of logistics and transportation generally constitutes a sizeable proportion of any enterprise, it is not surprising that the efficient design of routes to visit customers for pickup or delivery can result in large savings. As a result, several companies have started to develop and market packages for routing applications, either as stand-alone packages or integrated into large ERP (Enterprise Resources Planning) packages such as SAP. Typically, these packages are put to work in highly complex and dynamic environments. This is illustrated in Figures 1 and 2, that show a graphical representation of the solution to an academic vehicle routing problem and a screen shot of a commercial software package displaying the solution to a real-life routing Corresponding author: Kenneth Sörensen, University of Antwerp, Prinsstraat 13, B 2000 Antwerp, kenneth.sorensen@ua.ac.be 1

2 problem. It is clear that real-life routing problems are several orders of magnitude more complex than their academic counterparts. Although there is an increasing academic focus on so-called rich vehicle routing problems (that incorporate more complex constraints and objectives), they have not in any way caught up with the whole complexity of real-life routing problems. Figure 1: A typical academic VRP solution Real-life vehicle routing problems should be able to accommodate the following (non exhaustive) list of characteristics. Customer characteristics: time windows (soft/hard), pick-up/delivery/both, special requirements with respect to driver or vehicle visiting,... Driver characteristics: hours available, required resting times, ability to drive some vehicles and others not, legal regulations,... Vehicle characteristics: heterogeneous fleet (different types/sizes of vehicles), some vehicles may have multiple compartments for different products, special equipment (some vehicles may have cranes or loading equipment, others not,...), not all vehicles start and/or end at the depot, some vehicles require a special licence, different cost structures,... Route characteristics: travel time may change over time (e.g. longer during rush hours), some vehicles may not be able to traverse certain routes or make certain turns, as a consequence sometimes extra decisions have to be made, for example where to drop off a trailer in order to be able to visit less accessible clients... General characteristics: completely different routing problems (buses, taxis, garbage collector cars, transport of disabled people,...) multiple heterogeneous depots (e.g. carrying different products and having different stock levels for each product), stochasticity, dynamic information, objective function (cost, balance between route lengths),... Moreover, real-life vehicle routing problems are not stand-alone problems, but have an impact on other decisions taken in the company s supply chain. Ideally, the vehicle routing software should be able to assist in taking such decisions as determination of drop size in a VMI environment, trailer drop-off location, driver assignment, etc. Currently, commercial VRP packages rarely provide the necessary tools for making these decisions. In June 2006, ORMS ran a survey of 20 packages for vehicle routing from 17 companies (Hall, 2006). It should be mentioned that this survey presents information provided by the companies, 2

3 Figure 2: A real-life VRP solution 3

4 which may be unverified. The survey underlines the fact that commercial vehicle routing software is used in a large variety of environments and traditionally fulfils a number of different functions: sequencing stops, scheduling stops and assigning stops to drivers. It also discusses several recent developments in commercial VRP software, such as the integration with the company s ERP package and the ability to communicate with the drivers in order to be able to perform last-minute route changes. Unsurprisingly, a conclusion of the survey is that specialization, i.e. gathering experience in a certain sector, may give the software a competitive advantage. Another conclusion is that the size and complexity of real-life routing problems have rendered them intractable to solve using exact methods. Designers of commercial routing packages have therefore resorted to using heuristics. 2 Variable neighbourhood search in commercial VRP applications Variable neighbourhood search (VNS), a recently proposed metaheuristic technique (Mladenović, 1995; Hansen and Mladenović, 1997, 1999) has quickly gained a widespread success and a large number of successful applications have been reported (Hansen and Mladenović, 2001a,b). We should mention that in this paper, we use the term variable neighbourhood search to refer to all local-search based approaches that are based on the principle of systematically exploring more than one type of neighbourhood. Several researchers have applied some form of variable neighbourhood search to (more or less academic) vehicle routing problems. In Cordone and Calvo (2001), a variable neighbourhood search algorithm for the vehicle routing problem with time windows is developed. Crispim and Brandao (2001) present a VNS approach to the vehicle routing problem with backhauls. It should be mentioned that different neighbourhoods are sometimes used without mentioning the term variable neighbourhood search. In Prins (2004), e.g., an evolutionary algorithm is proposed that uses a large number of different neighbourhoods. Although companies developing VRP softwares are understandably reluctant to share the code of their programs, the authors have through informal contact with software developers at several of such companies gained a superficial understanding of the internal workings of such software. Remarkably, a large number of commercial VRP packages (all packages that the authors are aware of) use some form of VNS, i.e. they attempt to improve upon solutions (obtained by initial heuristics) by using a relatively large arsenal of local search improvement heuristics, based around different neighbourhoods. Techniques such as memory structures, random perturbations, let alone complicated operators like crossover or mutation, are hardly ever used. The heuristics uses several type of strategies like for example: Different construction heuristics (savings, clustering,...) Replace/swap one or more stops within one route Replace/swap one or more stops between routes Replace/swap one route or more between vehicles Equalize route lengths... 4

5 2.1 Overcoming the myopic behaviour of a single neigbourhood When watching a local search approach improve upon a VRP solution, it is often remarkable to see how an improvement that is clear upon first sight, is not executed by the metaheuristic or only after several (often random) perturbation moves. Such behaviour is clearly unacceptable for expensive commercial VRP packages: if a dispatcher notices upon first inspection of the solution that the software has missed several important opportunities for improving the solution, confidence in the software will drop considerably. The reason for this is often the fact that the metaheuristic is stuck in a local optimum: the move required to improve the solution cannot be performed and each of the moves in the neighbourhood would lead to a deterioration of the quality. Instead of relying on advanced metaheuristic mechanisms such as random perturbations (iterated local search) or memory structures (tabu search), or crossover and mutation (evolutionary algorithms) variable neighbourhood search proceeds in this case by using a different type of neighbourhood, which might contain the required improving move. This is illustrated in Figure 3. Suppose we are optimizing this simple VRP using a local search algorithm that uses an insert move (i.e. move a customer to another location in the solution). Some investigation shows that this solution cannot be improved by the insert move type. Any solution in the neighbourhood of this one is worse, and therefore the search is stuck in a local optimum. A 2-opt move however (remove two edges and reconnect the solution) has no problems with this solution and will find the much better solution depicted in Fig. 4 in one move. Figure 3: Part of a solution unimprovable by an insert move type Figure 4: The solution improved with a 2-opt move 5

6 2.2 Flexibility and adaptability to different problems Vendors of commercial VRP packages face a number of challenges that are different from the ones faced by academic researchers. One of these is the inability to develop completely new methods each time a new problem is encountered. This would generally require rewriting large portions of the code base of the algorithms used in the software packages for every single customer and would quickly render the operations far less profitable. On the other hand, a black box optimizer that does not take the problem structure into account at all, does not provide the solution quality required. We believe that it is for these reasons that designers of commercial routing packages have opted for an approach that supplies a (relatively large) set of components. These components can generally be divided into two categories: constructive heuristics and improvement heuristics. Whereas the former construct a good initial solution using a heuristic construction rule, the latter use local search to improve upon a solution. Consultants of the software vendor can then use these components to quickly and often effectively create a solution method partially tailored to the specific needs of the company using the software. The way in which these components are combined and exactly how they work is of course specific to the software package, but it can be stated that they all use different neighbourhood structures to search for better solutions and can hence be considered to be variable neighbourhood search. Having a large library of search modules and being able to combine them to suit the needs of the specific client, allows the routing software vendor to adapt to the different environments in which the software may be installed. This includes adapting it to specific constraints or objectives (e.g. some heuristics may perform well if the problem has time windows and otherwise not), but also adapting it to completely different problems, such as school bus routing problems or dynamic routing of ambulances. It is through this process that the program is adapted to the computational resources and required solution times imposed by the customers. Some companies may require their solutions after a few seconds, whereas others require them only after one night of calculation time. The drawback of this approach, however, is that it requires a lot of manual intervention from the part of the software vendor. Adapting the software to the specific requirements of a customer can only be done by skilled consultants, that know both the software and the clients environment very well. 3 Towards adaptive VNS for real-life vehicle routing One of the main problems with the approach described above is that the implementation of a commercial routing package typically requires quite a lot of manual work to be done. In some areas, this situation has dramatically improved over the last few years. Data import and export, for example, are typical areas in which customized modules would be written in order for the routing package to be able to communicate with the clients data warehouse. Recently, however, through increased standardization and the use of XML technologies, data integration has become less of a problem and requires less and less manual intervention. 6

7 An area where there is far less progress is exactly in the mentioned manual tuning of the optimization approach. To date, this step in the roll-out of the software package still needs to be done by expensive consultants. There is a strong need for far more automation in this field, which naturally would require the algorithms to be self-adaptive. It can be envisaged that future implementations of commercial routing packages would include some kind of hyper -algorithm that would tune the configuration of the software before or during the actual optimization. This can be done off-line (using e.g. a set of test data) or on-line (while optimization is going on, using the actual data that is being processed). Ideally, an off-line algorithm that determines the configuration should be able to do this based only on a number of historical data sets, perhaps updated with a prediction of future changes to the data (e.g. expected growth of problem size), and some maximum solution time. Based on this information, the configuration module should be able to determine the ideal configuration to produce a good solution to a problem similar to those in the test set, in a computation time that is within the bounds set by the decision maker. An on-line algorithm can do the same, but should also be capable of updating the configuration while the optimization is running. One can expect on-line algorithms to be useful for settings in which the allowed computation time is rather large (e.g. 12 hours) and off-line algorithms when the allowed computation time is rather small (e.g. a few minutes). Recently, a new type of heuristic coined hyperheuristic has been proposed (Cowling et al., 2001a,b). A hyperheuristic is a high-level heuristic that adaptively controls a set of lower-level heuristics in order to achieve a more robust optimization approach. It is claimed by the authors that a hyperheuristic may approach the speed and solution quality of an approach that uses problem-specific information while only using cheap and easy-to-implement low-level heuristics. The potential of hyperheuristics has yet to be established, but they certainly provide a valuable direction for future research in this area. However, it the authors belief that a high-level approach to determine the configuration of the optimization algorithm must make use of the relationship between the problem structure and the quality of a heuristics optimization strategy. In other words, it is our opinion that a hyperapproach may only work well if there is an understanding of why a certain heuristic works better on a certain problem type than on another one. Armed with this knowledge, a hyperheuristic can then efficiently and effectively determine the optimal configuration of the underlying search heuristics. It can be argued that heuristics has always been a rather empirical research domain and that the quality of a metaheuristic approach has only been judged based on its actual performance on a set of test problems. Recently, some research into the mechanisms that determine the effectiveness of a (meta)heuristic optimization approach, have been undertaken (see e.g. Watson et al. (2006)), but a lot more research is needed in this domain, especially with respect to more complex problems. 4 Conclusions In this paper, we have argued that the fact that all commercial packages for vehicle routing use some form of variable neighbourhood search is due to two factors, both related to the complexity of real-life problems. On the one hand, an approach that uses many neighbourhoods simultaneously may overcome the myopic behaviour of one that uses only a single neighbourhood. Secondly, supplying a large arsenal of local search strategies based on different neighbourhoods allows the consultants of the routing software vendor to flexibly adapt the software to the specific requirements of each client. We have further argued that there is a strong trend towards more 7

8 self-adaptive approaches, that overcome the need for manual parametrization of the software package. A promising research domain is that of hyperheuristics, but a lot more research is needed in this area. References R. Cordone and R.W. Calvo. A heuristic for the vehicle routing problem with time windows. Journal of Heuristics, 7: , P. Cowling, G. Kendall, and E. Soubeiga. A hyperheuristic approach to scheduling a sales summit. In E. Burke and W. Erben, editors, Selected Papers of the Third International Conference on the Practice And Theory of Automated Timetabling PATAT2000, Springer Lecture Notes in Computer Science, pages , 2001a. P. Cowling, G. Kendall, and E. Soubeiga. A parameter-free hyperheuristic for scheduling a sales summit. In MIC2001, pages , Porto, 2001b. J. Crispim and J. Brandao. Reactive tabu search and variable neighborhood descent applied to the vehicle routing problem with backhauls. In MIC2001, pages , Porto, R. Hall. The 2006 vehicle routing survey. ORMS Today, 33(3), June P. Hansen and N. Mladenović. Industrial applications of the variable neighbourhood search metaheuristic. In Decisions and Control in Management Science, pages , Boston, 2001a. Kluwer. P. Hansen and N. Mladenović. Variable neighbourhood search: Principles and applications. European Journal of Operational Research, 130: , 2001b. P. Hansen and N. Mladenović. Variable neighborhood search for the p-median. Location Science, 5: , P. Hansen and N. Mladenović. An introduction to variable neighborhood search. In S. Voss, S. Martello, I. Osman, and C. Roucairol, editors, Metaheuristics: Advances and Trends in Local Search Paradigms for Optimization, pages , Boston, Kluwer. N. Mladenović. A variable neighborhood algorithm - a new metaheuristic for combinatorial optimization. In Abstracts of Papers Presented at Optimization Days, page 112, C. Prins. A simple and effective evolutionary algorithm for the vehicle routing problem. Computers and Operations Research, 31: , J.P. Watson, A.E. Howe, and L.D. Whitley. Deconstructing nowicki and smutnicki s i-tsab tabu search algorithm for the job-shop scheduling problem. Computers and Operations Research, 33: ,