This chapter concerns a heuristic algorithm for solving the dynamic CARP. It begins by describing main components of a dynamic CARP solver, including an update schedule, how the current state of the problem can be determined, a method of integrating new tasks into the solution, and a heuristic algorithm for improving the solution, which in this thesis is based on tabu search. The purpose of this chapter is to investigate how the performance of a heuristic algorithm for solving the dynamic CARP can be affected by adjusting its configuration. In particular, here we consider adjusting 3 components of the solver: a maximum iteration limit for tabu search in each update, the frequency of solution updates, and a method of integrating new tasks to an existing solution. A novel analysis is conducted to compare several options of these components and to investigate how each of the components could affect the solution quality with respect to total distance and service completion time. Regarding the maximum iteration limit, experiment results show that increasing the maximum iteration limit for tabu search in each update yields little improvement. Moreover, a larger maximum iteration limit could sometimes give worse results. This suggests that to consistently achieve a better solution in the dynamic CARP, it is not sufficient to rely solely on running the tabu search algorithm at each update for
5Figure B.7 contains the same information as Figure 4.4(b) and Figure 4.6(b) but is organised
more iterations. This suggests the need to improve the dynamic CARP solver by other means.
Two ways of amending the dynamic CARP are then investigated: adjusting the frequency of solution updates and the way of integrating new tasks to the solution in each update. Here we consider 3 regular update schedules (with 5, 10, and 20 update) and 2 methods of integrating new tasks. In the existing literature, the problem at each update is usually solved from scratch, which we call here the Reconstruction method. Based on the intuition that solutions from previous updates are likely to contain some promising features as they have undergone the tabu search process, an alternative way of integrating new tasks is proposed, namely the Random Insertion method, which retains a solution from a preceding update and inserts new tasks to the solution in a greedy way before it is further improved by tabu search. Computational results show that the effect of adjusting the frequency of solution updates and the way of integrating new tasks to the solution in each update varies with the degree of dynamism, i.e. the ratio of the number of dynamic tasks (known after vehicles leave the depot at the beginning of the planning horizon) to the number of all tasks in the whole the planning horizon.
More precisely, for relatively low degrees of dynamism (up to 0.4 for the instances considered here), a more frequent update schedule tends to give better results,
regardless of the method of integrating new tasks. Nevertheless, the Random
Insertion method yields more promising results than the Reconstruction method. In contrast, for relatively high degrees of dynamism (at least 0.5 for the instances considered here), the performance of different update schedules depends on the method of integrating new tasks. With the Reconstruction method, a less frequent update schedule tends to give better results. In contrast, with the Random Insertion method, a more frequent update schedule tends to give better results.
Among all variants of the dynamic CARP solver considered, the Random Insertion method with 20 updates give the best results; it is significantly better than the other variants in many cases (see Tables B.1 and B.2). This highlights the benefit of retaining solutions from previous updates as opposed to solving the problem at each update from scratch.
In the next chapter, we will attempt to improve dynamic CARP solutions by means of waiting strategies. The goal will be to further reduce total distance while avoiding an overly large increase in service completion time.
Waiting Strategies
5.1
Introduction
Recall that the dynamic CARP can be viewed as a sequence of static CARPs, each of which occurs at a certain time in the planning horizon. Given that the dynamic CARP involves the notion of time, focussing solely on developing an algorithm for finding a solution to the static CARP in each update would limit the capability of a route planner to amend vehicle routes for the overarching dynamic CARP. In Chapter 4, we attempted to exploit the notion of time in the dynamic CARP by means of varying the frequency of solution updates. This chapter further explores ways of exploiting the notion of time and anticipating changes that can occur at a later time to improve the dynamic CARP solution.
One way of exploiting the notion of time is to instruct vehicles to wait and stand by at certain locations, especially when they finish servicing all tasks that have been assigned to them. Without waiting instructions, the problem at each update would largely depend on the solution from the previous update. In particular, the positions of vehicles at a given update are solely determined by that solution. The dynamic CARP solver in Chapter 4 amends the solution in each update using only available information in that update, and thus it cannot be guaranteed that the positions of vehicles, or other solution features, will still be favourable in the current state of the problem. Utilising waiting instructions gives a route planner more control over the locations at which the vehicles will be, or the current state of the problem in general, at the upcoming update. This allows more possibilities of amending the solution and potentially improves effectiveness of route planning in the dynamic CARP.
Section 5.2 discusses possible undesirable features in the solution without waiting and proposes a waiting strategy that can prevent such features. Section 5.3 proposes a way to amend the waiting strategy by specifying a rule to decide which vehicle should wait based on its current capacity. Section 5.4 proposes another waiting strategy which is focussed specifically on the positions of vehicles. Section 5.5 introduces the idea of employing extra routes as a way of anticipating new tasks in the future. The conclusions of this chapter are given in Section 5.6.