Dynamic Discretization Discovery for Solving the Time-Dependent Traveling Salesman Problem with Time Windows

Abstract

We present a new solution approach for the time-dependent traveling salesman problem with time windows. This problem considers a salesman who departs from his home, has to visit a number of cities within a predetermined period of time, and then, returns home. The problem allows for travel times that can depend on the time of departure. We consider two objectives for the problem: (1) a makespan objective that seeks to return the salesman to his home as early as possible and (2) a duration objective that seeks to minimize the amount of time that he is away from his home. The solution approach is based on an integer programming formulation of the problem on a time-expanded network, because doing so enables time dependencies to be embedded in the definition of the network. However, because such a time-expanded network (and thus, the integer programming formulation) can rapidly become prohibitively large, the solution approach uses a dynamic discretization discovery framework, which has been effective in other contexts. Our computational results indicate that the solution approach outperforms the best-known methods on benchmark instances and is robust with respect to instance parameters.

Applying Metaheuristic for Time-Dependent Traveling Salesman Problem in Postdisaster

“…The direct works to the classic TDTSP provided in [2][3][4][5][6] are divided into two categories: 1) The exact algorithms [3,4,19,22] solve exactly instances with small sizes; 2) Several heuristic or metaheuristic algorithms [2,5,11,18,22,23] can produce good solutions fast for large instances. Moreover, some variants of the classic TDTSP [24,25] are known as the TDTSP Time Windows. The above algorithms are the state-of-the-art algorithms for the variants of the TDTSP.…”

On the impact of spatio-temporal granularity of traffic conditions on the quality of pickup and delivery optimal tours

“…Later on, several approaches have been devised, for example, [17,19,21]. Recently, Vu et al [20] have proposed an approach based on time-expanded networks which outper-6 forms all other ILP approaches for the time-dependent TSP with time windows.…”

“…Experiments reported in [4,5,6,10,12,15,16,17,19,20,21,22] mainly aim at evaluating the efficiency of a new solving approach. In this case, the main performance criterion is the search effort (which is usually measured by means of CPU time) and solutions computed with time-dependent data are usually not compared with solutions computed with constant data.…”

“…State-of-the-art ILP and CP approaches described in Section 2.1 do not scale well when considering instances without time windows. For example, the ILP approach of [20] 4 cannot solve our instances of P 1 (TD-TSP without time windows) within a reasonable amount of time even for small instances with 20 points to visit. Similarly, the CP approach of [18] does not scale well when there are no time window constraints.…”

An efficient parallel genetic algorithm solution for vehicle routing problem in cloud implementation of the intelligent transportation systems

“…Using efficient vehicle routes provides a direct competitive advantage to transportation companies, which usually operate with limited profitability margins. Moreover, the fact that these problems share a simple yet rich structure, generalizing the traveling salesman problem, has helped to elevate the VRP family into one of the main testbed for studies in optimization and heuristics [3,4]. Recently, integration of the traffic management systems (TMSs) with cloud computing paradigm has brought the extensibility and scalability for these systems [5].…”