The problem of mobile sequential recommendation is presented to suggest a route connecting some pick-up points for a taxi driver so that he she is more likely to get passengers with less travel cost. Essentially, a key challenge of this problem is its high computational complexity. In this paper, we propose a dynamical programming based method to solve this problem. Our method consists of two separate stages: an offline pre-processing stage and an online search stage. The offline stage pre-computes optimal potential sequence candidates from a set of pick-up points, and the online stage selects the optimal driving route based on the pre-computed sequences with the current position of an empty taxi. Specifically, for the offline pre-computation, a backward incremental sequence generation algorithm is proposed based on the iterative property of the cost function. Simultaneously, an incremental pruning policy is adopted in the process of sequence generation to reduce the search space of the potential sequences effectively. In addition, a batch pruning algorithm can also be applied to the generated potential sequences to remove the non-optimal ones of a certain length. Since the pruning effect continuously increases with the increase of the sequence length, our method can search the optimal driving route efficiently in the remaining potential sequence candidates. Experimental results on real and synthetic data sets show that the pruning percentage of our method is significantly improved compared to the state-of-the-art methods, which makes our method can be used to handle the problem of mobile sequential recommendation with more pick-up points and to search the optimal driving routes in arbitrary length ranges.
Lu . @cite_8 introduced a problem of finding optimal trip route with time constraint. They also proposed an efficient trip planning method considering the current position of a user. However, their method uses the score of attractions to measure the preference of a route.
@cite_8
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With the rapid development of wireless telecommunication technologies, a number of studies have been done on the Location-Based Services (LBSs) due to wide applications. Among them, one of the active topics is travel recommendation. Most of previous studies focused on recommendations of attractions or trips based on the useri¦s location. However, such recommendation results may not satisfy the travel time constraints of users. Besides, the efficiency of trip planning is sensitive to the scalability of travel regions. In this paper, we propose a novel data mining-based approach, namely Trip-Mine, to efficiently find the optimal trip which satisfies the useri¦s travel time constraint based on the useri¦s location. Furthermore, we propose three optimization mechanisms based on Trip-Mine to further enhance the mining efficiency and memory storage requirement for optimal trip finding. To the best of our knowledge, this is the first work that takes efficient trip planning and travel time constraints into account simultaneously. Finally, we performed extensive experimental evaluations and show that our proposals deliver excellent results. We investigate the exact solution of the vehicle routing problem with time windows, where multiple trips are allowed for the vehicles. In contrast to previous works in the literature, we specifically consider the case in which it is mandatory to visit all customers and there is no limitation on duration. We develop two branch-and-price frameworks based on two set covering formulations: a traditional one where columns (variables) represent routes, that is, a sequence of consecutive trips, and a second one in which columns are single trips. One important difficulty related to the latter is the way mutual temporal exclusion of trips can be handled. It raises the issue of time discretization when solving the pricing problem. Our dynamic programming algorithm is based on concept of groups of labels and representative labels. We provide computational results on modified small-sized instances (25 customers) from Solomon’s benchmarks in order to evaluate and compare the two methods. Results show that some difficult instances are out of reach for the first branch-and-price implementation, while they are consistently solved with the second. The Time Dependent Orienteering Problem with Time Windows (TDOPTW) consists of a set of locations with associated time windows and scores Visiting a location allows to collect its score as a reward Traveling time between locations varies depending on the leave time The objective is to obtain a route that maximizes the obtained score within a limited amount of time In this paper we target the use of public transportation in a city, where users may move on foot or by public transportation The approach can also be applied to the logistic sector, for example to the multimodal freight transportation We apply an hybrid approach to tackle the problem Experimental results for the city of San Sebastian show we are able to obtain valid routes in real-time. The time-dependent orienteering problem is dual to the time-dependent traveling salesman problem. It consists of visiting a maximum number of sites within a given deadline. The traveling time between two sites is in general dependent on the starting time.For any ɛ > 0, we provide a (2 + ɛ)-approximation algorithm for the time-dependent orienteering problem which runs in polynomial time if the ratio between the maximum and minimum traveling time between any two sites is constant. No prior upper approximation bounds were known for this time-dependent problem.