Orienteering Problem With Time Windows Research Articles

Route recombination for deterministic and non-deterministic orienteering problems with time windows: A dynamic programming approach

In this paper, we consider the Orienteering Problem with Time Windows (OPTW) where the goal is to visit customers within available time windows while maximizing the total reward provided by successive customer visits. For this problem, we introduce a new route recombination procedure that takes a set of solutions as input and returns the best combination containing at most k subsequences of customer visits from these solutions. This route recombination procedure is based on a dynamic programming algorithm enhanced with pruning strategies that can significantly reduce the size of the search space. It is also able to deal with time-dependent transition times. The experiments show that the algorithm proposed can be used as a lightweight and efficient post-optimization procedure working on elite solutions provided by a standard incomplete OPTW solver. Moreover, it can be used in a non-deterministic context where the reward values are not precisely known in advance; in this case, OPTW solutions can be first generated for various reward scenarios during an offline phase, and then combined during an online phase to quickly get a high-quality solution given the last-known reward values.

A constraint programming approach for multi-objective tourist trip design problem with mandatory visits: A case study for İzmir Turkey

The Orienteering Problem (OP) is an optimization problem that finds the locations and routes that will return the highest profit/benefit, starting from the initial location of the traveler/vehicle, visiting these locations, and ending with the starting location of the tour within a given time or distance limit. There is no obligation to visit all locations in the problem structure. OP has many real-life applications, such as staff routing and disaster relief routing. In this study, OP with Time Windows (OPTW), an extension of OP, is discussed with hotel selection and mandatory visits. Although the main objective of OPTW is profit maximization, it is also essential to minimize the total travel time to complete the tour efficiently. For this reason, we consider the OPTW as a multi-objective problem. In the problem considered here, it is assumed that the profit/benefit, travel time between locations, service period, and time interval that each location can be visited are determined to be known. Within the scope of the study, first, a Mixed Integer Programming (MIP) model is prepared for the problem. Since the proposed mathematical model does not provide solutions in a reasonable time for large networks, the problem is solved by a Constraint Programming (CP) approach. Attractive tourist points of interest for Izmir, one of Turkey's major tourist cities, are determined, and the proposed method is applied to the real-life problem. The problem is modeled as Multi-Objective OPTW with MIP and CP and solved. Also, sensitivity analysis is performed by considering two different scenarios.

Multi-Objective Trip Planning With Solution Ranking Based on User Preference and Restaurant Selection

The tourist trip design problem (TTDP) helps the trip planners, such as tourists, tour companies, and government agencies, automate their trip planning. TTDP solver chooses and sequences an optimal subset of point of interest (POIs), which adhere to the POIs attributes and tourist preferences, and then generates a travel itinerary that maximizes their pleasure. However, the traditional TTDP does not include the lunch period at a local restaurant, which causes the rest of the itinerary in the afternoon to shift, nor compulsory POIs that the trip planners must be included in the itinerary. Moreover, as tourism contributes to high greenhouse gas emissions, especially from its transportation, minimizing the itinerary’s total distance is also considered. Unfortunately, this objective conflicts with the profit scores; no single itinerary can optimize both objectives simultaneously. Hence, the multi-objective technique and the results of non-dominated itineraries can be organized as a Pareto front. The trip planners can choose one suitable itinerary from the Pareto front based on their preferences. To address these real-world issues, we formulate a new variant of the well-known orienteering problem with time windows (OPTW) called the multi-objective orienteering problem with Time Windows, Restaurant Selection, and Compulsory POIs (MOPTW-RSCP). The proposed problem is provided with a mathematical formulation and two exact algorithms for solving them, i.e., greedy and branch-and-cut Pareto-based techniques. The algorithms’ performance is tested against the Rattanakosin island (the old city of Bangkok) dataset. We conduct 24 test cases, and the computational results confirm the algorithms’ efficiency.

A reinforcement learning approach to the orienteering problem with time windows

The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial optimization has recently shown promising results in dealing with similar problems, like the Travelling Salesman Problem. A neural network allows learning solutions using reinforcement learning or supervised learning, depending on the available data. After the learning stage, it can be generalized and quickly fine-tuned to further improve performance and personalization. The advantages are evident since, for real-world applications, solution quality, personalization, and execution times are all important factors that should be taken into account.This study explores the use of Pointer Network models trained using reinforcement learning to solve the OPTW problem. We propose a modified architecture that leverages Pointer Networks to better address problems related with dynamic time-dependent constraints. Among its various applications, the OPTW can be used to model the Tourist Trip Design Problem (TTDP). We train the Pointer Network with the TTDP problem in mind, by sampling variables that can change across tourists visiting a particular instance-region: starting position, starting time, available time, and the scores given to each point of interest. Once a model-region is trained, it can infer a solution for a particular tourist using beam search. We based the assessment of our approach on several existing benchmark OPTW instances. We show that it generalizes across different tourists that visit each region and that it generally outperforms the most commonly used heuristic, while computing the solution in realistic times.

An Exact Algorithm for Agile Earth Observation Satellite Scheduling with Time-Dependent Profits

The scheduling of an Agile Earth Observation Satellite (AEOS) consists of selecting and scheduling a subset of possible targets for observation in order to maximize the collected profit related to the images while satisfying its operational constraints. In this problem, a set of candidate targets for observation is given, each with a time-dependent profit and a visible time window. The exact profit of a target depends on the start time of its observation, reaching its maximum at the midpoint of its visible time window. This time dependency stems from the fact that the image quality is determined by the look angle between the satellite and the target to be observed. We present an exact algorithm for the single-orbit scheduling for an AEOS considering the time-dependent profits. The algorithm is called Adaptive-directional Dynamic Programming with Decremental State Space Relaxation (ADP-DSSR). This algorithm is based on the dynamic programming approach for the Orienteering Problem with Time Windows (OPTW). Several algorithmic improvements are proposed to address the time-dependent profits. The proposed algorithm is evaluated based on extensive computational tests. The experimental results show that the algorithmic improvements significantly reduce the required computational time. The comparison between the proposed exact algorithm and a state-of-the-art heuristic illustrates that our algorithm can find the optimal solutions for sufficiently large instances within limited computational time. The results also show that our algorithm is capable of efficiently solving benchmark OPTW instances.

Orienteering Problem with Functional Profits for multi-source dynamic path construction.

Orienteering problem (OP) is a routing problem, where the aim is to generate a path through set of nodes, which would maximize total score and would not exceed the budget. In this paper, we present an extension of classic OP—Orienteering Problem with Functional Profits (OPFP), where the score of a specific point depends on its characteristics, position in the route, and other points in the route. For solving OPFP, we developed an open-source framework for solving orienteering problems, which utilizes four core components of OP in its modular architecture. Fully-written in Go programming language our framework can be extended for solving different types of tasks with different algorithms; this was demonstrated by implementation of two popular algorithms for OP solving—Ant Colony Optimization and Recursive Greedy Algorithm. Computational efficiency of the framework was shown through solving four well-known OP types: classic Orienteering Problem (OP), Orienteering Problem with Compulsory Vertices (OPCV), Orienteering Problem with Time Windows (OPTW), and Time Dependent Orienteering Problem (TDOP) along with OPFP. Experiments were conducted on a large multi-source dataset for Saint Petersburg, Russia, containing data from Instagram, TripAdvisor, Foursquare and official touristic website. Our framework is able to construct touristic paths for different OP types within few seconds using dataset with thousands of points of interest.

Tourism Route Planning Route Based on Tourist Category using Orientee ring Problem with Time Windows

Indonesia has a large number of favorable tourism destinations, for example like Besuki in East Java that has some potential tourist attractions. The complexity to plan a tourism travel routes for particular tourist category become a problem. Hence, travel recommendations for tourists are required. To solve this problem, the first step is accumulating data from questionnaires, Google Map, TripAdvisor, and website of the Tourism Office in Besuki. The questionnaires were distributed to respondents with dominant age between 15-24 years (60%) and most of them were students (44%). Most respondents were single (74%) and traveling with their family (52%). Using LINGO, model Orienteering Problem with Time Windows (OPTW) with objective function is maximizing scores and having restrictions in opening and closing hours of each tourist attractions. The database that required are opening and closing hours, the distance between tourist attractions, and maximum tourist’s hours per day. Score for each tourist attraction and service time will be taken from each tourist category. There are 3 tourists’ categories such as Simplicity Searchers (42%), Cultural Purists (34%), and Reward Hunters (24%). Eventhough there is no significant difference among service time for all categories, the median service time will give different results in total score and routes.

Bi-objective orienteering for personal activity scheduling

We propose and solve a rich, bi-objective extension of the orienteering problem with time windows (OPTW) to model a combined routing and scheduling problem. Our research is motivated by the problem faced by mobile freelancers who have to integrate irregular appointments and tasks into their daily routines. Those people have a number of tasks which they need to perform at various locations (e.g. meetings with different clients), subject to varying time constraints (e.g. opening hours), and with different levels of importance or urgency (e.g. submitting a deliverable versus cleaning the home office). Furthermore, sets of related tasks may be subject to precedence relations and time dependencies. We explicitly consider the trade-off between planning more tasks and enjoying more free time by means of a bi-objective model. The extension of the OPTW and the bi-objective formulation result in the Personal Planning Problem (PPP). We present a mathematical formulation of the PPP and a metaheuristic based on Large Neighborhood Search (LNS) is developed to generate a set of non-dominated solutions to the problem. Solution quality is analyzed on real-world-inspired test instances. Exact reference sets based on a linear single-commodity flow model are used as benchmarks. Extensive computational experiments show that the proposed metaheuristic generates near-optimal solution sets and scales well to larger instances.

Iterated local search algorithm for solving the orienteering problem with soft time windows.

In this paper we study the orienteering problem with time windows (OPTW) and the impact of relaxing the time windows on the profit collected by the vehicle. The way of relaxing time windows adopted in the orienteering problem with soft time windows (OPSTW) that we study in this research is a late service relaxation that allows linearly penalized late services to customers. We solve this problem heuristically by considering a hybrid iterated local search. The results of the computational study show that the proposed approach is able to achieve promising solutions on the OPTW test instances available in the literature, one new best solution is found. On the newly generated test instances of the OPSTW, the results show that the profit collected by the OPSTW is better than the profit collected by the OPTW.

Solving the Orienteering Problem with Time Windows via the Pulse Framework

The Orienteering Problem with Time Windows (OPTW) is the problem of finding a path that maximizes the profit available at the nodes in a time-constrained network. The OPTW has multiple applications in transportation, telecommunications, and scheduling. First, we extend an exact method for shortest path problems with side constraints into a general-purpose framework for hard shortest path variants. Then, using this framework, we develop a new method for the OPTW that incorporates problem-specific knowledge. Our method outperforms the state-of-the-art algorithm on instances derived from benchmark datasets from the literature achieving speedups of up to 266 times and is able to find optimal solutions to large-scale problems with up to 562 nodes in short computational times.

Genetic Algorithm with Path Relinking for the Orienteering Problem with Time Windows

The Orienteering Problem with Time Windows (OPTW) is an optimisation NP-hard problem. This paper proposes a hybrid genetic algorithm (GAPR) for approximating a solution to the OPTW. Instead of a crossover we use a path relinking (PR) strategy as a form of intensification solution. PR generates a new solution by exploring trajectories between two random solutions: genes not present in one solution are included in the other one. Experiments performed on popular benchmark instances show that the proposed GAPR gives good quality solutions using short computing times. Moreover, GAPR gives new best solutions for some test instances.

Addendum to “Heuristics for the multi-period orienteering problem with multiple time windows”

This is an addendum to the paper by Tricoire et al. on various orienteering problems [1]. We present experimental results on the orienteering problem with time windows (OPTW) and team orienteering problem with time windows (TOPTW) test instances introduced by Montemanni et al. [2].

Decremental state space relaxation strategies and initialization heuristics for solving the Orienteering Problem with Time Windows with dynamic programming

We present an exact optimization algorithm for the Orienteering Problem with Time Windows (OPTW). The algorithm is based on bi-directional and bounded dynamic programming with decremental state space relaxation. We compare different strategies proposed in the literature to guide decremental state space relaxation: our experiments on instances derived from the literature show that there is no dominance between these strategies. We also propose a new heuristic technique to initialize the critical vertex set and we provide experimental evidence of its effectiveness.