Time-dependent Traveling Salesman Problem Research Articles

Exact and anytime approach for solving the time dependent traveling salesman problem with time windows

The Time Dependent (TD) Traveling Salesman Problem (TSP) is a generalization of the TSP which allows one to take traffic conditions into account when planning tours in an urban context, by making the travel time between locations dependent on the departure time instead of being constant. The TD-TSPTW further generalizes this problem by adding Time Window constraints. Existing exact approaches such as Integer Linear Programming and Dynamic Programming usually do not scale well. We therefore introduce a new exact approach based on an anytime extension of A*. We combine this approach with local search, to converge faster towards better solutions, and bounding and time window constraint propagation, to prune parts of the state space. We experimentally compare our approach with state-of-the-art approaches on both TD-TSPTW and TSPTW benchmarks.

Active Debris Removal Mission Planning Method Based on Machine Learning

To prevent the proliferation of space debris and stabilize the space environment, active debris removal (ADR) has increasingly gained public concern. Considering the complexity of space operations and the viability of ADR missions, it would be necessary to schedule the ADR process in order to remove as much debris as possible. This paper presents an active debris removal mission planning problem, devoted to generate an optimal debris removal plan to guide the mission process. According to the problem characteristics, a two-layer time-dependent traveling salesman problem(TSP) mathematical model is established, involving the debris removal sequence planning and the transfer trajectory planning. Subsequently, two main novel methods based on machine learning are proposed for the ADR mission planning problem, including a deep neural networks(DNN)-based estimation method for approximating the optimal velocity increments of perturbed multiple-impulse rendezvous and an reinforcement learning(RL)-based method for optimizing the sequence of debris removal and rendezvous time. Experimental results of different simulation scenarios have verified the effectiveness and superiority of the proposed method, indicating the good performance for solving the active debris removal mission planning problem.

Learned Upper Bounds for the Time-Dependent Travelling Salesman Problem

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to define tight upper bounds for this problem by reusing the information gained when solving instances with similar features. This is customary in distribution management, where vehicle routes have to be generated over and over again with similar input data. To this aim, we devise an upper bounding technique based on the solution of a classical (and simpler) time-independent Asymmetric Travelling Salesman Problem, where the constant arc costs are suitably defined by the combined use of a Linear Program and a mix of unsupervised and supervised Machine Learning techniques. The effectiveness of this approach has been assessed through a computational campaign on the real travel time functions of two European cities: Paris and London. The overall average gap between our heuristic and the best-known solutions is about 0.001\%. For 31 instances, new best solutions have been obtained.

Optimizing travel routes using temporal networks constructed from global positioning system data in kyoto tourism

Owing to the complexity of urban transportation networks and temporal changes in traffic conditions, the assessment of real-time traffic situations is a challenge. However, the development of mobile information devices using the global positioning system (GPS) has made it easier to obtain personal mobility information. In this study, we developed a method for evaluating the mobility of people in a city using GPS data. We applied two methods: evaluating human mobility using temporal networks constructed from GPS data, and searching for the shortest path by constructing and solving the time-dependent traveling salesman problem (TDTSP). The estimation is expected to be more realistic if transportation delays from congestion are considered. This study makes two major contributions. First, we propose a new method for estimating the time weights of edges in temporal networks using probability density functions for the travel time. Second, to apply ant colony optimization to the TDTSP, we propose a new method for estimating the congestion level from GPS data and calculating the transition probability using the estimated congestion level. As a case study, we conducted a human mobility analysis in Kyoto City.

Dynamic Programming for the Time-Dependent Traveling Salesman Problem with Time Windows

The time-dependent traveling salesman problem with time windows (TDTSPTW) is a variant of the well-known traveling salesman problem with time windows, in which travel times are not assumed to be constant. The TDTSPTW accounts for the effects of congestion at the planning level, being particularly suited for distribution problems in large cities. In this paper we develop a labeling-based algorithm for the TDTSPTW that incorporates partial dominance and generalizes several state-of-the-art components from the time-independent related literature. We propose a framework general enough to be applied to the TDTSPTW and its variant without time windows, with the objective of minimizing the duration or the makespan. As part of the framework, we introduce a new state-space relaxation specifically designed for the time-dependent context. Extensive computational experiments show the effectiveness of the overall approach and the impact of the new relaxation, outperforming several recent algorithms proposed for these variants on more than 9,000 benchmark instances. In addition, we frame the minimum tour duration problem within the time-dependent literature and include it as a benchmark for our algorithm, obtaining improved computation times and 31 new optimal solutions. Summary of Contribution: In this paper, we study the time-dependent traveling salesman problem with time windows (TDTSPTW), a difficult single-vehicle routing problem that incorporates more realistic travel time functions than its classic time-independent counterpart. As a result, the TDTSPTW is harder to solve, as it requires more complex models and algorithms. Using state-of-the-art optimization techniques, we propose an efficient solution approach for the TDTSPTW and some related variants that outperforms the previous approaches in the literature. Our paper emphasizes the importance of algorithmic design and efficient implementations to tackle relevant practical combinatorial optimization problems—in particular, for time-dependent problems. Moreover, the resulting algorithm fosters a new research direction regarding exact algorithms for time-dependent problems using dynamic programming and relaxation techniques. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research has been funded by Fondo para la Investigación Científica y Tecnológica (FONCyT) [Grants PICT-2016-2677 and PICT-2018-2961] from the Ministry of Science, Argentina, and by the Google Latin America Research Award (LARA) 2019. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1236 .

Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery

In this paper, we present exact methods for solving the Time Dependent Minimum Tour Duration Problem (TD-MTDP) and the Time Dependent Delivery Man Problem (TD-DMP). Both methods are based on a Dynamic Discretization Discovery (DDD) approach for solving the Time Dependent Traveling Salesman Problem with Time Windows (TD-TSPTW). Unlike the TD-TSPTW, these problems involve objective functions that depend in part on the time at which the vehicle departs the depot. As such, optimizing these problems adds a scheduling dimension to the problem. We present multiple enhancements to the DDD method, including enabling it to dynamically determine which waiting opportunities at the depot to model. With an extensive computational study we demonstrate that the resulting methods outperform all known methods for both the TD-MTDP and TD-DMP on instances taken from the literature.

Timeline Club: An optimization algorithm for solving multiple debris removal missions of the time-dependent traveling salesman problem model

Timeline Club: An optimization algorithm for solving multiple debris removal missions of the time-dependent traveling salesman problem model

Dynamic Shortest Paths Methods for the Time-Dependent TSP

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

Applying Metaheuristic for Time-Dependent Traveling Salesman Problem in Postdisaster

Applying Metaheuristic for Time-Dependent Traveling Salesman Problem in Postdisaster

Lifting the Performance of a Heuristic for the Time-Dependent Travelling Salesman Problem through Machine Learning

In recent years, there have been several attempts to use machine learning techniques to improve the performance of exact and approximate optimization algorithms. Along this line of research, the present paper shows how supervised and unsupervised techniques can be used to improve the quality of the solutions generated by a heuristic for the Time-Dependent Travelling Salesman Problem with no increased computing time. This can be useful in a real-time setting where a speed update (or the arrival of a new customer request) may lead to the reoptimization of the planned route. The main contribution of this work is to show how to reuse the information gained in those settings in which instances with similar features have to be solved over and over again, as it is customary in distribution management. We use a method based on the nearest neighbor procedure (supervised learning) and the K-means algorithm with the Euclidean distance (unsupervised learning). In order to show the effectiveness of this approach, the computational experiments have been carried out for the dataset generated based on the real travel time functions of two European cities: Paris and London. The overall average improvement of our heuristic over the classical nearest neighbor procedure is about 5% for London, and about 4% for Paris.

The hybridization of ACO + GA and RVNS algorithm for solving the time-dependent traveling salesman problem

The time-dependent traveling salesman problem is a class of combinatorial optimization problems. Naturally, metaheuristic is a suitable approach to solve the problem with large sizes in short computation time. Previously, several metaheuristics have been proposed for solving the problem. These algorithms might have a strong search intensification, and their diversification mechanisms may not be sufficient. Due to the random nature, population-based algorithms improve on the chance of finding a globally. In this paper, we propose a population-based algorithm that combines an ant colony algorithm (ACO), genetic algorithm (GA), and neighborhood descent with random neighborhood ordering (RVND). In the algorithm, the ACO and GA are used to explore the promising solution areas that are yet to refined while the RVND exploits them with the hope of improving a solution. Therefore, our metaheuristic algorithm balances between exploration and exploitation. Extensive numerical experiments and comparisons with the state-of-the-art metaheuristic algorithms in the literature show that the proposed algorithm reaches better solutions in many cases.

Optimization of the Time-Dependent Traveling Salesman Problem Using Interval-Valued Intuitionistic Fuzzy Sets

This study proposes a new model and approach for solving a realistic extension of the Time-Dependent Traveling Salesman Problem, by using the concept of distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interval-valued fuzzy degree repository based on the relations between rush hour periods and traffic regions in the “city center areas”, and then we utilized the interval-valued intuitionistic fuzzy weighted arithmetic average to aggregate fuzzy information to be able to quantify the delay in any given trip between two nodes (cities). The proposed method is illustrated by a simple numerical example.

Intuitionistic fuzzy rule-base model for the time dependent traveling salesman problem

Intuitionistic fuzzy rule-base model for the time dependent traveling salesman problem

An enhanced lower bound for the Time-Dependent Travelling Salesman Problem

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem amounts to find a Hamiltonian tour of least total duration. In this paper we exploit a new degree of freedom in the Cordeau et al. (2014) speed decomposition. This approach results in a parameterized family of lower bounds. The parameters are chosen by fitting the traffic data. The first model is nonlinear and difficult to solve. Hence, we devise a linearization which gives rise to a compact Mixed Integer Linear Programming model. Then, we develop an optimality condition which allows to further reduce the size of the model. Computational results show that, when embedded into a branch-and-bound procedure, this lower bounding mechanism allows to solve to optimality a larger number of instances than state-of-the-art algorithms.

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

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.

A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints

In this paper we study the time-dependent profitable tour problem with resource constraints (TDPTPRC), a generalization of the profitable tour problem (PTP) which includes variable travel times to account for road congestion. In this problem, the set of customers to be served is not given and must be determined based on the profit collected when visited, keeping a balance with the total travel time. We propose a mixed integer linear programming (MILP) formulation that exploits the travel time function to reduce the size of a standard formulation from the literature. We derive four new families of valid inequalities and study the connections among them, as well as their associated separation problems. We develop a tailored Branch and Cut (BC) algorithm including these new families in addition to some well known valid inequalities from related problems. Computational results on four different problems, with alternative resources and objectives, show that the approach is flexible and effective. The algorithm achieves significant reductions in the computing times on benchmark instances from the related literature, and outperforms a recent method proposed for the time-dependent traveling salesman problem with time windows.

An efficient two-phase metaheuristic algorithm for the time dependent traveling Salesman problem

The Time Dependent Traveling Salesman Problem (TDTSP) is a class of NP-hard combinatorial optimization problems which has many practical applications. To the best of our knowledge, developing metaheuristic algorithm for the problem has not been studied much before, even though it is a natural and general extension of the Minimum Latency Problem (MLP) or Traveling Salesman Problem (TSP). In this paper, we propose an effective two-phase metaheuristic which combines the Insertion Heuristic (IH), Variable Neighborhood Search (VNS) and the tabu search (TS) to solve the problem. In a construction phase, the IH is used to create an initial solution that is good enough. In an improvement phase, the VNS is employed to generate diverse and various neighborhoods, while the main attribute of tabu search is to prohibit our algorithm from getting trapped into cycles, and to guide the search to escape local optima. Moreover, we introduce a novel neighborhoods’ structure in VNS and present a O(1) operation for calculating the cost of each neighboring solution in a special case of TDTSP where the TDTSP becomes the MLP. Extensive computational experiments on 355 benchmark instances show that our algorithm can find the optimal solutions for small instances with up to 100 vertices in a reasonable amount of time. For larger instances, our algorithm obtains the new best solutions in comparison with the state-of-the-art algorithm solutions.

A biobjective branch and bound procedure for planning spatial missions

More than 90% of the space objects orbiting around the earth are space debris. Since the orbits of these debris often overlap the trajectories of spacecraft, they create a potential collision risk. The problem of removing the most dangerous space debris can be modeled as a biobjective time dependent traveling salesman problem (BiTDTSP). In this paper, we study an approach based on a branch and bound procedure to determine the Pareto frontier of the BiTDTSP.

An integer programming approach for the time-dependent traveling salesman problem with time windows

Congestion in large cities and populated areas is one of the major challenges in urban logistics, and should be addressed at different planning and operational levels. The Time Dependent Travelling Salesman Problem (TDTSP) is a generalization of the well known Traveling Salesman Problem (TSP) where the travel times are not assumed to be constant along the day. The motivation to consider the time dependency factor is that it enables to have better approximations to many problems arising from practice. In this paper, we consider the Time-Dependent Traveling Salesman Problem with Time Windows (TDTSP-TW), where the time dependence is captured by considering variable average travel speeds. We propose an Integer Linear Programming model for the problem and develop an exact algorithm, which is compared on benchmark instances with another approach from the related literature. The results show that the approach is able to solve instances with up to 40 customers.

Can the Agent with Limited Information Solve Travelling Salesman Problem?

Here, we develop new heuristic algorithm for solving TSP (Travelling Salesman Problem). In our proposed algorithm, the agent cannot estimate tour lengths but detect only a few neighbor sites. Under the circumstances, the agent occasionally ignores the NN method (choosing the nearest site from current site) and chooses the other site far from current site. It is dependent on relative distances between the nearest site and the other site. Our algorithm performs well in symmetric TSP and asymmetric TSP (time-dependent TSP) conditions compared with the NN algorithm using some TSP benchmark datasets from the TSPLIB. Here, symmetric TSP means common TSP, where costs between sites are symmetric and time-homogeneous. On the other hand, asymmetric TSP means TSP where costs between sites are time-inhomogeneous. Furthermore, the agent exhibits critical properties in some benchmark data. These results suggest that the agent performs adaptive travel using limited information. Our results might be applicable to nonclairvoyant optimization problems.