Selective Traveling Salesman Problem Research Articles

Arrival and service time dependencies in the single- and multi-visit selective traveling salesman problem

We analyze several time dependency issues for the selective traveling salesman problem with time-dependent profits. Specifically, we consider the case in which the profit collected at a vertex depends on the service time, understood as the time spent at this vertex, and when the service time at each vertex depends on the arrival time at the vertex. For each of these two cases, we formulate two continuous-time problems: (i) a vertex can be visited at most once, and (ii) vertices may be visited more than once. In each case, we consider general profit functions at the vertices, i.e., the profit functions are not limited to monotonic functions of time. We also formulate the problems as discrete-time problems using appropriate variants of an auxiliary time-extended graph, and we solve them with Gurobi. We apply our methodology to two sets of instances. First, we use a set of artificial instances to illustrate the main differences amongst the different versions of the problem. We then solve several instances adapted from TSPLIB to evaluate the computational capabilities of the methodology.

Analysis of the selective traveling salesman problem with time-dependent profits

We consider a generalization of the selective traveling salesman problem (STSP) in which the benefit of visiting a location changes over time. This new problem, called the selective travelling salesman problem with time-dependent profits (STSP-TDP), is defined on a graph with time-dependent profits associated with the vertices, and consists of determining a circuit of maximal total profit. In the STSP-TDP the tour length must not exceed a maximum value, and its starting and ending times must both lie within a prespecified planning horizon. This problem arises in planning tourist itineraries, mailbox collection, military surveillance, and water sampling, where the traveler accumulates different profits upon visiting the locations throughout the day. We focus on analyzing several variants of the problem depending on the shape of the time-dependent profit function. If this function is not monotonic, it may be worth visiting a site more than once. We propose formulations for the single-visit case and for when multiple visits are allowed, in which case the problem reduces to an STSP, which is adapted to be solved as a longest path problem. These formulations are then solved for piecewise-linear profit functions using a general-purpose solver, and tested on several artificially created instances and on four TSPLib instances involving up to 535 vertices. A detailed analysis of the problem and the solution is performed.

The selective traveling salesman problem with draft limits

This paper introduces the selective traveling salesman problem with draft limits, an extension of the traveling salesman problem with draft limits, wherein the goal is to design a maximum profit tour respecting draft limit constraints at the visited nodes. We propose a mixed integer linear programming (MILP) formulation for this problem. This MILP model is used to solve—to optimality—small size instances and to assess the quality of solutions obtained using a general variable neighborhood search heuristic that explores several neighborhood structures. Our extensive computational experiments confirm the efficiency of the method and the quality of the reported solutions.

A non-assignment problem-based formulation for the asymmetric travelling salesman problem and its variation

In this paper, an exact formulation for the asymmetric travelling salesman problem (ATSP) is presented by approaching it as a single commodity flow problem. This approach is different from existing exact formulations in the literature which are based on the assignment problem (AP), thus, it resolves issues that the AP-based formulations pose for solving certain real world instances by standard integer programming methods such as branch and bound. Moreover, in our computational experiments, half of the total computational time is expended to find the first feasible solution, then it is converged quickly to optimality. In contrast, the AP-based models rapidly computed an initial feasible solution but showed slow convergence to the optimum. Moreover, it is extendable to other variations of the travelling salesman problem (TSP) such as the multiple TSP and the selective TSP.

Review of routing problems with uncertain factors

Routing problems is used to find an optimal path from the starting point to the target point There are some problems with traditional path planning problem For example before the path planning path planning personnel cannot fully grasp all the relevant information about path planning some information may be unknown vague or uncertain After the path planning partial information may change in the process of actual transportation such as vehicle traffic time customer demand etc So uncertain path problem is more meaningful in practical application In this paper different path planning algorithm with uncertain factors was summarized by Probabilistic Travelling Salesman Problem PTSP and Selective Traveling Salesman Problem STSP and their advantages were analyzed and compared

The selective Traveling Salesman Problem with emission allocation rules

The paper introduces the selective Traveling Salesman Problem with emission allocation rules (sTSP-EA). This is to select a subset of transport requests from the set of requests given to a carrier, and find a corresponding route such that the transport emission allocatable to one particular request takes a minimum consistent with the emission reporting standard EN 16258. The sTSP-EA is relevant for collaborating shippers who consolidate their shipments and thus need to allocate the total emission caused by a transport process to the shipments moved in the process. A mixed-integer linear optimization model is presented for the problem. Since only small-sized instances can be solved this way, a Large Neighborhood Search heuristic is proposed for the sTSP-EA and tested in a comprehensive computational study.

New Formulations for the Team Orienteering Problem

Routing problems have many practical applications in distribution and logistics management. The Traveling Salesman Problem (TSP) and its variants lie at the heart of routing problems. The Orienteering Problem (OP) is a subset selection version of well-known TSP which comes from an outdoor sport played on mountains. In the OP, the traveller must finish its journey within a predetermined time (cost, distance), and gets a gain (profit, reward) from the visited nodes. The objective is to maximize the total gain that the traveller collects during the predetermined time. The OP is also named as the selective TSP since not all cities have to be visited. The Team Orienteering Problem (TOP) is the extension of OP by multiple-traveller. As far as we know, there exist a few formulations for the TOP. In this paper we present two new integer linear programming formulations (ILPFs) for the TOP with O(n2) binary variables and O(n2) constraints, where n is the number of nodes on the underlying graph. The proposed formulations can be directly used for the OP when we take the number of traveller as one. We demonstrate that, additional restrictions and/or side conditions can be easily imported for both of the formulations. The performance of our formulations is tested on the benchmark instances from the literature. The benchmark instances are solved via CPLEX 12.6 by using the proposed and existing formulations. The computational experiments demonstrate that both of the new formulations outperform the existing one. The new formulations are capable of solving optimally most of the benchmark instances, which have solved by using special heuristics so far. As a result, the proposed formulations can be used to find the optimal solution of small- and moderate-size real life OP and TOP by using an optimizer.
 
 Keywords: Traveling salesman problem, orienteering problem, modeling;

New Formulations for the Orienteering Problem

Abstract Problems associated with determining optimal routes from one or several depots (origin, home city) to a set of nodes (vertices, cities, customers, locations) are known as routing problems. The Traveling Salesman Problem (TSP) lies at the heart of routing problems. One of the new variants of the TSP is named as TSP with Profits where the traveler must finish its journey within a predetermined time (cost, distance), by optimizing given objective. In this variant of TSP, all cities ought to not to be visited. The Orienteering Problem (OP) is the most studied case of TSP with Profits which comes from an outdoor sport played on mountains. In OP, traveler gets a gain (profit, reward) from the visited node and the objective is to maximize the total gain that the traveler collects during the predetermined time. The OP is also named as selective TSP. In this paper, we present two polynomial size formulations for OP. The performance of our proposed formulations is tested on benchmark instances. We solved the benchmark problems from the literature via CPLEX 12.5 by using the proposed formulations and existing formulation. The computational experiments demonstrate that; (1) both of the new formulations over estimates the existing one; and (2) the proposed formulations are capable of solving all the benchmark instances that were solved by using special heuristics so far.

A new approach to treat the selective travelling salesman problem

A new approach to treat the selective travelling salesman problem

GRASP with path relinking for the orienteering problem

In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.

A location-routing problem in glass recycling

In this study, a location-routing problem encountered in glass recycling is addressed. We formulate a combined maximal covering location problem in the presence of partial coverage and selective traveling salesman problem to determine the location of bottle banks and the route of a collecting vehicle that will daily visit a number of customers and the bottle banks. We propose a nested heuristic procedure to solve the problem. The outer loop of the heuristic is based on variable neighborhood search while the inner loop solves the traveling salesman problem on the locations defined. The performance of the heuristic procedure is demonstrated with computational experimentation on instances that are both randomly generated and are taken from the literature. An application of the procedure on a case study using a geographical information system is also reported.

The Clustered Orienteering Problem

In this paper we study a generalization of the Orienteering Problem (OP) which we call the Clustered Orienteering Problem (COP). The OP, also known as the Selective Traveling Salesman Problem, is a problem where a set of potential customers is given and a profit is associated with the service of each customer. A single vehicle is available to serve the customers. The objective is to find the vehicle route that maximizes the total collected profit in such a way that the duration of the route does not exceed a given threshold. In the COP, customers are grouped in clusters. A profit is associated with each cluster and is gained only if all customers belonging to the cluster are served. We propose two solution approaches for the COP: an exact and a heuristic one. The exact approach is a branch-and-cut while the heuristic approach is a tabu search. Computational results on a set of randomly generated instances are provided to show the efficiency and effectiveness of both approaches.

A model for fisheries patrol dispatch in the Canadian Atlantic offshore fishery

Fisheries patrol routing involves routing a patrol vessel over a network of fishing grounds to maximize the deterrent effect of the patrol subject to trip length or budget constraints. This paper develops a prescriptive model for routing a multi-unit surveillance fleet through a set of fish stocks in the Canadian Atlantic offshore groundfish fishery. The decision problem is formulated as a 0–1 integer-programming model which is related to the well-known selective traveling salesman problem. In the fisheries patrol problem, the fishing grounds represent the cities, and all or a subset of grounds is visited on a given trip. We offer an efficient formulation and solution approach to the problem. Computational results for a hypothetical but realistic problem setting are provided.

Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers...

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

This paper considers the Cardinality Constrained Quadratic Knapsack Problem (QKP) and the Quadratic Selective Travelling Salesman Problem (QSTSP). The QKP is a generalization of the Knapsack Problem and the QSTSP is a generalization of the Travelling Salesman Problem. Thus, both problems are NP hard. The QSTSP and the QKP can be solved using branch-and-cut methods. Good bounds can be obtained if strong constraints are used. Hence it is important to identify strong or even facet-defining constraints. This paper studies the polyhedral combinatorics of the QSTSP and the QKP, i.e. amongst others we identify facet-defining constraints for the QSTSP and the QKP, and provide mathematical proofs that they do indeed define facets.

A branch-and-cut algorithm for the undirected selective traveling salesman problem

The Selective Traveling Salesman Problem (STSP) is defined on a graph in which profits are associated with vertices and costs are associated with edges. Some vertices are compulsory. The aim is to construct a tour of maximal profit including all compulsory vertices and whose cost does not exceed a preset constant. We developed several classes of valid inequalities for the symmetric STSP and used them in a branch-and-cut algorithm. Depending on problem parameters, the proposed algorithm can solve instances involving up to 300 vertices. q 1998 John Wiley & Sons, Inc. Networks 32: 263-273, 1998

A branch‐and‐cut algorithm for the undirected selective traveling salesman problem

A branch‐and‐cut algorithm for the undirected selective traveling salesman problem

A tabu search heuristic for the undirected selective travelling salesman problem

The undirected Selective Travelling Salesman Problem (STSP) is defined on a graph G=(V, E) with positive profits associated with vertices, and distances associated with edges. The STSP consists of determining a maximal profit Hamiltonian cycle over a subset of V whose length does not exceed a preset limit L. We describe a tabu search (TS) heuristic for this problem. The algorithm iteratively inserts clusters of vertices in the current tour or removes a chain of vertices. Tests performed on randomly generated instances with up to 300 vertices show that the algorithm consistently yields near-optimal solutions.

Sequencing by Hybridization with Positive Faults.

The paper is concerned with a computational phase of the sequencing DNA chains by hybridization. It is assumed that positive faults can occur in the hybridization experiment. An approach based on a reduction of the problem to a variant of a Selective Traveling Salesman Problem and an algorithm for solving the latter, have been proposed. The algorithm behaves extremely well, even for a fault rate exceeding 50%.

The Vehicle Routing-Allocation Problem: A unifying framework

In this paper the Vehicle Routing-Allocation Problem (VRAP) is presented. In VRAP not all customers need be visited by the vehicles. However customers not visited either have to be allocated to some customer on one of the vehicle tours or left isolated. We concentrate our discussion on the Single Vehicle Routing-Allocation Problem (SVRAP). An integer linear programming formulation of SVRAP is presented and we show how SVRAP provides a unifying framework for understanding a number of the papers and problems presented in the literature. Specifically the covering tour problem, the covering salesman problem, the median tour problem, the maximal covering tour problem, the travelling salesman problem, the generalised travelling salesman problem, the selective travelling salesman problem, the prize collecting travelling salesman problem, the maximum covering/shortest path problem, the maximum population/shortest path problem, the shortest covering path problem, the median shortest path problem, the minimum covering/shortest path problem and the hierarchical network design problem are special cases/variants of SVRAP.