Team Orienteering Problem Research Articles

A Randomized Population Constructive Heuristic for the Team Orienteering Problem

The NP-hard (complete) team orienteering problem is a particular vehicle routing problem with the aim of maximizing the profits gained from visiting control points without exceeding a travel cost limit. The team orienteering problem has a number of applications in several fields such as athlete recruiting, technician routing and tourist trip. Therefore, solving optimally the team orienteering problem would play a major role in logistic management. In this study, a novel randomized population constructive heuristic is introduced. This heuristic constructs a diversified initial population for population-based metaheuristics. The heuristics proved its efficiency. Indeed, experiments conducted on the well-known benchmarks of the team orienteering problem show that the initial population constructed by the presented heuristic wraps the best-known solution for 131 benchmarks and good solutions for a great number of benchmarks.

A branch‐and‐cut algorithm for the Team Orienteering Problem

AbstractThe Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two‐index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch‐and‐cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.

An orienteering-based approach to manage emergency situation

Abstract: The emergencies management in industrial plants is an issue widely discussed in the literature and in the European legislative framework. Despite the large interest shown by the different actors involved in emergencies management, neither scientific nor in industrial field, have developed intelligent tools to support the decisions in these particular contexts. This work, realized inside an Italian financed project (DIEM-SSP), faces the problem to evacuate the greater number of persons from a risky area and transfer them in a unique destination outside from this area using the available and limited resources. Supposing that these persons have problem of mobility, the problem to solve becomes this: collect the highest number of persons from several origins and bring them into a unique destination, using a limited number of capacitated vehicles respecting a time limit. This problem has been modelled as a Multi origins Capacitated Team Orienteering Problem (Mo-CTOP) and solved implementing Ants Colony Optimization algorithm (ACOa). Results and tests are given in order to validate the proposed model and to offer a solution for a real case treaty into the abovementioned project.

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;

Solving the team orienteering problem with cutting planes

The Team Orienteering Problem (TOP) is an attractive variant of the Vehicle Routing Problem (VRP). The aim is to select customers and at the same time organize the visits for a vehicle fleet so as to maximize the collected profits and subject to a travel time restriction on each vehicle.In this paper, we investigate the effective use of a linear formulation with polynomial number of variables to solve TOP. Cutting planes are the core components of our solving algorithm. It is first used to solve smaller and intermediate models of the original problem by considering fewer vehicles. Useful information are then retrieved to solve larger models, and eventually reaching the original problem. Relatively new and dedicated methods for TOP, such as identification of irrelevant arcs and mandatory customers, clique and independent-set cuts based on the incompatibilities, and profit/customer restriction on subsets of vehicles, are introduced.We evaluated our algorithm on the standard benchmark of TOP. The results show that the algorithm is competitive and is able to prove the optimality for 12 instances previously unsolved.

An adaptive heuristic for the Capacitated Team Orienteering Problem

The Capacitated Team Orienteering Problem (CTOP) is a new variant of the well-known Team Orienteering Problem (TOP) where an additional constraint is imposed on the vehicles capacities. By associating a profit and a demand to each customer, the objective of solving CTOP is to select the set of customers to be served in such a way that the total amount of profits collected from the visited customers is maximized, while respecting all the resource limitations, i.e., maximum length limit and maximum capacity of each vehicle. We present in this paper a new adaptive heuristic to solve CTOP. Our method is based on an adaptive iterative destructive constructive heuristic, which adjusts its parameters according to the solution progress. Computational experiments applied on the benchmark of CTOP show the effectiveness of our proposed method, which provided some results of high quality with a competitive computational time. Moreover, an improvement was found in the score of one of the hardest instances of the benchmark.

Enhanced exact solution methods for the Team Orienteering Problem

The Team Orienteering Problem (TOP) is one of the most investigated problems in the family of vehicle routing problems with profits. In this paper, we propose a Branch-and-Price approach to find proven optimal solutions to TOP. The pricing sub-problem is solved by a bounded bidirectional dynamic programming algorithm with decremental state space relaxation featuring a two-phase dominance rule relaxation. The new method is able to close 17 previously unsolved benchmark instances. In addition, we propose a Branch-and-Cut-and-Price approach using subset-row inequalities and show the effectiveness of these cuts in solving TOP.

Customized Travel Planner using MapReduce and Approximation Algorithm

It is fun to travel but painful to arrange the trip. When travelers start off planning they need flights, accommodation and attractions. Which scattered across multiple websites on the internet? Traveler spends time scouting each of them for the best deals, and gets the attraction reviews from established planners in the market. It will be always good if traveler gives specified designations and time he wants to spend for the trip and some platform will automatically did everything for traveler with added bonus of optimal and customized itineraries. This system is designed for such travelers to design customized itineraries which will be optimal and consist of Point-Of-Interest (POI) selected by traveler, rather than go and visit the traditional and static trip plans by many travel agencies. This system is two-stage processing system for cost effective and optimal results. First is preprocessing stage works offline uses parallel processing engine as MapReduce to precompute Single-Day Itineraries. In further stage which is online the precomputed itineraries are combined to give multiday itineraries. These itineraries produced are optimal as per travelers selected Point-OfInterest (POI).Here Greedy Approximation Algorithm is used to combine the single day itineraries. In this way TeamOrienteering-Problem (TOP) is transferred to Set-Packing Problem another NP-complete problem.

Research on the Bilateral Sweep Heuristic for Single Path’s Construction

The team orienteering problem (TOP) is the generation to the case of multi tours of the Orienteering Problem (OP). A pair of origin and destination is specified and a set of potential customers with profits are provided. A single path's initial construction which is considered as the main procedure for feasible solution initialization for the TOP is formulated as an integer program, then the BS heuristic's implementing process is illustrated and the process of bilateral sweep heuristic algorithm (BS) is detailed. Applying the BS to solve the related combinatorial optimization problems ap- pears to be a very promising technique.

A Hybrid Heuristic for the Team Orienteering Problem

A Hybrid Heuristic for the Team Orienteering Problem

Applying Particle Swarm Optimization for Solving Team Orienteering Problem with Time Windows

The Team Orienteering Problem With Time Windows (TOPTW) is a transportation problem case that have a set of vertices with a score, service time, and the time windows, start and final at a depot location. A number of paths are constructed to maximize the total collected score by the vertices which is visited. Each vertice can be visited only once and the visit can only start during the time window of vertices. This paper proposes a Particle Swarm Optimization algorithm for solving the TOPTW, by defining a specific particle for representing the solution of TOPTW within the PSO algorithm and two alternatives, called PSO_TOPTW1 and PSO_TOPTW2, for translating the particle position to form the routes of the path. The performance of the proposed PSO algorithm is evaluated through some benchmark data problem available in the literature. The computational results show that the proposed PSO is able to produce sufficiently good TOPTW solutions that are comparable with corresponding solutions from other existing methods for solving the TOPTW.

Automatic Itinerary Planning for Traveling Services

Creating an efficient and economic trip plan is the most annoying job for a backpack traveler. Although travel agency can provide some predefined itineraries, they are not tailored for each specific customer. Previous efforts address the problem by providing an automatic itinerary planning service, which organizes the points-of-interests (POIs) into a customized itinerary. Because the search space of all possible itineraries is too costly to fully explore, to simplify the complexity, most work assume that user's trip is limited to some important POIs and will complete within one day. To address the above limitation, in this paper, we design a more general itinerary planning service, which generates multiday itineraries for the users. In our service, all POIs are considered and ranked based on the users' preference. The problem of searching the optimal itinerary is a team orienteering problem (TOP), a well-known NP-complete problem. To reduce the processing cost, a two-stage planning scheme is proposed. In its preprocessing stage, single-day itineraries are precomputed via the MapReduce jobs. In its online stage, an approximate search algorithm is used to combine the single day itineraries. In this way, we transfer the TOP problem with no polynomial approximation into another NP-complete problem (set-packing problem) with good approximate algorithms. Experiments on real data sets show that our approach can generate high-quality itineraries efficiently.

Solving the Team Orienteering Problem with Particle Swarm Optimization

The team orienteering problem (TOP) or the multiple tour maximum collection problem can be considered as a generic model that can be applied to a number of challenging applications in logistics, tourism, and other fields. This problem is generally defined as the problem of determining P paths, in which the traveling time of each path is limited by <TEX>$T_{max}$</TEX> that maximizes the total collected score. In the TOP, a set of N vertices i is given, each with a score <TEX>$S_i$</TEX>. The starting point (vertex 1) and the end point (vertex N) of all paths are fixed. The time <TEX>$t_{ij}$</TEX> needed to travel from vertex i to j is known for all vertices. Some exact and heuristics approaches had been proposed in the past for solving the TOP. This paper proposes a new solution methodology for solving the TOP using the particle swarm optimization, especially by proposing a solution representation and its decoding method. The performance of the proposed algorithm is then evaluated using several benchmark datasets for the TOP. The computational results show that the proposed algorithm using specific settings is capable of finding good solution for the corresponding TOP instance.

Team Orienteering Problem with Decreasing Profits

Team Orienteering with Decreasing Profits (DP-TOP) extends the classical Team Orienteering problem (TOP) by considering the profit of each client as a decreasing function of time. It consists of maximizing the sum of collected profit by a fixed number K of vehicles, visiting each client at most once. In this work, we present lower bounds based on a Dantzig-Wolfe decomposition and column generation as well as upper bounds obtained by an evolutionary local search approach (ELS).

Managing vehicle breakdown incidents during urban distribution of a common product

This paper addresses a case in which a vehicle, member of a fleet distributing a single product, is immobilized while executing its distribution plan. Some active vehicles of the fleet are then rerouted to serve selected clients of the immobilized vehicle. We model this re-planning problem as a variation of the Team Orienteering Problem constraining all vehicle routes to an upper time, or distance, limit, and taking into account limited vehicle capacity. We propose an efficient heuristic to provide solutions in almost real-time. The heuristic progressively constructs new routes for each active vehicle, which may load additional product by visiting the warehouse or the immobilized vehicle. If appropriate, we solve this replenishment sub-problem by a fast labelling algorithm. We test the effectiveness of the proposed heuristic by comparing its solutions with those obtained by an appropriate Genetic Algorithm (GA) that yields high quality (but computationally expensive) results.

An effective PSO-inspired algorithm for the team orienteering problem

The Team Orienteering Problem (TOP) is a particular vehicle routing problem in which the aim is to maximize the profit gained from visiting customers without exceeding a travel cost/time limit. This paper proposes a new and fast evaluation process for TOP based on an interval graph model and a Particle Swarm Optimization inspired Algorithm (PSOiA) to solve the problem. Experiments conducted on the standard benchmark of TOP clearly show that our algorithm outperforms the existing solving methods. PSOiA reached a relative error of 0.0005% whereas the best known relative error in the literature is 0.0394%. Our algorithm detects all but one of the best known solutions. Moreover, a strict improvement was found for one instance of the benchmark and a new set of larger instances was introduced.

An augmented large neighborhood search method for solving the team orienteering problem

In the Team Orienteering Problem (TOP), a team of vehicles attempts to collect rewards at a given number of stops within a specified time frame. Once a vehicle visits a stop and collects its reward, no other vehicles can collect the reward again. Typically, a team cannot visit all stops and therefore has to identify the “best” set of stops to visit in order to maximize total rewards. We propose a large neighborhood search method with three improvement algorithms: a local search improvement, a shift and insertion improvement, and replacement improvement. Our proposed approach can find the best known solutions for 386 of the 387 benchmark instances, for the one instance which our solution is not the current best it is only varies by one from the best. Our approach outperforms all the previous approaches in terms of solution quality and computation time.

Solving the team orienteering problem using effective multi-start simulated annealing

The team orienteering problem (TOP) is known as an NP-complete problem. A set of locations is provided and a score is collected from the visit to each location. The objective is to maximize the total score given a fixed time limit for each available tour. Given the computational complexity of this problem, a multi-start simulated annealing (MSA) algorithm which combines a simulated annealing (SA) based meta-heuristic with a multi-start hill climbing strategy is proposed to solve TOP. To verify the developed MSA algorithm, computational experiments are performed on well-known benchmark problems involving numbers of locations ranging between 42 and 102. The experimental results demonstrate that the multi-start hill climbing strategy can significantly improve the performance of the traditional single-start SA. Meanwhile, the proposed MSA algorithm is highly effective compared to the state-of-the-art meta-heuristics on the same benchmark instances. The proposed MSA algorithm obtained 135 best solutions to the 157 benchmark problems, including five new best solutions. In terms of both solution quality and computational expense, this study successfully constructs a high-performance method for solving this challenging problem.

The capacitated team orienteering problem with incomplete service

In this paper we study the capacitated version of the Team Orienteering Problem (TOP), that is the Capacitated TOP (CTOP) and the impact of relaxing the assumption that a customer, if served, must be completely served. We prove that the profit collected by the CTOP with Incomplete Service (CTOP-IS) may be as large as twice the profit collected by the CTOP. A computational study is also performed to evaluate the average increase of the profit due to allowing incomplete service. The results show that the increase of the profit strongly depends on the specific instance. On the tested instances the profit increase ranges between 0 and 50 %. We complete the computational study with the increase of the profit of the CTOP due to split deliveries, that is multiple visits to the same customer, and to split deliveries combined with incomplete service.

The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search

The Team Orienteering Problem (TOP) is a known NP-hard problem that typically arises in vehicle routing and production scheduling contexts. In this paper we introduce a new solution method to solve the TOP with hard Time Window constraints (TOPTW). We propose a Variable Neighborhood Search (VNS) procedure based on the idea of exploring, most of the time, granular instead of complete neighborhoods in order to improve the algorithm’s efficiency without loosing effectiveness. The method provides a general way to deal with granularity for those routing problems based on profits and complicated by time constraints. Extensive computational results are reported on standard benchmark instances. Performance of the proposed algorithm is compared to optimal solution values, when available, or to best known solution values obtained by state-of-the-art algorithms. The method comes out to be, on average, quite effective allowing to improve the best know values for 25 test instances.