A simulated annealing heuristic for the team orienteering problem with time windows

This paper presents a simulated annealing based heuristic approach for the team orienteering problem with time windows (TOPTW). Given a set of known locations, each with a score, a service time, and a time window, the TOPTW finds a set of vehicle tours that maximizes the total collected scores. Each tour is limited in length and a visit to a location must start within the location’s service time window. The proposed heuristic is applied to benchmark instances. Computational results indicate that the proposed heuristic is competitive with other solution approaches in the literature.     

An exact algorithm for team orienteering problems

Optimising routing of vehicles constitutes a major logistic stake in many industrial contexts. We are interested here in the optimal resolution of special cases of vehicle routing problems, known as team orienteering problems. In these problems, vehicles are guided by a reward that can be collected from customers, while the length of routes is limited. The main difference with classical vehicle routing problems is that not all customers have to be visited. The solution method we propose here is based on a Branch & Price algorithm. It is, as far as we know, the first exact method proposed for such problems, except for a preliminary work from Gueguen (Methodes de résolution exacte pour problémes de tournées de véhicules. Thése de doctorat, école Centrale Paris 1999) and a work from Butt and Ryan (Comput Oper Res 26(4):427–441 1999). It permits to solve instances with up to 100 customers.      

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 is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.     

An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem

In the capacitated team orienteering problem (CTOP), we are given a set of homogeneous vehicles and a set of customers each with a service demand value and a profit value. A vehicle can get the profit of a customer by satisfying its demand, but the total demand of all customers in its route cannot exceed the vehicle capacity and the length of the route must be within a specified maximum. The problem is to design a set of routes that maximizes the total profit collected by the vehicles. In this article, we propose a new heuristic algorithm for the CTOP using the ejection pool framework with an adaptive strategy and a diversification mechanism based on toggling between two priority rules. Experimental results show that our algorithm can match or improve all the best known results on the standard CTOP benchmark instances proposed by Archetti et al. (2008).     

Proportion-based robust optimization and team orienteering problem with interval data

In this paper, a proportion-based robust optimization approach is developed to deal with uncertain combinatorial optimization problems. This approach assumes that a certain proportion of uncertain coefficients in each solution are allowed to change and optimizes a deterministic model so as to achieve a trade-off between optimality and feasibility when the coefficients change. We apply this approach on team orienteering problem with interval data (TOPID), a variant of vehicle routing problem, which has not yet been studied before. A branch and price algorithm is proposed to solve the robust counterpart by using two novel dominance relations. Finally, numerical study is performed. The results show the usefulness of the proposed robust optimization approach and the effectiveness of our algorithm.     

Two-stage vehicle routing problem with arc time windows: A mixed integer programming formulation and a heuristic approach

In this paper, we introduce a new variant of the Vehicle Routing Problem (VRP), namely the Two-Stage Vehicle Routing Problem with Arc Time Windows (TS_VRP_ATWs) which generally emerges from both military and civilian transportation. The TS_VRP_ATW is defined as finding the vehicle routes in such a way that each arc of the routes is available only during a predefined time interval with the objective of overall cost minimization. We propose a Mixed Integer Programming (MIP) formulation and a heuristic approach based on Memetic Algorithm (MA) to solve the TS_VRP_ATW. The qualities of both solution approaches are measured by using the test problems in the literature. Experimental results show that the proposed MIP formulation provides the optimal solutions for the test problems with 25 and 50 nodes, and some test problems with 100 nodes. Results also show that the proposed MA is promising quality solutions in a short computation time.     

Simulated annealing metaheuristics for the vehicle routing problem with time windows

This paper develops simulated annealing metaheuristics for the vehicle routing and scheduling problem with time window constraints. Two different neighborhood structures, the λ-interchange mechanism of Osman and thek-node interchange process of Christofides and Beasley, are implemented. The enhancement of the annealing process with a short-term memory function via a tabu list is examined as a basis for improving the metaheuristic approach. Computational results on test problems from the literature as well as large-scale real-world problem are reported. The metaheuristics achieve solutions that compare favorably with previously reported results.     

An effective and fast heuristic for the Dial-a-Ride problem

Dial-a-Ride is an emerging transport system, in which a fleet of vehicles, without fixed routes and schedules, carries people from the desired pickup point to the desired delivery point, during a pre-specified time interval. It can be modeled as an -hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too limited to tackle real-life instances (hundred of trips), therefore heuristics are needed. The heuristic method proposed in this paper builds an auxiliary graph and then solves an assignment problem on this graph. The auxiliary graph is obtained by replacing pairs of nodes with a single one and associating an ad hoc cost function to the new set of arcs. Two different simple methods are employed to transform the infeasible solution given by the assignment problem into a feasible one. The proposed algorithms have been tested on instances created using the Milan network and shown to be fast and effective.      

Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt^*, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.     

An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We propose an iterated local search algorithm for the vehicle routing problem with time window constraints. We treat the time window constraint for each customer as a penalty function, and assume that it is convex and piecewise linear. Given an order of customers each vehicle to visit, dynamic programming (DP) is used to determine the optimal start time to serve the customers so that the total time penalty is minimized. This DP algorithm is then incorporated in the iterated local search algorithm to efficiently evaluate solutions in various neighborhoods. The amortized time complexity of evaluating a solution in the neighborhoods is a logarithmic order of the input size (i.e., the total number of linear pieces that define the penalty functions). Computational comparisons on benchmark instances with up to 1000 customers show that the proposed method is quite effective, especially for large instances.     

A General VNS heuristic for the traveling salesman problem with time windows

This paper presents a General Variable Neighborhood Search (GVNS) heuristic for the Traveling Salesman Problem with Time Windows (TSPTW). The heuristic is composed by both constructive and optimization stages. In the first stage, the heuristic constructs a feasible solution using VNS, and in the optimization stage the heuristic improves the feasible solution with a General VNS heuristic. Both constructive and optimization stages take advantage of elimination tests, partial neighbor evaluation and neighborhood partitioning techniques. Experimental results show that this approach is efficient, reducing significantly the computation time and improving some best known results from the literature.     

A powerful route minimization heuristic for the vehicle routing problem with time windows

We suggest an efficient route minimization heuristic for the vehicle routing problem with time windows. The heuristic is based on the ejection pool, powerful insertion and guided local search strategies. Experimental results on the Gehring and Homberger’s benchmarks demonstrate that our algorithm outperforms previous approaches and found 18 new best-known solutions.     

An exact algorithm for a single-vehicle routing problem with time windows and multiple routes

This paper describes an exact algorithm for solving a problem where the same vehicle performs several routes to serve a set of customers with time windows. The motivation comes from the home delivery of perishable goods, where vehicle routes are short and must be combined to form a working day. A method based on an elementary shortest path algorithm with resource constraints is proposed to solve this problem. The method is divided into two phases: in the first phase, all non-dominated feasible routes are generated; in the second phase, some routes are selected and sequenced to form the vehicle workday. Computational results are reported on Euclidean problems derived from benchmark instances of the classical vehicle routing problem with time windows.     

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.     

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.     

A heuristic algorithm for the free newspaper delivery problem

This paper addresses the problem of finding an effective distribution plan to deliver free newspapers from a production plant to subway, bus, or tram stations. The overall goal is to combine two factors: first, the free newspaper producing company wants to minimize the number of vehicle trips needed to distribute all newspapers produced at the production plant. Second, the company is interested in minimizing the time needed to consume all newspapers, i.e., the time needed to get all the newspapers taken by the final readers. The resulting routing problem combines aspects of the vehicle routing problem with time windows, the inventory routing problem, and additional constraints related to the production schedule. We propose a formulation and different heuristic approaches, as well as a hybrid method. Computational tests with real world data show that the hybrid method is the best in various problem settings.     

The multiple TSP with time windows: vehicle bounds based on precedence graphs

Vehicle bounds for the multiple traveling salesman problem with time windows are found by covering two precedence graphs with the minimum number of paths. Instances with tight bounds are presented, as well as instances for which the bounds are loose. The similarity of these instances is discussed.     

A stochastic dynamic traveling salesman problem with hard time windows

Just-in-time (JIT) trucking service, i.e., arriving at customers within specified time windows, has become the norm for freight carriers in all stages of supply chains. In this paper, a JIT pickup/delivery problem is formulated as a stochastic dynamic traveling salesman problem with time windows (SDTSPTW). At a customer location, the vehicle either picks up goods for or delivers goods from the depot, but does not provide moving service to transfer goods from one location to another. Such routing problems are NP-hard in deterministic settings, and in our context, complicated further by the stochastic, dynamic nature of the problem. This paper develops an efficient heuristic for the SDTSPTW with hard time windows. The heuristic is shown to be useful both in controlled numerical experiments and in applying to a real-life trucking problem.     

Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure.