Geraldo Robson Mateus

A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows

Abstract The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem, which has received considerable attention in recent years. This problem has been addressed using many different techniques including both exact and heuristic methods. The VRPTW benchmark problems of Solomon [Algorithms for the vehicle routing and scheduling problems with time window constraints, Operations Research 1987; 35(2): 254–65] have been most commonly chosen to evaluate and compare all algorithms. Results from exact methods have been improved considerably because of parallel implementations and modern branch-and-cut techniques. However, 24 out of the 56 high order instances from Solomons original test set still remain unsolved. Additionally, in many cases a prohibitive time is needed to find the exact solution. Many of the heuristic methods developed have proved to be efficient in identifying good solutions in reasonable amounts of time. Unfortunately, whilst the research efforts based on exact methods have been focused on the total travel distance, the focus of almost all heuristic attempts has been on the number of vehicles. Consequently, it is more difficult to compare and take advantage of the strong points from each approach. This paper proposes a robust heuristic approach for the VRPTW using travel distance as the main objective through an efficient genetic algorithm and a set partitioning formulation. The tests were produced using real numbers and truncated data type, allowing a direct comparison of its results against previously published heuristic and exact methods. Furthermore, computational results show that the proposed heuristic approach outperforms all previously known and published heuristic methods in terms of the minimal travel distance.

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

A scheduling problem with unrelated parallel machines, sequence and machine-dependent setup times, due dates and weighted jobs is considered in this work. A branch-and-bound algorithm (B&B) is developed and a solution provided by the metaheuristic GRASP is used as an upper bound. We also propose a set of instances for this type of problem. The results are compared to the solutions provided by two mixed integer programming models (MIP) with the solver CPLEX 9.0. We carry out computational experiments and the algorithm performs extremely well on instances with up to 30 jobs.

Iterated local search heuristics for the Vehicle Routing Problem with Cross-Docking

This work addresses the Vehicle Routing Problem with Cross-Docking (VRPCD). The problem consists in defining a minimum cost set of routes for a fleet of vehicles that meets the demands of products for a set of suppliers and customers. The vehicles leave a single Cross-Dock (CD) towards the suppliers, pick up products and return to the CD, where products can be exchanged before being delivered to their customers. The vehicle routes must respect the vehicle capacity constraints, as well as the time window constraints. We adapted a constructive heuristic and six local search procedures from the literature of VRP, and made them efficient in the presence of the synchronization constraints of VRPCD. Besides, we propose three Iterated Local Search (Lourenco et al., 2010) heuristics for VRPCD. The first heuristic is a standard implementation of ILS, while the second extends the classic ILS framework by keeping a set of elite solutions, instead of a single current solution. The latter set is used in a restart procedure. As far as we can tell, this is the first ILS heuristic in the literature that keeps a population of current elite solutions. The third heuristic is an extension of the second that relies on an intensification procedure based on an Integer Programming formulation for the Set Partitioning problem. The latter allows a neighborhood with an exponential number of neighbors to be efficiently evaluated. We report computational results and comparisons with the best heuristics in the literature. Besides, we also present a new set with the largest instances in the literature of VRPCD, in order to demonstrate that the improvements we propose for the ILS metaheuristic are efficient even for large size instances. Results show that the best of our heuristics is competitive with the best heuristics in the literature of VRPCD. Besides, it improved the best solution known for half of the benchmark instances in the literature.

The Pickup and Delivery Problem with Cross-Docking

Usual models that deal with the integration of vehicle routing and cross-docking operations impose that every vehicle must stop at the dock even if the vehicle collects and delivers the same set of goods. In order to allow vehicles to avoid the stop at the dock and thus, reduce transportation costs, we introduce the Pickup and Delivery Problem with Cross-Docking (PDPCD). An Integer Programming formulation and a Branch-and-price algorithm for the problem are discussed. Our computational results indicate that optimal or near optimal solutions for PDPCD indeed allow total costs to be significantly reduced. Due to improvements in the resolution of the pricing problems, the Branch-and-price algorithm for PDPCD works better than similar algorithms for other models in the literature.

Branch-and-price algorithms for the Two-Echelon Capacitated Vehicle Routing Problem

In this paper, we propose an Integer Programming formulation and two branch-and-price implementations for the Two-Echelon Capacitated Vehicle Routing Problem. One algorithm considers routes that satisfy the elementarity condition, while the other relaxes such constraint when pricing routes. For instances that could not be solved to proven optimality within a given time limit, our computational experience suggests that the former provides sharper upper bounds while the latter offers tighter lower bounds. As a by-product, ten new best upper bounds and two new optimality certificates are provided here.

Balancing message delivery latency and network lifetime through an integrated model for clustering and routing in Wireless Sensor Networks

One common approach to extend Wireless Sensors Networks (WSN) lifetime is to use mobile sinks to gather sensed information through the network, avoiding that sensor nodes spend their limited energy in relaying other nodes messages to the sinks. Such approach, however, tends to significantly increase message delivery latency. On the other hand, it is widely recognized that the optimization of any Quality of Service parameter in WSN, message delivery latency included, must always be conducted bearing in mind the implied impact in the network lifetime. In this paper, we introduce a network model to seek for a good solution for this inherent multi-objective optimization problem. In our approach, optimization algorithms are used to define optimal (or near-optimal) density control policies, sensors clustering and sink routes to collect sensed data. We deal with the multi-objective nature of the design in WSN by explicitly minimizing message delivery latency and by imposing topology constraints that help to reduce energy consumption. Our proposal differs from most studies in the literature by the integrated way in which we tackle clustering and routing decisions. Various metaheuristic based heuristics that solve the integrated problem were incorporated into a dynamic simulation environment. Through extensive simulation experiments, we compared our approach to others in the literature, in terms of Quality of Service parameters. Our results indicate that the integrated model proposed here compares favorably to other approaches, allowing a good balance among conflicting parameters like message delivery latency, network lifetime and rate of messages received.

A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

In this paper, we introduce a branch-and-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. The algorithm relies on a reformulation based on q-routes that combines two important features. First, it overcomes symmetry issues observed in a formulation coming from a previous study of the problem. Second, it is strengthened with several classes of valid inequalities. As a result, the branch-and-cut-and-price implementation compares favorably with previous exact solution approaches for the problem-namely, two branch-and-price algorithms and a branch-and-cut method. Overall, 10 new optimality certificates and 8 new best upper bounds are provided in this study. New best lower bounds are also presented for all instances in the hardest test set from the literature.

An edge-swap heuristic for generating spanning trees with minimum number of branch vertices

This paper presents a new edge-swap heuristic for generating spanning trees with a minimum number of branch vertices, i.e. vertices of degree greater than two. This problem was introduced in Gargano et al. (Lect Notes Comput Sci 2380:355–365, 2002) and has been called the minimum branch vertices problem by Cerulli et al. (Comput Optim Appl 42:353–370, 2009). The heuristic starts with a random spanning tree and iteratively reduces the number of branch vertices by swapping tree edges with edges not currently in the tree. It can be easily implemented as a multi-start heuristic. We report on extensive computational experiments comparing single-start and multi-start variants on our heuristic with other heuristics previously proposed in the literature.

A hierarchical approach to solve a production planning and scheduling problem in bulk cargo terminal

Abstract The integration of planning and scheduling decisions is key to obtain an efficient and reliable production operation in a modern manufacturing and service company. In this work we propose a mathematical model for this integration, the model is defined considering logistic operations at bulk port, however is generic enough to be adapted to several situations. The integration takes place in a hierarchical scheme where the problems exchange data and they are solved through a commercial solver and heuristics. When scheduling is not feasible, capacity information is forwarded to production planning to adjust or indicate the use of new tasks. The model and algorithms are validated considering data from a real case. Computational results show the efficiency of the approach, producing strong bounds for large instances.

On a vector space representation in genetic algorithms for sensor scheduling in wireless sensor networks.

Recent works raised the hypothesis that the assignment of a geometry to the decision variable space of a combinatorial problem could be useful both for providing meaningful descriptions of the fitness landscape and for supporting the systematic construction of evolutionary operators (the geometric operators) that make a consistent usage of the space geometric properties in the search for problem optima. This paper introduces some new geometric operators that constitute the realization of searches along the combinatorial space versions of the geometric entities descent directions and subspaces. The new geometric operators are stated in the specific context of the wireless sensor network dynamic coverage and connectivity problem (WSN-DCCP). A genetic algorithm (GA) is developed for the WSN-DCCP using the proposed operators, being compared with a formulation based on integer linear programming (ILP) which is solved with exact methods. That ILP formulation adopts a proxy objective function based on the minimization of energy consumption in the network, in order to approximate the objective of network lifetime maximization, and a greedy approach for dealing with the systems dynamics. To the authors’ knowledge, the proposed GA is the first algorithm to outperform the lifetime of networks as synthesized by the ILP formulation, also running in much smaller computational times for large instances.