Dag Haugland

A tabu search heuristic for the vehicle routing problem with time windows and split deliveries

Abstract The routing of a fleet of vehicles to service a set of customers is important in the field of distribution. Vehicle routing problems (VRP) arise in many real-life applications within transportation and logistics. In this paper, we study a variant of the general VRP, VRP with time windows and split deliveries (VRPTWSD). Time constrained routing is relevant for applications where a schedule has to be followed. The option of splitting a demand makes it possible to service a customer whose demand exceeds the vehicle capacity. Splitting also allows to decrease costs. Although VRPTWSD is a relaxation of the VRP with time windows, the problem does not become easier to solve, and is still NP-hard. In this work, we propose a solution method based on tabu search for solving the VRPTWSD without imposing any restrictions on the split delivery options. We also give an analysis of experimental results on problems with 100 customers.

A bilinear approach to the pooling problem

In this paper we present an algorithm for the pooling problem in refinery optimization based on a bilinear programming approach. The pooling problem occurs frequently in process optimization problems, especially refinery planning models. The main difficulty is that pooling causes an inherent nonlinearity in the otherwise linear models. We shall define the problem by formulating an aggregate mathematical model of a refinery, comment on solution methods for pooling problems that have been presented in the literature, and develop a new method based on convex approximations of the bilinear terms. The method is illustrated on numerical examples

Designing delivery districts for the vehicle routing problem with stochastic demands

This paper considers the problem of designing districts for vehicle routing problems with stochastic demands. In particular, demands are assumed to be uncertain at the time when the districts are made, and these are revealed only after the districting decisions are determined. Tabu search and multistart heuristics for this stochastic districting problem are developed and compared. Computational results show that tabu search is superior over multistart.

Models for petroleum field exploitation

Abstract This paper presents some models for an early evaluation of a petroleum field. Based on crude assumptions about a reservoir, our models suggest decisions concerning platform capacity, drilling programme and production. We start out with a simple production planning model using linear programming. By mixed integer programming techniques the model is gradually extended. The most sophisticated version of the model can propose platform capacity, where and when wells should be drilled, and the production from the wells. The models are tested on numerical examples, and the results are discussed. From the experiments we conclude that the problems are very hard to solve, and that the size of problems that can be solved is limited by the computational burden. Finally we give some ideas for future work that may provide better solution methods.

Strong formulations for the pooling problem

The pooling problem is a well-studied global optimization problem with applications in oil refining and petrochemical industry. Despite the strong NP-hardness of the problem, which is proved formally in this paper, most instances from the literature have recently been solved efficiently by use of strong formulations. The main contribution from this paper is a new formulation that proves to be stronger than other formulations based on proportion variables. Moreover, we propose a promising branching strategy for the new formulation and provide computational experiments confirming the strength of the new formulation and the effectiveness of the branching strategy.

Minimum-energy broadcast and multicast in wireless networks: An integer programming approach and improved heuristic algorithms

Both integer programming models and heuristic algorithms have been proposed for finding minimum-energy broadcast and multicast trees in wireless ad hoc networks. Among heuristic algorithms, the broadcast/multicast incremental power (BIP/MIP) algorithm is most known. The theoretical performance of BIP/MIP has been quantified in several studies. To assess the empirical performance of BIP/MIP and other heuristic algorithms, it is necessary to compute an optimal tree or a very good lower bound of the optimum. In this paper, we present an integer programming approach as well as improved heuristic algorithms. Our integer programming approach comprises a novel integer model and a relaxation scheme. Unlike previously proposed models, the continuous relaxation of our model leads to a very sharp lower bound of the optimum. Our relaxation scheme allows for performance evaluation of heuristics without having to compute optimal trees. Our contributions to heuristic algorithms consist of the power-improving algorithm successive power adjustment (SPA), and improved time complexity of some previously suggested algorithms. We report extensive numerical experiments. Algorithm SPA finds better solutions in comparison to a host of other algorithms. Moreover, the integer programming approach shows that trees found by algorithm SPA are optimal or near-optimal.

Minimizing fuel cost in gas transmission networks by dynamic programming and adaptive discretization

In this paper, the problem of computing optimal transportation plans for natural gas by means of compressor stations in pipeline networks is addressed. The non-linear (non-convex) mathematical model considers two types of continuous decision variables: mass flow rate along each arc, and gas pressure level at each node. The problem arises due to the presence of costs incurred when running compressors in order to keep the gas flowing through the system. Hence, the assignment of optimal values to flow and pressure variables such that the total fuel cost is minimized turns out to be essential to the gas industry. The first contribution from the paper is a solution method based on dynamic programming applied to a discretized version of the problem. By utilizing the concept of a tree decomposition, our approach can handle transmission networks of arbitrary structure, which makes it distinguished from previously suggested methods. The second contribution is a discretization scheme that keeps the computational effort low, even in instances where the running time is sensitive to the size of the mesh. Several computational experiments demonstrate that our methods are superior to a commercially available local optimizer.

Compressing ECG signals by piecewise polynomial approximation

Compression of digital electrocardiogram (ECG) signals has traditionally been tackled by heuristical approaches. It has been demonstrated that exact optimization algorithms outclass these heuristical approaches by a wide margin with respect to the reconstruction error. As opposed to traditional time-domain algorithms, where some heuristic is used to extract representative signal samples from the original signal, the exact optimization algorithm proposed by Haugland, Heber and Husoy (see Medical & Biological Engineering & Computing, vol.35, p.420-24, 1997) formulates the sample selection problem as a graph theory problem. Thus well known optimization theory can be applied in order to yield optimal compression. Haughland et al. applied linear interpolation in the reconstruction of the signal. This paper generalizes the optimization algorithm such that reconstruction can be made by second order polynomial interpolation in the extracted signal samples. The polynomials are fitted in a way that guarantees minimal reconstruction error, and the method proves the good performance compared to the case where linear interpolation is used in the reconstruction of the signal.

Local search heuristics for the probabilistic dial-a-ride problem

This paper introduces the probabilistic dial-a-ride problem, and describes an efficient request-relocation neighborhood evaluation procedure for the problem. The running time of the procedure is