The method of imbedded Lagrangian element to estimate wave power absorption by some submerged devices

A simple approach is described to estimate the wave power absorption potential of submerged devices known to cause wave focusing and flow enhancement. In particular, the presence of a flow-through power take-off （PTO） system, such as low-head turbines, can be accounted for. The wave radiation characteristics of an appropriately selected Lagrangian element （LE） in the fluid domain are first determined. In the limit of a vanishing mass, the LE reduces to a patch of distributed normal dipoles. The hydrodynamic coefficients of this virtual object are then input in a standard equation of motion where the effect of the PTO can be represented, for example, as a dashpot damping term. The process is illustrated for a class of devices recently proposed by Carter and Ertekin （2011）, although in a simplified form. Favorable wave power absorption is shown for large ratios of the LE wave radiation coefficient over the LE added mass coefficient. Under optimal conditions, the relative flow reduction from the PTO theoretically lies between 0.50 and 1 2 ≈ 0.71, with lower values corresponding to better configurations. Wave power capture widths, the sensitivity of results to PTO damping and sample spectral calculations at a typical site in Hawaiian waters are proposed to further illustrate the versatility of the method.     

Evolution of the open-sea eddy ALGERS'98 in the Algerian Basin with Lagrangian trajectories and remote sensing observations

The westward evolution of an open-sea anticyclonic eddy along the western Algerian Basin is shown, for the first time, by means of 15 buoy trajectories and remote sensing observations. For 3 months, the buoy trajectories described several anticyclonic loops in periods of 4–21 days. The eddy's movement, translation, and rotation were separated with a kinematic model, resulting in a mean translation speed of 2 km/day, which fits the self-propulsion speed predicted on theoretical models for isolated eddies on a beta plane. Fluctuations in translation speed were associated with advection of the mean flow and topographic interactions. Both mechanisms changed the eddy's horizontal shape from circular to elliptical, inducing fluctuations in its swirl velocity and solid-body rotation. The initial stage of the eddy is an isolated asymmetric dipole, comprised by a small cyclone and a large anticyclone, the latter generated from a frontal instability, which under the Coriolis term acquires anticyclonic relative vorticity. During its first days of life, the anticyclonic eddy was shallow Ro=0.9 and small (diameter less than 50 km). Later on, it reached a diameter of 150 km and a vertical structure of 3 km (Ro=0.1). A retrospective analysis with infrared images shows that the eddy's generation took place at about 3–4°E. Then, the eddy completed a counterclockwise circuit never before reported in other studies and ended up at the entrance of the Algerian Basin, where the interaction with the topography and the coastal instability induced its decay. The eddy's life span was 10 months. Computations of the heating rate following clusters of buoy trajectories show fluctuations throughout the eddy's journey, induced by advection and a seasonal warming.     

Controlled installation of spudcan foundations on loose sand overlying weak clay

Offshore jack-up rigs are often used for site exploration and oil well drilling. The footings of jack-up rigs are known as spudcan foundations. The risk of rapid uncontrolled penetration of spudcan in seabed (“punch-through”) exposes jack-ups to significant risk during installation in strong over weak layered seabeds. An example for this is a thin loose sand layer overlying a weaker stratum of clay. To prevent spudcans from “punch-through”, an in-situ measurement concept is suggested in this paper to control the installation process of spudcan foundations. First, three-dimensional finite element studies using a Coupled Eulerian–Lagrangian method are carried out to simulate the penetration process. The numerical results have been validated with existing analytical solutions and centrifuge model test data. Furthermore, parametric studies are carried out to quantify the influences of the sand thickness and shear strength of the clay on the bearing capacity of spudcans. Based on the numerical studies an idea for the development of an in-situ measurement concept is suggested to control the spudcan penetration process in-situ.     

基于Lagrangian算法的目标跟踪与信息融合效果评估

指挥自动化系统（C4ISR）作为现代战争中对作战部队和武器系统实施高效指挥与控制的主要手段,通过对来自多个传感器的资料以及相关情报进行分析和综合处理,研究复杂战场态势环境下的指挥自动化系统目标跟踪与信息融合的效果评估。用Lagrangian算法得到评价体系中定义的性能指标,并根据这些指标进行综合评估,提高系统的有效性和可靠性。     

Biofuel refinery location and supply chain planning under traffic congestion

This research focuses on planning biofuel refinery locations where the total system cost for refinery investment, feedstock and product transportation and public travel is minimized. Shipment routing of both feedstock and product in the biofuel supply chain and the resulting traffic congestion impact are incorporated into the model to decide optimal locations of biofuel refineries. A Lagrangian relaxation based heuristic algorithm is introduced to obtain near-optimum feasible solutions efficiently. To further improve optimality, a branch-and-bound framework (with linear programming relaxation and Lagrangian relaxation bounding procedures) is developed. Numerical experiments with several testing examples demonstrate that the proposed algorithms solve the problem effectively. An empirical Illinois case study and a series of sensitivity analyses are conducted to show the effects of highway congestion on refinery location design and total system costs.     

Joint inventory-location problem under the risk of probabilistic facility disruptions

This paper studies a reliable joint inventory-location problem that optimizes facility locations, customer allocations, and inventory management decisions when facilities are subject to disruption risks (e.g., due to natural or man-made hazards). When a facility fails, its customers may be reassigned to other operational facilities in order to avoid the high penalty costs associated with losing service. We propose an integer programming model that minimizes the sum of facility construction costs, expected inventory holding costs and expected customer costs under normal and failure scenarios. We develop a Lagrangian relaxation solution framework for this problem, including a polynomial-time exact algorithm for the relaxed nonlinear subproblems. Numerical experiment results show that this proposed model is capable of providing a near-optimum solution within a short computation time. Managerial insights on the optimal facility deployment, inventory control strategies, and the corresponding cost constitutions are drawn.     

基于覆盖理论的铁路救援列车部署方案研究

基于弧段覆盖理论、覆盖衰退理论和考虑时间满意度的覆盖理论,设计考虑时间满意度和最大覆盖率的救援列车部署方案。构建铁路救援时间满意函数,通过最小二乘法拟合相应的系数。考虑从不同方向对弧段的联合覆盖率,借鉴复杂网络理论为路网环境中的线路和节点赋予权重,建立最大时间满意度和最大覆盖率的救援列车部署模型,运用拉格朗日松弛算法求解。结合兰州铁路局路网数据,给出算例,验证模型的有效性,为铁路运营者在救援列车部署方案设计中提供借鉴。     

Model and algorithm for container ship stowage planning based on bin-packing problem

In a general case, container ship serves many different ports on each voyage. A stowage planning for container ship made at one port must take account of the influence on subsequent ports. So the complexity of stowage planning problem increases due to its multi-ports nature. This problem is NP-hard problem. In order to reduce the computational complexity, the problem is decomposed into two sub-problems in this paper. First, container ship stowage problem （CSSP） is regarded as “packing problem”, ship-bays on the board of vessel are regarded as bins, the number of slots at each bay are taken as capacities of bins, and containers with different characteristics （homogeneous containers group） are treated as items packed. At this stage, there are two objective functions, one is to minimize the number of bays packed by containers and the other is to minimize the number of overstows. Secondly, containers assigned to each bays at first stage are allocate to special slot, the objective functions are to minimize the metacentric height, heel and overstows. The taboo search heuristics algorithm are used to solve the subproblem. The main focus of this paper is on the first subproblem. A case certifies the feasibility of the model and algorithm.     

General stochastic user equilibrium traffic assignment problem with link capacity constraints

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.     

Optimal shipment decisions for an airfreight forwarder: Formulation and solution methods

We study the freight forwarder’s shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times.After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems.