Scheduling Tugboats in a Seaport

In a seaport, vessels need the assistance of tugboats when mooring and unmooring. Tugboats assist a vessel by pushing or towing the vessel’s tug points, and the vessel can moor (or unmoor) successfully only if each of the tug points is operated with sufficient horsepower. For a busy port where vessels frequently require the service of tugboats, effectively scheduling tugboats for serving incoming and outgoing vessels is a key to successful execution of the vessels’ berth plans. In this paper, we study a tugboat scheduling problem in a busy port, where incoming and outgoing vessels frequently require the assistance of tugboats, but the number of available tugboats is limited. We make use of a network representation of the problem and develop an integer programming formulation, which takes into account the berth plans of vessels, the tug points of vessels for different move types, and the horsepower requirements of the tug points, to minimize the weighted sum of the berthing and departure tardiness of vessels, the operating cost of tugboats, and the number of vessels that cannot be served successfully. We analyze the computational complexity of the problem and develop a novel iterative solution method, which combines Lagrangian relaxation and Benders decomposition, for generating near-optimal solutions. Computational performance of the proposed solution method is evaluated on problem instances generated from the operational data of a container port in Shanghai.

On a Multigrid Method for Tempered Fractional Diffusion Equations

In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation. Our discretizations will be based on tempered weighted and shifted Grünwald difference (tempered-WSGD) operators in space and the Crank–Nicolson scheme in time. We will prove, and show numerically, that a classical multigrid method, based on direct coarse grid discretization and weighted Jacobi relaxation, performs highly satisfactory for this type of equation. We also employ the multigrid method to solve the second- and third-order discrete schemes for the tempered fractional Black–Scholes equation. Some numerical experiments are carried out to confirm accuracy and effectiveness of the proposed method.

Fluence map optimisation for prostate cancer intensity modulated radiotherapy planning using iterative solution method

Here we projected a model-based IMRT treatment plan to produce the optimal radiation dosage by considering that the maximum amount of prescribed dose should be delivered to the target without affecting the surrounding healthy tissues especially the OARs. Fluence mapping is used for inverse planning. This suggested method can generate global minima for IMRT plans with reliable plan quality among diverse treatment planners and to provide better safety for significant parallel OARs in an effective way. The whole methodology is having the capability to handles various objectives and to generate effective treatment procedures as validated with illustrations on the CORT dataset. For the validation of our methodology, we have compared our result with the two other approaches for calculating the objectives based on dose-volume bounds and found that in our methodology dose across the prostate and lymph nodes is maximum and the time required for the convergence is minimum.

A method of analysis of complex hydraulic networks

A simple and reliable iterative solution method of classical hydraulic network flow rate distribution problem is described. The method is based on chord linearization of inverse branch loss function which keeps basic branch properties. It has good speed of convergency which is practically independent of initial values.

Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems

Time-harmonic problems arise in many important applications, such as eddy current optimally controlled electromagnetic problems. Eddy current modelling can also be used in non-destructive testings of conducting materials. Using a truncated Fourier series to approximate the solution, for linear problems the equation for different frequencies separate, so it suffices to study solution methods for the problem for a single frequency. The arising discretized system takes a two-by-two or four-by-four block matrix form. Since the problems are in general three-dimensional in space and hence of very large scale, one must use an iterative solution method. It is then crucial to construct efficient preconditioners. It is shown that an earlier used preconditioner for optimal control problems is applicable here also and leads to very tight eigenvalue bounds and hence very fast convergence such as for a Krylov subspace iterative solution method. A comparison is done with an earlier used block diagonal preconditioner.

A Note on Using Partitioning Techniques for Solving Unconstrained Optimization Problems on Parallel Systems

We deal with the design of parallel algorithms by using variable partitioning techniques to solve nonlinear optimization problems. We propose an iterative solution method that is very efficient for separable functions, our scope being to discuss its performance for general functions. Experimental results on an illustrative example have suggested some useful modifications that, even though they improve the efficiency of our parallel method, leave some questions open for further investigation.