Nonlinear control for non-Newtonian flows

PDE-constrained optimization is an important area in the field of numerical analysis, with problems arising in a wide variety of applications including optimal design, optimal control and parameter estimation. The aim of such problems is to minimize a functional J(u,d) whilst adhering to constraints posed by a system of partial differential equations (PDE), with u and d used respectively to denote the state and control of the system. In this thesis, we describe the steady-state generalized Stokes equations for incompressible fluids. We proceed to derive the weak formulation of the problem, and show that the resulting system may be written in terms of a mixed formulation of the Stokes problem. Based on this formulation, the problem is discretized through use of the Galerkin finite element method, before investigating control problems based on the generalized Stokes equations, along with numerical experimentation. This work will be used to achieve the main aim of this thesis, namely the exploration and investigation of solution methods for optimal control problems constrained by non- Newtonian flow. Ultimately, an iterative solution method designed for such problems coupled with an appropriate preconditioning strategy will be described and analyzed, and used to produce effective numerical results

Metaheuristic algorithm for ship routing and scheduling problems with time window

This paper describes a Tabu Search (TS) heuristic for a Ship Routing and Scheduling Problem (SRSP). The method was developed to address the problem of loading cargos for many customers using heterogeneous ships. Constraints include delivery time windows imposed by customers, the time horizon by which all deliveries must be made, and ship capacities. The proposed algorithm aims to minimize the overall cost of shipping operation without any violations. The TS algorithm is compared with a similar method that uses the Set Partitioning Problem (SPP) in terms of solution quality and computational time. The results of a computational investigation are presented. Solution quality and execution time are explored with respect to problem size and parameters controlling the TS such neighborhood size. It is found that while the SPP method solves small-scale problems efficiently, treating large-scale problems with this method becomes complicated due to computational problems; however, the TS method can overcome this challenge. Furthermore, TS consistently returns near-optimal solution within a reasonable time