Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

The effective use of implicit parallelism through the use of an object-oriented programming language

This thesis explores translating well-written sequential programs in a subset of the Eiffel programming language - without syntactic or semantic extensions - into parallelised programs for execution on a distributed architecture. The main focus is on constructing two object-oriented models: a theoretical self-contained model of concurrency which enables a simplified second model for implementing the compiling process. There is a further presentation of principles that, if followed, maximise the potential levels of parallelism. Model of Concurrency. The concurrency model is designed to be a straightforward target for mapping sequential programs onto, thus making them parallel. It aids the compilation process by providing a high level of abstraction, including a useful model of parallel behaviour which enables easy incorporation of message interchange, locking, and synchronization of objects. Further, the model is sufficient such that a compiler can and has been practically built. Model of Compilation. The compilation-model's structure is based upon an object-oriented view of grammar descriptions and capitalises on both a recursive-descent style of processing and abstract syntax trees to perform the parsing. A composite-object view with an attribute grammar style of processing is used to extract sufficient semantic information for the parallelisation (i.e. code-generation) phase. Programming Principles. The set of principles presented are based upon information hiding, sharing and containment of objects and the dividing up of methods on the basis of a command/query division. When followed, the level of potential parallelism within the presented concurrency model is maximised. Further, these principles naturally arise from good programming practice. Summary. In summary this thesis shows that it is possible to compile well-written programs, written in a subset of Eiffel, into parallel programs without any syntactic additions or semantic alterations to Eiffel: i.e. no parallel primitives are added, and the parallel program is modelled to execute with equivalent semantics to the sequential version. If the programming principles are followed, a parallelised program achieves the maximum level of potential parallelisation within the concurrency model.