Advances in design and implementation of optimization software

Developing optimization software that is capable of solving large and complex real-life problems is a huge effort. It is based on a deep knowledge of four areas: theory of optimization algorithms, relevant results of computer science, principles of software engineering, and computer technology. The paper highlights the diverse requirements of optimization software and introduces the ingredients needed to fulfill them. After a review of the hardware/software environment it gives a survey of computationally successful techniques for continuous optimization. It also outlines the perspective offered by parallel computing, and stresses the importance of optimization modeling systems. The inclusion of many references is intended to both give due credit to results in the field of optimization software and help readers obtain more detailed information on issues of interest

Calculation of chemical and phase equilibria

Bibliography: pages 167-169.The computation of chemical and phase equilibria is an essential aspect of chemical engineering design and development. Important applications range from flash calculations to distillation and pyrometallurgy. Despite the firm theoretical foundations on which the theory of chemical equilibrium is based there are two major difficulties that prevent the equilibrium state from being accurately determined. The first of these hindrances is the inaccuracy or total absence of pertinent thermodynamic data. The second is the complexity of the required calculation. It is the latter consideration which is the sole concern of this dissertation

Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods

Analysis of large scale linear programming problems with embedded network structures: Detection and solution algorithms

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Linear programming (LP) models that contain a (substantial) network structure frequently arise in many real life applications. In this thesis, we investigate two main questions; i) how an embedded network structure can be detected, ii) how the network structure can be exploited to create improved sparse simplex solution algorithms. In order to extract an embedded pure network structure from a general LP problem we develop two new heuristics. The first heuristic is an alternative multi-stage generalised upper bounds (GUB) based approach which finds as many GUB subsets as possible. In order to identify a GUB subset two different approaches are introduced; the first is based on the notion of Markowitz merit count and the second exploits an independent set in the corresponding graph. The second heuristic is based on the generalised signed graph of the coefficient matrix. This heuristic determines whether the given LP problem is an entirely pure network; this is in contrast to all previously known heuristics. Using generalised signed graphs, we prove that the problem of detecting the maximum size embedded network structure within an LP problem is NP-hard. The two detection algorithms perform very well computationally and make positive contributions to the known body of results for the embedded network detection. For computational solution a decomposition based approach is presented which solves a network problem with side constraints. In this approach, the original coefficient matrix is partitioned into the network and the non-network parts. For the partitioned problem, we investigate two alternative decomposition techniques namely, Lagrangean relaxation and Benders decomposition. Active variables identified by these procedures are then used to create an advanced basis for the original problem. The computational results of applying these techniques to a selection of Netlib models are encouraging. The development and computational investigation of this solution algorithm constitute further contribution made by the research reported in this thesis.This study is funded by the Turkish Educational Council and Mugla University

Computational analysis of real-time convex optimization for control systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000.Includes bibliographical references (p. 177-189).Computational analysis is fundamental for certification of all real-time control software. Nevertheless, analysis of on-line optimization for control has received little attention to date. On-line software must pass rigorous standards in reliability, requiring that any embedded optimization algorithm possess predictable behavior and bounded run-time guarantees. This thesis examines the problem of certifying control systems which utilize real-time optimization. A general convex programming framework is used, to which primal-dual path-following algorithms are applied. The set of all optimization problem instances which may arise in an on-line procedure is characterized as a compact parametric set of convex programming problems. A method is given for checking the feasibility and well-posedness of this compact set of problems, providing certification that every problem instance has a solution and can be solved in finite time. The thesis then proposes several algorithm initialization methods, considering the fixed and time-varying constraint cases separately. Computational bounds are provided for both cases. In the event that the computational requirements cannot be met, several alternatives to on-line optimization are suggested. Of course, these alternatives must provide feasible solutions with minimal real-time computational overhead. Beyond this requirement, these methods approximate the optimal solution as well as possible. The methods explored include robust table look-up, functional approximation of the solution set, and ellipsoidal approximation of the constraint set. The final part of this thesis examines the coupled behavior of a receding horizon control scheme for constrained linear systems and real-time optimization. The driving requirement is to maintain closed-loop stability, feasibility and well-posedness of the optimal control problem, and bounded iterations for the optimization algorithm. A detailed analysis provides sufficient conditions for meeting these requirements. A realistic example of a small autonomous air vehicle is furnished, showing how a receding horizon control law using real-time optimization can be certified.by Lawrence Kent McGovern.Ph.D

User-Oriented Methodology and Techniques of Decision Analysis and Support

This volume contains 26 papers selected from Workshop presentations. The book is divided into two sections; the first is devoted to the methodology of decision analysis and support and related theoretical developments, and the second reports on the development of tools -- algorithms, software packages -- for decision support as well as on their applications. Several major contributions on constructing user interfaces, on organizing intelligent DSS, on modifying theory and tools in response to user needs -- are included in this volume