Linear, integer separable and fuzzy programming problems: a united approach towards automatic reformulation

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper modelling techniques that allow logical restrictions to be modelled in integer programming terms are described and their implications discussed. In addition it is demonstrated that many classes of non-linearities which are not variable separable may be after suitable algebraic manipulation put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a Max-Min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programs, reformulation of nonlinear programs as variable separable programs and reformulation of fuzzy linear programs. It is observed that as well as incorporating an interface between the modeller and the optimiser there is a need to make available to the modeller software facilities which support the model reformulation techniques described here

The Utility of Nonlinear Programming Algorithms: A Comparative Study -- Part I

A comprehensive comparative study of nonlinear programming algorithms, as applied to problems in engineering design, is presented. Linear approximation methods, interior penalty and exterior penalty methods were tested on a set of thirty problems and are rated on their ability to solve problems within a reasonable amount of computational time. In this paper we discuss the organization and conduct of the study, and in a companion paper, we give numerical results and algorithm performance curves

Determination of Cost-Effective Range in Surface Finish for Single Pass Turning

Surface finish is considered a critical characteristic for manufacturing components when manufacturers strive to produce components with high-quality characteristics predefined by design engineers. The objective of this research is to provide a cost-effective range in surface finish for single pass turning that enables the design engineers to explore a wider spectrum of alternative solutions without significantly affecting the functionality of the part. Apart from the one optimal solution, the proposed methodology, which is based on Geometric Programming, would provide a range of cutting conditions solutions that satisfy the economic and functional needs for the designer. This can be achieved by switching cost reduction focus from tooling to labor cost, particularly by adjusting variables values such as spindle speed and feed. An algorithm has been developed to find the new variables values. In addition, a sensitivity analysis model, based on metaheuristic techniques, will also be developed to further give a set of possible solutions that are practically preferable to the practitioners. In addition, the developed methodology can be applied to other engineering applications. The proposed methodology will provide a tool that enhances the design for manufacturability for companies to become more competitive

An investigation of computer based tools for mathematical programming modelling

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Science and Engineering Research Counci

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact setThis research was supported by National Science Foundation grant DDMo9204208, Department of Energy grant DE-FG03-92ER25117, Office of Naval Research grant N00014-90-J-1242, and the Bank of SpainPublicad