A software system for large-scale structural optimization

This work is driven by recent developments in mathematical programming, the state-of-the-art of structural optimization, the spectacular performance of linear programming algorithms, and computer hardware developments which imply that applications of structural optimization might be used commonly in engineering design. Currently, there are few general purpose optimization routines available to the structural engineer and much of the work has addressed specific classes of problems. Further, there is little widespread use of the available routines, partly due to the large amount of familiarity one must have with the specific details of both the problem and the optimization method. In response, it is the intention here to prototype a software system that implements a general approach for structural optimization using the latest in mathematical programming techniques. This work develops a general system that can be used for a variety of structural optimization problems in a manner analogous to the finite element method for structural analysis. The most commonly used structural elements, truss and beam, are included as well as techniques for plate optimization. Consideration is given to the software requirements of a general purpose structural optimization system and the demands of large structural systems typically encountered in design practice. This general approach is aimed at using classical methods taken directly from the area of mathematical programming, specifically linear programming, which has seen considerable change in the last ten years. Here, sequential linear programming (SLP) techniques are shown to handle a wide variety of structural constraints including stress constraints, displacement constraints, buckling, and frequency constraints. It is the purpose of this thesis to bring the latest developments in linear programming to the field of structural optimization in the form of a general purpose, state-of-the-art structural optimization system. The model was tested for sample structures and it was shown to effect a reduction in total structure volume of up to 80%

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

User-friendly Support for Common Concepts in a Lightweight Verifier

Machine verification of formal arguments can only increase our confidence in the correctness of those arguments, but the costs of employing machine verification still outweigh the benefits for some common kinds of formal reasoning activities. As a result, usability is becoming increasingly important in the design of formal verification tools. We describe the "aartifact" lightweight verification system, designed for processing formal arguments involving basic, ubiquitous mathematical concepts. The system is a prototype for investigating potential techniques for improving the usability of formal verification systems. It leverages techniques drawn both from existing work and from our own efforts. In addition to a parser for a familiar concrete syntax and a mechanism for automated syntax lookup, the system integrates (1) a basic logical inference algorithm, (2) a database of propositions governing common mathematical concepts, and (3) a data structure that computes congruence closures of expressions involving relations found in this database. Together, these components allow the system to better accommodate the expectations of users interested in verifying formal arguments involving algebraic and logical manipulations of numbers, sets, vectors, and related operators and predicates. We demonstrate the reasonable performance of this system on typical formal arguments and briefly discuss how the system's design contributed to its usability in two case studies

A method for pricing American options using semi-infinite linear programming

We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these functions. The resulting problem is a linear semi-infinite programming problem, that can be solved using standard algorithms. This leads to good upper bounds for the original problem. For our algorithms no discretization of space and time and no simulation is necessary. Furthermore it is applicable even for high-dimensional problems. The algorithm provides an approximation of the value not only for one starting point, but for the complete value function on the continuation set, so that the optimal exercise region and e.g. the Greeks can be calculated. We apply the algorithm to (one- and) multidimensional diffusions and to L\'evy processes, and show it to be fast and accurate

Evolutionary multi-stage financial scenario tree generation

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper