Principles, Opportunism and Seeing in Design: A Computational Approach

This thesis introduces elements of a theory of design activity and a computational framework for developing design systems. The theory stresses the opportunistic nature of designing and the complementary roles of focus and distraction, the interdependence of evaluation and generation, the multiplicity of ways of seeing over the history of a design session versus the exclusivity of a given way of seeing over an arbitrarily short period, and the incommensurability of criteria used to evaluate a design. The thesis argues for a principle based rather than rule based approach to designing documents. The Discursive Generator is presented as a computational framework for implementing specific design systems, and a simple system for arranging blocks according to a set of formal principles is developed by way of illustration. Both shape grammars and constraint based systems are used to contrast current trends in design automation with the discursive approach advocated in the thesis. The Discursive Generator is shown to have some important properties lacking in other types of systems, such as dynamism, robustness and the ability to deal with partial designs. When studied in terms of a search metaphor, the Discursive Generator is shown to exhibit behavior which is radically different from some traditional search techniques, and to avoid some of the well-known difficulties associated with them.

On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice