Adaptive Pareto Set Estimation for Stochastic Mixed Variable Design Problems

Many design problems require the optimization of competing objective functions that may be too complicated to solve analytically. These problems are often modeled in a simulation environment where static input may result in dynamic (stochastic) responses to the various objective functions. System reliability, alloy composition, algorithm parameter selection, and structural design optimization are classes of problems that often exhibit such complex and stochastic properties. Since the physical testing and experimentation of new designs can be prohibitively expensive, engineers need adequate predictions concerning the viability of various designs in order to minimize wasteful testing. Presumably, an appropriate stochastic multi-objective optimizer can be used to eliminate inefficient designs through the analysis of simulated responses. This research develops an adaptation of Walston’s [56] Stochastic Multi-Objective Mesh Adaptive Direct Search (SMOMADS) and Paciencia’s NMADS [45] based on Kim and de Weck’s [34] Adaptive Weighted Sum (AWS) procedure and standard distance to a reference point methods. This new technique is compared to standard heuristic based methods used to evaluate several real-world design problems. The main contribution of this paper is a new implementation of MADS for Mixed Variable and Stochastic design problems that drastically reduces dependence on subjective decision maker interaction

Optimal Control of Fully Routed Air Traffic in the Presence of Uncertainty and Kinodynamic Constraints

A method is presented to extend current graph-based Air Traffic Management optimization frameworks. In general, Air Traffic Management is the process of guiding a finite set of aircraft, each along its pre-determined path within some local airspace, subject to various physical, policy, procedural and operational restrictions. This research addresses several limitations of current graph-based Air Traffic Management optimization methods by incorporating techniques to account for stochastic effects, physical inertia and variable arrival sequencing. In addition, this research provides insight into the performance of multiple methods for approximating non-differentiable air traffic constraints, and incorporates these methods into a generalized weighted-sum representation of the multi-objective Air Traffic Management optimization problem that minimizes the total time of flight, deviation from scheduled arrival time and fuel consumption of all aircraft. The methods developed and tested throughout this dissertation demonstrate the ability of graph-based optimization techniques to model realistic air traffic restrictions and generate viable control strategies

Implementing Conditional Inequality Constraints for Optimal Collision Avoidance

Current Federal Aviation Administration regulations require that passing aircraft must either meet a specified horizontal or vertical separation distance. However, solving for optimal avoidance trajectories with conditional inequality path constraints is problematic for gradient-based numerical nonlinear programming solvers since conditional constraints typically possess non-differentiable points. Further, the literature is silent on robust treatment of approximation methods to implement conditional inequality path constraints for gradient-based numerical nonlinear programming solvers. This paper proposes two efficient methods to enforce conditional inequality path constraints in the optimal control problem formulation and compares and contrasts these approaches on representative airborne avoidance scenarios. The first approach is based on a minimum area enclosing superellipse function and the second is based on use of sigmoid functions. These proposed methods are not only robust, but also conservative, that is, their construction is such that the approximate feasible region is a subset of the true feasible region. Further, these methods admit analytically derived bounds for the over-estimation of the infeasible region with a demonstrated maximum error of no greater than 0.3% using the superellipse method, which is less than the resolution of typical sensors used to calculate aircraft position or altitude. However, the superellipse method is not practical in all cases to enforce conditional inequality path constraints that may arise in the nonlinear airborne collision avoidance problem. Therefore, this paper also highlights by example when the use of sigmoid functions are more appropriate

Tracing postrepresentational visions of the city: representing the unrepresentable Skateworlds of Tyneside

In any visualisation of the city more is left unseen than made visible. Contemporary visualisations of the city are increasingly influenced by quantification, and thus anything which cannot be quantified is hidden. In contrast, we explore the use of ‘lo-fi’, doodled, participatory maps made by skateboarders in Tyneside, England, as a means to represent their cityscape. Drawing on established work an skateboarding and recent developments in cartography, we argue that skateboarders understand the city from a postrepresentational perspective. Such a framing presents a series of challenges to map their worlds which we explore through a processual account of our mapmaking practice. In this process we chart how skateboarders’ mappings became part of a more significant interplay of performance, identity, visualisation, and exhibition. The paper makes contributions to the emerging field of postrepresentational cartography and argues that its processual focus provides useful tools to understand how visions of the city are produced

Identifying single copy orthologs in Metazoa

The identification of single copy (1-to-1) orthologs in any group of organisms is important for functional classification and phylogenetic studies. The Metazoa are no exception, but only recently has there been a wide-enough distribution of taxa with sufficiently high quality sequenced genomes to gain confidence in the wide-spread single copy status of a gene. Here, we present a phylogenetic approach for identifying overlooked single copy orthologs from multigene families and apply it to the Metazoa. Using 18 sequenced metazoan genomes of high quality we identified a robust set of 1,126 orthologous groups that have been retained in single copy since the last common ancestor of Metazoa. We found that the use of the phylogenetic procedure increased the number of single copy orthologs found by over a third more than standard taxon-count approaches. The orthologs represented a wide range of functional categories, expression profiles and levels of divergence. To demonstrate the value of our set of single copy orthologs, we used them to assess the completeness of 24 currently published metazoan genomes and 62 EST datasets. We found that the annotated genes in published genomes vary in coverage from 79% (Ciona intestinalis) to 99.8% (human) with an average of 92%, suggesting a value for the underlying error rate in genome annotation, and a strategy for identifying single copy orthologs in larger datasets. In contrast, the vast majority of EST datasets with no corresponding genome sequence available are largely under-sampled and probably do not accurately represent the actual genomic complement of the organisms from which they are derived