Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.Siirretty Doriast

Boosting Randomized Smoothing with Variance Reduced Classifiers

Randomized Smoothing (RS) is a promising method for obtaining robustness certificates by evaluating a base model under noise. In this work, we: (i) theoretically motivate why ensembles are a particularly suitable choice as base models for RS, and (ii) empirically confirm this choice, obtaining state-of-the-art results in multiple settings. The key insight of our work is that the reduced variance of ensembles over the perturbations introduced in RS leads to significantly more consistent classifications for a given input. This, in turn, leads to substantially increased certifiable radii for samples close to the decision boundary. Additionally, we introduce key optimizations which enable an up to 55-fold decrease in sample complexity of RS, thus drastically reducing its computational overhead. Experimentally, we show that ensembles of only 3 to 10 classifiers consistently improve on their strongest constituting model with respect to their average certified radius (ACR) by 5% to 21% on both CIFAR10 and ImageNet, achieving a new state-of-the-art ACR of 0.86 and 1.11, respectively. We release all code and models required to reproduce our results upon publication

Robustness of resource allocation in parallel and distributed computing systems, The

Includes bibliographical references (page [9]).This paper gives an overview of the material to be discussed in the invited keynote presentation by H. J. Siegel; it summarizes our research in [1]. Performing computing and communication tasks on parallel and distributed systems involves the coordinated use of different types of machines, networks, interfaces, and other resources. Decisions about how best to allocate resources are often based on estimated values of task and system parameters, due to uncertainties in the system environment. An important research problem is the development of resource management strategies that can guarantee a particular system performance given such uncertainties. We have designed a methodology for deriving the degree of robustness of a resource allocation - the maximum amount of collective uncertainty in system parameters within which a user-specified level of system performance (QoS) can be guaranteed. Our four-step procedure for deriving a robustness metric for an arbitrary system will be presented. We will illustrate this procedure and its usefulness by deriving robustness metrics for some example distributed systems

The Robustness of Resource Allocation in Parallel and Distributed Computing Systems

This paper gives an overview of the material to be discussed in the invited keynote presentation by H. J. Siegel. Performing computing and communication tasks on parallel and distributed systems involves the coordinated use of different types of machines, networks, interfaces, and other resources. Decisions about how best to allocate resources are often based on estimated values of task and system parameters, due to uncertainties in the system environment. An important research problem is the development of resource management strategies that can guarantee a particular system performance given such uncertainties. We have designed a methodology for deriving the degree of robustness of a resource allocation - the maximum amount of collective uncertainty in system parameters within which a user-specified level of system performance (QoS) can be guaranteed. Our four-step procedure for deriving a robustness metric for an arbitrary system will be presented. We will illustrate this procedure and its usefulness by deriving robustness metrics for some example distributed systems

Broadcast Scheduling in Interference Environment

Broadcast is a fundamental operation in wireless networks, and nai¨ve flooding is not practical, because it cannot deal with interference. Scheduling is a good way of avoiding interference, but previous studies on broadcast scheduling algorithms all assume highly theoretical models such as the unit disk graph model. In this work, we reinvestigate this problem by using the 2-Disk and the signal-to-interference-plus-noise-ratio (SINR) models. We first design a constant approximation algorithm for the 2-Disk model and then extend it to the SINR model. This result, to the best of our knowledge, is the first result on broadcast scheduling algorithms in the SINR model

UWB MAC Design Constraints and Considerations

In this paper, we consider the possibility of developing an optimal medium access control (MAC)layer for high data rate ultra-wideband (UWB) transmission systems that transmit minimal power. MAC in UWB wireless networks is required to coordinate channel access among competing devices. The unique UWB characteristics offer great challenges and opportunities in effective UWB MAC design. We first study the background of UWB and available MAC protocols that have been used in UWB. Secondly, we explore the constraints on UWB MAC design. Finally we present the considerations that need to be made in designing an optimal UWB MAC protocol

Robustness of Mission Plans for Unmanned Aircraft.

This thesis studies the robustness of optimal mission plans for unmanned aircraft. Mission planning typically involves tactical planning and path planning. Tactical planning refers to task scheduling and in multi aircraft scenarios also includes establishing a communication topology. Path planning refers to computing a feasible and collision-free trajectory. For a prototypical mission planning problem, the traveling salesman problem on a weighted graph, the robustness of an optimal tour is analyzed with respect to changes to the edge costs. Specifically, the stability region of an optimal tour is obtained, i.e., the set of all edge cost perturbations for which that tour is optimal. The exact stability region of solutions to variants of the traveling salesman problems is obtained from a linear programming relaxation of an auxiliary problem. Edge cost tolerances and edge criticalities are derived from the stability region. For Euclidean traveling salesman problems, robustness with respect to perturbations to vertex locations is considered and safe radii and vertex criticalities are introduced. For weighted-sum multi-objective problems, stability regions with respect to changes in the objectives, weights, and simultaneous changes are given. Most critical weight perturbations are derived. Computing exact stability regions is intractable for large instances. Therefore, tractable approximations are desirable. The stability region of solutions to relaxations of the traveling salesman problem give under approximations and sets of tours give over approximations. The application of these results to the two-neighborhood and the minimum 1-tree relaxation are discussed. Bounds on edge cost tolerances and approximate criticalities are obtainable likewise. A minimum spanning tree is an optimal communication topology for minimizing the cumulative transmission power in multi aircraft missions. The stability region of a minimum spanning tree is given and tolerances, stability balls, and criticalities are derived. This analysis is extended to Euclidean minimum spanning trees. This thesis aims at enabling increased mission performance by providing means of assessing the robustness and optimality of a mission and methods for identifying critical elements. Examples of the application to mission planning in contested environments, cargo aircraft mission planning, multi-objective mission planning, and planning optimal communication topologies for teams of unmanned aircraft are given.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120837/1/mniendo_1.pd