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

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.Siirretty Doriast

Robust Control Structure Selection

Screening tools for control structure selection in the presence of model/plant mismatch are developed in the context of the Structured Singular Value (μ) theory. The developed screening tools are designed to aid engineers in the elimination of undesirable control structure candidates for which a robustly performing controller does not exist. Through application on a multicomponent distillation column, it is demonstrated that the developed screening tools can be effective in choosing an appropriate control structure while previously existing methods such as the Condition Number Criterion can lead to erroneous results

Component-based synthesis of motion planning algorithms

Combinatory Logic Synthesis generates data or runnable programs according to formal type specifications. Synthesis results are composed based on a user-specified repository of components, which brings several advantages for representing spaces of high variability. This work suggests strategies to manage the resulting variations by proposing a domain-specific brute-force search and a machine learning-based optimization procedure. The brute-force search involves the iterative generation and evaluation of machining strategies. In contrast, machine learning optimization uses statistical models to enable the exploration of the design space. The approaches involve synthesizing programs and meta-programs that manipulate, run, and evaluate programs. The methodologies are applied to the domain of motion planning algorithms, and they include the configuration of programs belonging to different algorithmic families. The study of the domain led to the identification of variability points and possible variations. Proof-of-concept repositories represent these variability points and incorporate them into their semantic structure. The selected algorithmic families involve specific computation steps or data structures, and corresponding software components represent possible variations. Experimental results demonstrate that CLS enables synthesis-driven domain-specific optimization procedures to solve complex problems by exploring spaces of high variability.Combinatory Logic Synthesis (CLS) generiert Daten oder lauffähige Programme anhand von formalen Typspezifikationen. Die Ergebnisse der Synthese werden auf Basis eines benutzerdefinierten Repositories von Komponenten zusammengestellt, was diverse Vorteile für die Beschreibung von Räumen mit hoher Variabilität mit sich bringt. Diese Arbeit stellt Strategien für den Umgang mit den resultierenden Variationen vor, indem eine domänen-spezifische Brute-Force Suche und ein maschinelles Lernverfahren für die Untersuchung eines Optimierungsproblems aufgezeigt werden. Die Brute-Force Suche besteht aus der iterativen Generierung und Evaluation von Frässtrategien. Im Gegensatz dazu nutzt der Optimierungsansatz statistische Modelle zur Erkundung des Entwurfsraums. Beide Ansätze synthetisieren Programme und Metaprogramme, welche Programme bearbeiten, ausführen und evaluieren. Diese Methoden werden auf die Domäne der Bewegungsplanungsalgorithmen angewendet und sie beinhalten die Konfiguration von Programmen, welche zu unterschiedlichen algorithmischen Familien gehören. Die Untersuchung der Domäne führte zur Identifizierung der Variabilitätspunkte und der möglichen Variationen. Entsprechende Proof of Concept Implementierungen in Form von Repositories repräsentieren jene Variabilitätspunkte und beziehen diese in ihre semantische Struktur ein. Die gewählten algorithmischen Familien sehen bestimmte Berechnungsschritte oder Datenstrukturen vor, und entsprechende Software Komponenten stellen mögliche Variationen dar. Versuchsergebnisse belegen, dass CLS synthese-getriebene domänenspezifische Optimierungsverfahren ermöglicht, welche komplexe Probleme durch die Exploration von Räumen hoher Variabilität lösen

A frequency-domain full waveform inversion method of elastic waves in quantitative defection investigation

857-866Full waveform inversion is a challenging data-fitting procedure based on full wave field modeling to extract quantitative information on elastic properties of subsurface structures. We developed a frequency-domain full-waveform inversion method of elastic waves for stratified media, adopting a quasi-linearization method coupled with a random search algorithm. The inversion process of this method is irrelevant to hypocenter function and can be considered as a kind of combination between the heuristic and non-heuristic inversion methods. To verify our method, we apply it to three numerical two-dimensional models with different intermediate structures (dipping, arched and hollow), and their structures are well revealed. With some pretreatments on response waveforms, such as filtering, normalization and correlation analysis, the full-waveform inversion method is extended to models with damaged area and its feasibility and accuracy verified. Alignment of full waveform inversion method and its cost of computing, several strategies exist to treat this quantitative detecting problem. In Chengdu-Chongqing guest emergency project, the application of full waveform inversion method saves a lot of time. In this method, each section only needs 2 detectors and only need to be hammered twice, while the traditional CT (Computed Tomography) test requires 11 detection filters and at least 11 hammering, and each section has 121 waveform data. In some cases, we can obtain some important priori information through field investigation. The priori information can be used to accelerate the inversion process

A Hierarchal Planning Framework for AUV Mission Management in a Spatio-Temporal Varying Ocean

The purpose of this paper is to provide a hierarchical dynamic mission planning framework for a single autonomous underwater vehicle (AUV) to accomplish task-assign process in a limited time interval while operating in an uncertain undersea environment, where spatio-temporal variability of the operating field is taken into account. To this end, a high level reactive mission planner and a low level motion planning system are constructed. The high level system is responsible for task priority assignment and guiding the vehicle toward a target of interest considering on-time termination of the mission. The lower layer is in charge of generating optimal trajectories based on sequence of tasks and dynamicity of operating terrain. The mission planner is able to reactively re-arrange the tasks based on mission/terrain updates while the low level planner is capable of coping unexpected changes of the terrain by correcting the old path and re-generating a new trajectory. As a result, the vehicle is able to undertake the maximum number of tasks with certain degree of maneuverability having situational awareness of the operating field. The computational engine of the mentioned framework is based on the biogeography based optimization (BBO) algorithm that is capable of providing efficient solutions. To evaluate the performance of the proposed framework, firstly, a realistic model of undersea environment is provided based on realistic map data, and then several scenarios, treated as real experiments, are designed through the simulation study. Additionally, to show the robustness and reliability of the framework, Monte-Carlo simulation is carried out and statistical analysis is performed. The results of simulations indicate the significant potential of the two-level hierarchical mission planning system in mission success and its applicability for real-time implementation