346 research outputs found

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

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    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

    Approaching Sustainability in Engineering Design with Multiple Criteria Decision Analysis

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    This research aimed to the establishment of a general methodological framework, via which the "fuzzy" and "debatable" goal of sustainability can be practically achieved in engineering design. In-depth literature review on the sustainability concept was first conducted in an attempt to grasp its philosophical essence from various interpretations and distinct implementations. The application of the proposed framework was addressed by developing or identifying specific building block techniques, each of which accomplish a different task, such as criteria-attribute mapping, preference modeling, and search. The proposed building block techniques were selected based on systematic comparisons among a wide range of alternative methods and tested by case studies or test problems. Sustainability is a multiplex property of an integrated system. The key to make a reality of sustainability in engineering design is to properly handle its complex nature and deeply rooted conflicts. In this work, Multiple Criteria Decision Analysis (MCDA) was proven ideal for filling the vacuum of a general operational framework. To implement this framework, a four-step procedure needs to be first performed to formulate a sustainability-oriented design into a "standard" Multiple Criteria Decision Making (MCDM) problem. The proposed attribute hierarchy "Stressor-Status-Effect-Integrality-Well-being" and the 4-class metric classification scheme could help engineers to accomplish such a task in the environmental dimension. The achievement of the final "sustainable" design relies on making appropriate decisions. A MAVT-based technique developed in this study provides a rational and informed way of solving the decision problems with a discrete set of explicitly known alternatives. For Multi-Objective Programming (MOP) problems featuring an infinite and implicitly characterized alternative space, the proposed Ordinal Ranking-based Genetic Algorithm (ORGA) offers a desired searching tool by generating uniformly sampled solutions that are feasible and globally Pareto optimal.School of Chemical Engineerin

    A steepest descent method for set optimization problems with set-valued mappings of finite cardinality

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    In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent to find optimistic solutions to vector optimization problems under uncertainty with a finite uncertainty set. We develop optimality conditions for these types of problems and introduce two concepts of critical points. Furthermore, we propose a descent method and provide a convergence result to points satisfying the optimality conditions previously derived. Some numerical examples illustrating the performance of the method are also discussed. This paper is a modified and polished version of Chapter 5 in the dissertation by Quintana (On set optimization with set relations: a scalarization approach to optimality conditions and algorithms, Martin-Luther-Universität Halle-Wittenberg, 2020)

    Supervised Classification and Mathematical Optimization

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    Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data

    Optimization for Decision Making II

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    In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

    The MOEADr Package – A Component-Based Framework for Multiobjective Evolutionary Algorithms Based on Decomposition

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    Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) represent a widely used class of population-based metaheuristics for the solution of multicriteria optimization problems. We introduce the MOEADr package, which offers many of these variants as instantiations of a component-oriented framework. This approach contributes for easier reproducibility of existing MOEA/D variants from the literature, as well as for faster development and testing of new composite algorithms. The package offers an standardized, modular implementation of MOEA/D based on this framework, which was designed aiming at providing researchers and practitioners with a standard way to discuss and express MOEA/D variants. In this paper we introduce the design principles behind the MOEADr package, as well as its current components. Three case studies are provided to illustrate the main aspects of the package
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