96 research outputs found

    Supporting Safety Analysis of Deep Neural Networks with Automated Debugging and Repair

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    Notes on the value function approach to multiobjective bilevel optimization

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    This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization problems by a single-level multiobjective optimization problem. As a starting point, different value-function-type reformulations are suggested and their relations are discussed. Here, we focus on the situations where the lower level problem is solved up to efficiency or weak efficiency, and an intermediate solution concept is suggested as well. We study the graph-closedness of the associated efficiency-type and frontier-type mappings. These findings are then used for two purposes. First, we investigate existence results in multiobjective bilevel optimization. Second, for the derivation of necessary optimality conditions via the value function approach, it is inherent to differentiate frontier-type mappings in a generalized way. Here, we are concerned with the computation of upper coderivative estimates for the frontier-type mapping associated with the setting where the lower level problem is solved up to weak efficiency. We proceed in two ways, relying, on the one hand, on a weak domination property and, on the other hand, on a scalarization approach. Throughout the paper, illustrative examples visualize our findings, the necessity of crucial assumptions, and some flaws in the related literature.Comment: 30 page

    Multi-Objective Archiving

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    Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.Comment: 21 pages, 4 figures, journa

    MaxSAT Evaluation 2022 : Solver and Benchmark Descriptions

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    Seismic retrofitting of substandard frame buildings using steel shear walls

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    The use of steel shear panels represents an effective strategy to enhance the seismic performance of substandard framed buildings not designed to resist earthquakes. The seismic response of framed structures equipped with steel walls can be predicted using finite element models with accurate shell elements for representing the steel panels. However, such a detailed numerical description requires significant computational resources, especially for nonlinear dynamic analysis of large retrofitted buildings with steel infill plates. Besides, the design of steel shear walls for seismic retrofitting has been addressed mainly by trial-and-error methods in previous research and practical applications. Therefore, there is a clear need for more simplified and efficient numerical models for accurate simulations of steel shear walls under earthquake loading and enhanced seismic retrofitting design procedures with automatic selection of the retrofitting components. In this research, an 8-noded macroelement formulation is first proposed incorporating six nonlinear springs with asymmetric constitutive relationships. To improve the macroelement performance, material parameters are calibrated via genetic algorithms (GAs) based on the numerical results from validated shell element models. Subsequently, simple functions for macroelement material parameters in terms of steel plate geometrical properties are determined using multiple linear regressions. Applications to numerical examples have confirmed the accuracy and computational efficiency of the proposed macroelement with calibrated material properties. An improved optimal seismic retrofitting design procedure utilising steel shear wall macroelements is developed based on the capacity spectrum method. The proposed approach regards the selection and design of infill plates as a multi-objective optimisation problem with constraints solved by GA procedures. Nonlinear regression for equivalent viscous damping of steel shear walls is also carried out to determine the hysteretic damping ratio as a function of plate dimensions and drift demand. Afterwards, the proposed optimal design strategy is applied to the seismic retrofitting of a deficient 4-storey RC frame building. Seismic assessment is finally conducted for the retrofitted structure, where a significant enhancement of the seismic performance is observed.Open Acces

    Game Theory

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    The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner

    Mobile Ad-Hoc Networks

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    Being infrastructure-less and without central administration control, wireless ad-hoc networking is playing a more and more important role in extending the coverage of traditional wireless infrastructure (cellular networks, wireless LAN, etc). This book includes state-of-the-art techniques and solutions for wireless ad-hoc networks. It focuses on the following topics in ad-hoc networks: quality-of-service and video communication, routing protocol and cross-layer design. A few interesting problems about security and delay-tolerant networks are also discussed. This book is targeted to provide network engineers and researchers with design guidelines for large scale wireless ad hoc networks

    The Routledge Handbook of Philosophy of Economics

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    The most fundamental questions of economics are often philosophical in nature, and philosophers have, since the very beginning of Western philosophy, asked many questions that current observers would identify as economic. The Routledge Handbook of Philosophy of Economics is an outstanding reference source for the key topics, problems, and debates at the intersection of philosophical and economic inquiry. It captures this field of countless exciting interconnections, affinities, and opportunities for cross-fertilization. Comprising 35 chapters by a diverse team of contributors from all over the globe, the Handbook is divided into eight sections: I. Rationality II. Cooperation and Interaction III. Methodology IV. Values V. Causality and Explanation VI. Experimentation and Simulation VII. Evidence VIII. Policy The volume is essential reading for students and researchers in economics and philosophy who are interested in exploring the interconnections between the two disciplines. It is also a valuable resource for those in related fields like political science, sociology, and the humanities.</p

    Techniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition

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    Many real-world applications involve multiple competing objectives, but due to conflict between the objectives, it is generally impossible to find a feasible solution that optimizes all, simultaneously. In contrast to single objective optimization, the goal in multiobjective optimization is to generate a set of solutions that induces the nondominated (ND) frontier. This thesis presents two techniques for multiobjective optimization problems with discrete decision variables. First, the Boxed Line Method is an exact, criterion space search algorithm for biobjective mixed integer programs (Chapter 2). A basic version of the algorithm is presented with a recursive variant and other enhancements. The basic and recursive variants permit complexity analysis, which yields the first complexity results for this class of algorithms. Additionally, a new instance generation method is presented, and a rigorous computational study is conducted. Second, a novel weight space decomposition method for integer programs with three (or more) objectives is presented with unique geometric properties (Chapter 3). The weighted Tchebychev scalarization used for this weight space decomposition provides the benefit of including unsupported ND images but at the cost of convexity of weight set components. This work proves convexity-related properties of the weight space components, including star-shapedness. Further, a polytopal decomposition is used to properly define dimension for these nonconvex components. The weighted Tchebychev weight set decomposition is then applied as a “dual” perspective on the class of multiobjective “primal” algorithms (Chapter 4). It is shown that existing algorithms do not yield enough information for a complete decomposition, and the necessary modifications required to yield the missing information is proven. Modifications for primal algorithms to compute inner and outer approximations of the weight space components are presented. Lastly, a primal algorithm is restricted to solving for a subset of the ND frontier, where this subset represents the compromise between multiple decision makers’ weight vectors.Ph.D
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