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Fair Assortment Planning

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arXiv 2022年

作者： Chen, Qinyi Golrezaei, Negin Susan, Fransisca Operations Research Center Massachusetts Institute of Technology CambridgeMA02139 United States Sloan School of Management Massachusetts Institute of Technology CambridgeMA02139 United States

Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms often focus exclusively on achieving the platforms’ objectives, highlighting items with the highest popularity or revenue. This approach, however, can compromise the equality of opportunities for the rest of the items, in turn leading to less content diversity and increased regulatory scrutiny for the platform. Motivated by this, we introduce and study a fair assortment planning problem that enforces equality of opportunities via pairwise fairness, which requires any two items to be offered similar outcomes. We show that the problem can be formulated as a linear program (LP), called (FAIR), that optimizes over the distribution of all feasible assortments. To find a near-optimal solution to (FAIR), we propose a framework based on the Ellipsoid method, which requires a polynomial-time separation oracle to the dual of the LP. We show that finding an optimal separation oracle to the dual problem is an NP-complete problem, and hence we propose a series of approximate separation oracles, which then result in a 1/2-approx. algorithm and an FPTAS for Problem (FAIR). The approximate separation oracles are designed by (i) showing the separation oracle to the dual of the LP is equivalent to solving an infinite series of parameterized knapsack problems, and (ii) leveraging the structure of knapsack problems. Finally, we perform numerical studies on both synthetic data and real-world MovieLens data, showcasing the effectiveness of our algorithms and providing insights into the platform’s price of fairness. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms

A New Trajectory-Planning Beetle Swarm optimization Algorithm for Trajectory Planning of Robot Manipulators

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IEEE ACCESS 2019年 7卷 154331-154345页

作者： Wang, Lei Wu, Qing Lin, Fei Li, Shuai Chen, Dechao Hangzhou Dianzi Univ Dept Comp Sci & Technol Hangzhou 310018 Peoples R China Hong Kong Polytech Univ Dept Comp Hong Kong Peoples R China

Based on a heuristic optimization algorithm, this paper proposes a new algorithm named trajectory-planning beetle swarm optimization (TPBSO) algorithm for solving trajectory planning of robots, especially robot manipulators. Firstly, two specific manipulator trajectory planning problems are presented as the practical application of the algorithm, which are point-to-point planning and fixed-geometric-path planning. Then, in order to verify the effectiveness of the algorithm, this paper develops a control model and conducts numerical experiments on two planning tasks. Moreover, it compares with existing algorithms to show the superiority of our proposed algorithm. Finally, the results of numerical comparisons show that algorithm has a relatively faster computational speed and better control performance without increasing computational complexity.

关键词： Beetle swarm optimization robot manipulators trajectory planning optimization algorithms control systems

On the optimization of the support vector machine regression hyperparameters setting for gas sensors array applications

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2019年 184卷 22-27页

作者： Laref, R. Losson, E. Sava, A. Siadat, M. Univ Lorraine LCOMS EA 7306 F-57000 Metz France

Support Vector Machine Regression (SVR) has been shown to be more accurate compared to other machine learning techniques that are commonly used for chemical sensors arrays applications. However, the performance of SVR depends strongly on the selection of its hyperparameters. Most of time, researchers in this field rely on trivial grid search methods to find suitable values of SVR hyperparameters by minimizing the cross-validation prediction error. This method is not a practical solution because of the large domain of possible parameter values, which is further exacerbated by the lack of prior knowledge on the data. In this article, we investigate the optimization of SVR hyperparameters by combining the SVR algorithm with a simple algorithm for SVR parameters selection. We begin by studying the influence of each hyperparameter on SVR performance. We then propose the Generalized Pattern Search algorithm (GPS) as a faster alternative to determine these hyperparameters. Finally, we demonstrate that the proposed GPS algorithm, with its simplicity and robustness, gives similar results compared to more complicated alternatives, such as Genetic algorithms, Simulating Annealing, Bayesian optimization or Particle Swarm optimization.

关键词： Gas sensors Gas quantification Support vector machine regression optimization algorithms Generalized pattern search

Universal Online Convex optimization Meets Second-order Bounds

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arXiv 2021年

作者： Zhang, Lijun Wang, Yibo Wang, Guanghui Yi, Jinfeng Yang, Tianbao National Key Laboratory for Novel Software Technology Nanjing University China School of Artificial Intelligence Nanjing University China College of Computing Georgia Institute of Technology United States JD AI Research Beijing China Department of Computer Science and Engineering Texas A&M University United States

Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each type of functions, making it difficult to exploit the structure of the problem and utilize existing algorithms. In this paper, we propose a simple strategy for universal online convex optimization, which avoids these limitations. The key idea is to construct a set of experts to process the original online functions, and deploy a meta-algorithm over the linearized losses to aggregate predictions from experts. Specifically, the meta-algorithm is required to yield a second-order bound with excess losses, so that it can leverage strong convexity and exponential concavity to control the meta-regret. In this way, our strategy inherits the theoretical guarantee of any expert designed for strongly convex functions and exponentially concave functions, up to a double logarithmic factor. As a result, we can plug in off-the-shelf online solvers as black-box experts to deliver problem-dependent regret bounds. For general convex functions, it maintains the minimax optimality and also achieves a small-loss bound. Furthermore, we extend our universal strategy to online composite optimization, where the loss function comprises a time-varying function and a fixed regularizer. To deal with the composite loss functions, we employ a meta-algorithm based on the optimistic online learning framework, which not only possesses a second-order bound, but also can utilize estimations for upcoming loss functions. With appropriate configurations, we demonstrate that the additional regularizer does not contribute to the meta-regret, thus maintaining the universality in the composite setting. Copyright © 2021, The Authors. All rights reserved.

关键词： optimization algorithms

JamSys: Coverage optimization of a Microphone Jamming System Based on Ultrasounds

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IEEE ACCESS 2019年 7卷 67483-67496页

作者： Shen, Hao Zhang, Weiming Fang, Han Ma, Zehua Yu, Nenghai Chinese Acad Sci Univ Sci & Technol China Key Lab Electromagnet Space Informat Sch Informat Sci & Technol Hefei 230026 Anhui Peoples R China

With the development of digital devices, the recording process has become increasingly easier to conduct. However, the portability of the recording devices has also made recording difficult to monitor. If private conversations are illegally recorded, it will cause serious secret-leakage events. Therefore, it is imperative to prevent unauthorized recordings. Recent works have demonstrated that the nonlinearity effect of microphones can be leveraged to interfere with microphone recording using ultrasounds. However, an ultrasonic array has a limited jamming area. The design of an anti-recording system composed of multiple ultrasonic arrays remains to be addressed. In this paper, a jamming system, JamSys, is presented to prevent eavesdropping in a given region. We propose a new scheme composed of the angle coverage model and the modified harmony search algorithm (MHSA) to optimize the deployment of ultrasonic arrays, which achieves the maximum jamming area with the given number of arrays. In the simulation and experiments, three different optimization algorithms, the MHSA, the genetic algorithm (GA), and the regular coverage algorithm (RCA) are compared. The MHSA is demonstrated to provide the best results.

关键词： Privacy protection anti-recording microphones ultrasounds optimization algorithms

Gnowee: A Hybrid Metaheuristic optimization Algorithm for Constrained, Black Box, Combinatorial Mixed-Integer Design

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NUCLEAR TECHNOLOGY 2019年第4期205卷 542-562页

作者： Bevins, James E. Slaybaugh, R. N. Air Force Inst Technol Dept Engn Phys 2950 Hobson Way Wright Patterson AFB OH 45433 USA Univ Calif Berkeley Nucl Engn Dept 4173 Etcheverry Hall Berkeley CA 94720 USA

This paper introduces Gnowee, a modular, Python-based, open-source hybrid metaheuristic optimization algorithm (available from https://***/SlaybaughLab/Gnowee) . Gnowee is designed for rapid convergence to nearly globally optimum solutions for complex, constrained nuclear engineering problems with mixed-integer (MI) and combinatorial design vectors and high-cost, noisy, discontinuous, black box objective function evaluations. Gnowee's hybrid metaheuristic framework is a new combination of a set of diverse, robust heuristics that appropriately balance diversification and intensification strategies across a wide range of optimization problems. There are many potential applications for this novel algorithm both within the nuclear community and beyond. Given that a set of well-known and studied nuclear benchmarks does not exist for the purpose of testing optimization algorithms, comparisons between Gnowee and several well-established metaheuristic algorithms are made for a set of 18 established continuous, MI, and combinatorial benchmarks representing a wide range of types of engineering problems and solution space behaviors. These results demonstrate Gnoweee to have superior flexibility and convergence characteristics over this diverse set of design spaces. We anticipate this wide range of applicability will make this algorithm desirable for many complex engineering applications.

关键词： Evolutionary computation metaheuristic optimization algorithms

Discovering Sequenced Origami Folding Through Nonlinear Mechanics and Topology optimization

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JOURNAL OF MECHANICAL DESIGN 2019年第4期141卷 041401页

作者： Gillman, Andrew S. Fuchi, Kazuko Buskohl, Philip R. UES Inc Beavercreek OH 45432 USA Air Force Res Lab Mat & Mfg Directorate Wright Patterson AFB OH 45433 USA Univ Dayton Res Inst Appl Mech Div Dayton OH 45469 USA Air Force Res Lab Wright Patterson AFB OH 45433 USA

Origami folding provides a novel method to transform two-dimensional (2D) sheets into complex functional structures. However, the enormity of the foldable design space necessitates development of algorithms to efficiently discover new origami fold patterns with specific performance objectives. To address this challenge, this work combines a recently developed efficient modified truss finite element model with a ground structure-based topology optimization framework. A nonlinear mechanics model is required to model the sequenced motion and large folding common in the actuation of origami structures. These highly nonlinear motions limit the ability to define convex objective functions, and parallelizable evolutionary optimization algorithms for traversing nonconvex origami design problems are developed and considered. The ability of this framework to discover fold topologies that maximize targeted actuation is verified for the well-known "Chomper" and "Square Twist" patterns. A simple twist-based design is also discovered using the verified framework. Through these case studies, the role of critical points and bifurcations emanating from sequenced deformation mechanisms (including interplay of folding, facet bending, and stretching) on design optimization is analyzed. In addition, the performance of both gradient and evolutionary optimization algorithms are explored, and genetic algorithms (GAs) consistently yield solutions with better performance given the apparent nonconvexity of the response-design space.

关键词： Topology optimization Design algorithms Trusses (Building) optimization algorithms

Exact Penalization at D-Stationary Points of Cardinality- or Rank-Constrained Problem

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arXiv 2022年

作者： Yagishita, Shotaro Gotoh, Jun-Ya The Institute of Statistical Mathematics Japan Department of Data Science for Business Innovation Chuo University Japan

This paper studies the properties of d-stationary points of the trimmed lasso (Luo et al., 2013, Huang et al., 2015, and Gotoh et al., 2018) and the composite optimization problem with the truncated nuclear norm (Gao and Sun, 2010, and Zhang et al., 2012), which are known as tight relaxations of nonconvex optimization problems that have either cardinality or rank constraints, respectively. First, we extend the trimmed lasso for broader applications and for conducting a unified analysis of the property of the generalized trimmed lasso. Next, the equivalence between local optimality and d-stationarity of the generalized trimmed lasso is shown under a suitable assumption. More generally, the equivalence is shown for problems that minimize a function defined by the pointwise minimum of finitely many convex functions. Then, we present new results of the exact penalty at d-stationary points of the generalized trimmed lasso and the problem with the truncated nuclear norm penalty under mild assumptions. Our exact penalty results are not only new, but also intuitive, so that we can see what properties of the problems play a role for establishing the exact penalization. Lastly, matters relating to algorithms are also discussed. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms

Multi-Model Subset Selection

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arXiv 2022年

作者： Christidis, Anthony-Alexander Van Aelst, Stefan Zamar, Ruben Department of Statistics University of British Columbia 2207 Main Mall VancouverBCV6T 1Z4 Canada Department of Mathematics KU Leuven Celestijnenlaan 200B Leuven3001 Belgium

The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the 0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield interpretable models, in terms of prediction accuracy they are often outperformed by"blackbox" multi-model ensemble methods. A regression ensemble is introduced which combines the interpretability of sparse methods with the high prediction accuracy of ensemble methods. An algorithm is proposed to solve the joint optimization of the corresponding 0-penalized regression models by extending recent developments in 0-optimization for sparse methods to multi-model regression ensembles. The sparse and diverse models in the ensemble are learned simultaneously from the data. Each of these models provides an explanation for the relationship between a subset of predictors and the response variable. Empirical studies and theoretical knowledge about ensembles are used to gain insight into the ensemble method’s performance, focusing on the interplay between bias, variance, covariance, and variable selection. In prediction tasks, the ensembles can outperform state-of-the-art competitors on both simulated and real data. Forward stepwise regression is also generalized to multi-model regression ensembles and used to obtain an initial solution for the algorithm. The optimization algorithms are implemented in publicly available software packages. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms