This article presents a simple mathematical model for salary structure design that enhances clarity and allows for reasonable trade-off between internal equity and external market competitiveness considerations in sal...
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Kernel fuzzy c-means (KFCM) is a significantly improved version of fuzzy c-means (FCM) for processing linearly inseparable datasets. However, for fuzzification parameter m=1, the problem of KFCM (kernel fuzzy c-means)...
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Kernel fuzzy c-means (KFCM) is a significantly improved version of fuzzy c-means (FCM) for processing linearly inseparable datasets. However, for fuzzification parameter m=1, the problem of KFCM (kernel fuzzy c-means) cannot be solved by Lagrangian optimization. To solve this problem, an equivalent model, called kernel probabilistic k-means (KPKM), is proposed here. The novel model relates KFCM to kernel k-means (KKM) in a unified mathematic framework. Moreover, the proposed KPKM can be addressed by the active gradient projection (AGP) method, which is a nonlinear programming technique with constraints of linear equalities and linear inequalities. To accelerate the AGP method, a fast AGP (FAGP) algorithm was designed. The proposed FAGP uses a maximum-step strategy to estimate the step length, and uses an iterative method to update the projection matrix. Experiments demonstrated the effectiveness of the proposed method through a performance comparison of KPKM with KFCM, KKM, FCM and k-means. Experiments showed that the proposed KPKM is able to find nonlinearly separable structures in synthetic datasets. Ten real UCI datasets were used in this study, and KPKM had better clustering performance on at least six datsets. The proposed fast AGP requires less running time than the original AGP, and it reduced running time by 76-95% on real datasets.
A common requirement in optimal control problems arising in autonomous navigation is that the decision variables are constrained to be outside certain sets. Such set exclusion constraints represent obstacles that must...
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A common requirement in optimal control problems arising in autonomous navigation is that the decision variables are constrained to be outside certain sets. Such set exclusion constraints represent obstacles that must be avoided by the motion system. This paper presents a simple and efficient method for solving optimization problems with general set exclusion and implicit constraints. The method embeds the set exclusion constraints in a quadratic penalty framework and solves the inner optimization problems using a proximal algorithm that deals directly with the implicit constraints. We derive convergence results for this method by transforming the generated iterates to points of a reformulated problem with complementarity constraints. Furthermore, the practical application of the solution method is validated in numerical simulations of a model predictive control approach to path planning for a mobile robot. Finally, a runtime comparison with state-of-the-art solvers applied to the problem with complementarity constraints illustrates the efficiency of the proposed method. (C) 2021 Elsevier Ltd. All rights reserved.
Periodic metafoundations have proven to inherit valuable properties from wave propagating in phononic periodic structures in the very low-frequency regime. Therefore, finite locally resonant metafoundations (LRMs) rep...
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Periodic metafoundations have proven to inherit valuable properties from wave propagating in phononic periodic structures in the very low-frequency regime. Therefore, finite locally resonant metafoundations (LRMs) represent a novel type of seismic isolation for ultralow-frequency applications. In this context, it is still unknown the impact that massive resonators with varying frequencies or devices with hysteretic behavior can entail on the whole system performance. For this purpose, we develop and optimize two finite locally resonant multiple degrees of freedom (MDoF) metafoundations in this paper: i) a foundation endowed with resonators, linear springs and linear viscous dampers tuned to multiple frequencies;and ii) a foundation equipped with fully nonlinear hysteretic dampers. Both are optimized considering the stochastic nature of ground motion, modelled with a modified Kanai-Tajimi filter in the stationary frequency domain, and a massive MDoF superstructure, chosen to be a fuel storage tank. In order to take all of the above-mentioned effects into account, we establish a procedure based on nonlinear programming that is able to optimize any number of parameters. More precisely, to optimize the nonlinear behavior of damper devices we employ a Bouc-Wen hysteretic model. Therefore, we reduce the nonlinear differential equations of Bouc-Wen models to a system of linear equations through the stochastic (equivalent) linearization technique. Moreover, we test the optimized systems against natural seismic records both with linear and nonlinear time history analyses. To investigate the role of hysteresis on the nonlinear band structure, we derive linearized and nonlinear dispersion relationships for the uncoupled periodic metafoundation. Finally, we obtain further detailed information on the nonlinear wave propagation by means of a spectro-spatial analysis.
A warm start method is developed for efficiently solving complex chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation. To address the computational ch...
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A warm start method is developed for efficiently solving complex chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre-Gauss-Radau collocation.
Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomp...
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ISBN:
(纸本)9781728160757
Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior point non-linear programming solution.(1)
While digital interconnectivity of smart cities has significantly enhanced the quality of life of residents, it has introduced cybersecurity challenges that may interrupt the operation of critical infrastructures. Wat...
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While digital interconnectivity of smart cities has significantly enhanced the quality of life of residents, it has introduced cybersecurity challenges that may interrupt the operation of critical infrastructures. Water distribution systems are among the most critical infrastructures in smart cities that need to be secured against potential cyberattacks. False data injection cyberattacks in water distribution systems can be designed to bypass bad data detection algorithms, generating false measurements that ultimately lead to cascading failures. Developing models for these cyberattacks and analyzing them will elucidate hidden layers and tactics used to design the attacks, helping water systems' authorities to improve and upgrade state-estimation processes and detection algorithms accordingly. In this paper, a bi-level nonlinear optimization cyberattack model is proposed that will result in sequential tank's overflow or fully withdrawn in less than three hours. The attack model is developed based upon injecting false data into the hourly measurements of the pump(s) feeding the tank, as well as the total demand of the network. By modifying a few estimation parameters in the neighborhood of the targeted tank, these false data injections are deliberately designed to bypass the existing water system's state-estimation and bad data detection methods.
This work develops an algorithm for solving nonlinear multiperiod optimization (MPO) problems using a nested Schur decomposition (NSD) approach. The NSD approach decomposes MPO using a Schur complement and allows us t...
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This work develops an algorithm for solving nonlinear multiperiod optimization (MPO) problems using a nested Schur decomposition (NSD) approach. The NSD approach decomposes MPO using a Schur complement and allows us to solve the decomposed nonlinear programming (NLP) problem in parallel. The NSD partitions the MPO into a two-level problem with individual NLPs at the lower level. In MPO problems for chemical processes, the upper problem generally has inventory, demand, and design constraints set over the entire period. The lower problem consists of a single process model for each period. The problem-level decomposition facilitates the flexible selection of the lower-level solver. For example, an efficient barrier solver such as IPOPT can be used when the problem is well-conditioned. Conversely, a robust active-set solver such as CONOPT can be selected when degeneracy exists in the problem. In this paper, the NSD approach is demonstrated with different process models for MPO under uncertain demand in both serial and parallel implementation. The solutions are also compared with the direct approach, which solves the entire MPO problem simultaneously. The demonstration shows the capability of the flexible inner solver selection with IPOPT and CONOPT. The result shows that NSD converges to the same optimum as the direct approach, regardless of the choice of the inner solver. Furthermore, IPOPT could be more efficient than CONOPT when the problem is well-conditioned. Moreover, it is noted that the NSD outperforms the direct approach when the size of the process model is large with CONOPT as the inner solver. From those results, we observe that NSD is well-suited to solve large MPO problems for chemical processes in an efficient, flexible, and robust manner. (c) 2021 Elsevier Ltd. All rights reserved.
We discuss a novel method to train a neural network from noisy data, using Optimal Transport based filtering. We show a comparative study of this methodology with three other filters: the Extended Kalman filter, the E...
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ISBN:
(数字)9781624105951
ISBN:
(纸本)9781624105951
We discuss a novel method to train a neural network from noisy data, using Optimal Transport based filtering. We show a comparative study of this methodology with three other filters: the Extended Kalman filter, the Ensemble Kalman filter, and the Unscented Kalman filter, that can also be used for the purpose of training a neural network. We empirically establish that Optimal Transport based filter performs better than the other three filters with respect to root mean square error measure, for non-Gaussian noise in the output. We demonstrate the efficacy of utilizing the Optimal Transport based filtering for neural network training in the context of predicting Mackey-Glass chaotic time series data.
作者：
Castro, Pedro M.Univ Lisbon
Ctr Matemat Aplicacoes Fundamentais & Invest Oper Fac Ciencias P-1749016 Lisbon Portugal
Non-convex quadratically constrained problems frequently appear in chemical engineering when optimizing process networks. Some of these problems can be solved to global optimality by deterministic solvers like BARON a...
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Non-convex quadratically constrained problems frequently appear in chemical engineering when optimizing process networks. Some of these problems can be solved to global optimality by deterministic solvers like BARON and ANTIGONE that mostly use linear programming relaxations coupled with spatial branch and bound. An alternative is to rely on piecewise relaxations, which work by simultaneously partitioning the domain of one variable in every bilinear term and can be significantly tighter, even when setting the number of intervals in the partitions, N, to a small value. In this short note, we generalize the mixed integer linear programming relaxation formulation from the multiparametric disaggregation technique, to benefit from a logarithmic partitioning scheme in a wide variety of settings. The idea is to select the optimal interval in the partition of a variable by using a mixed-radix numeral system, following the prime factorization of N. (c) 2021 Elsevier Ltd. All rights reserved.
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