We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, cons...
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We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns out to be difficult in the presence of switching costs or switching constraints as the underlying problem is an Integer Program. We therefore reformulate the rounding problem into a shortest path problem on a parameterized family of directed acyclic graphs (DAGs). Solving the shortest path problem then allows to minimize switching costs and still maintain approximability with respect to the tunable DAG parameter theta. We provide a proof of a runtime bound on equidistant rounding grids, where the bound is linear in time discretization granularity and polynomial in theta. The efficacy of our approach is demonstrated by a comparison with an integer programming approach on a benchmark problem.
We present a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit -cycle oscillators. Our method is based on phase reduction that provides a...
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We present a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit -cycle oscillators. Our method is based on phase reduction that provides a concise low -dimensional representation of the synchronization dynamics of mutually coupled oscillators, including the case where the coupling depends on past time series of the oscillators. We first describe a method for a pair of identical oscillators and then generalize it to the case of slightly nonidentical oscillators. The coupling function is designed in two optimization steps for the functional form and amplitude, where the amplitude is numerically optimized to minimize the average convergence time under a constraint on the total power. We perform numerical simulations of the synchronization dynamics with the optimized coupling functions using the FitzHugh-Nagumo and R & ouml;ssler oscillators as examples. We show that the coupling function optimized by the present method can achieve global synchronization more efficiently than those obtained by the previous methods.
Optimal repair-replacement problem is an important aspect of economic decision making at the firm and aggregate levels. In this paper, we extend the continuous time optimal replacement model in the firm under technolo...
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Optimal repair-replacement problem is an important aspect of economic decision making at the firm and aggregate levels. In this paper, we extend the continuous time optimal replacement model in the firm under technological progress by considering the possibility of repairing/replacing the machines during their lifetime period. In our model, two possible decisions can be recognized by the managers in which the machines are repaired under the efficiency condition or replaced under the availability of technological progress in the firm. As a special case, we restrict the model to the more real case in which all the growth, purchase price and repair cost functions are assumed to be in the exponential form. The solvability of the model in this case is also discussed. (C) 2013 Elsevier B.V. All rights reserved.
In order to achieve robot trajectory tracking in fixed-time, a novel fixed-time zeroing neural network model is designed. Initially, the inverse kinematic model of robot trajectory tracking is translated into a time-v...
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In order to achieve robot trajectory tracking in fixed-time, a novel fixed-time zeroing neural network model is designed. Initially, the inverse kinematic model of robot trajectory tracking is translated into a time-varying quadratic programs problem. Subsequently, a novel fixed-time zeroing neural network is proposed for solving the time-varying quadratic programs problem. Furthermore, the fixed-time stability of this model is rigorously established, and an upper bound of convergence time, irrespective of the initial point, is estimated. Finally, numerical simulation results underscore the efficacy of the proposed methodologies. A novel fixed-time zeroing neural network model is designed to robot trajectory tracking by solving the time-varying quadratic programs problem. While, its fixed-time stability is proven and the upper bound of convergence time independent of initial point is estimated. image
This paper considers the capacitated facility location problem with convex and differentiable production costs functions, an optimization problem that finds numerous real-world applications such as queues in call-cent...
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This paper considers the capacitated facility location problem with convex and differentiable production costs functions, an optimization problem that finds numerous real-world applications such as queues in call-centers, server queuing or when production is pushed beyond normal capacity limits leading to over proportional growth in production costs. As opposed to most other solution methods for this and similar problems, we propose an exact method that instead of linearizing the cost functions deals directly with the nonlinear costs. To this end, we use a Lagrangian relaxation of the demand constraints leading to a Lagrangian subproblem with a nonlinear objective function. The Lagrangian dual is (approximately) solved by means of subgradient optimization. Proven optimal solutions to the facility location problem are then found by employing this lower bounding scheme in a branch and bound algorithm. We use this method for solving a large number of test problem instances with production costs that either follow a quadratic or an inverse cost function. Our computational experiments show that the proposed solution method is in most cases superior to other solution methods for this problem. (C) 2020 Elsevier B.V. All rights reserved.
Orbit prediction is crucial for space situational awareness operations. Low earth orbit satellites are subjected to external forces such as atmospheric drag, radiation, and gravity. However, the well-known Kepler prop...
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Orbit prediction is crucial for space situational awareness operations. Low earth orbit satellites are subjected to external forces such as atmospheric drag, radiation, and gravity. However, the well-known Kepler propagation model ignores these external forces. The simplified perturbation model included only the main external forces. In this study, a nonlinear programming model for orbit prediction using public two-line elements (TLE) is proposed. It has been proven that our models exhibit better performance than the standard Kepler and SPG4 models in terms of orbit prediction accuracy. Moreover, the proposed models were simple, computationally effective, and robust to disturbances. The sensitivity analysis indicates that a right ascension of the ascending node, a perigee argument, and a mean anomaly of the orbital elements are the most sensitive parameters in our models. The results also revealed that our method can be generalized to any low-earth orbit satellite with adequate data.
This paper addresses a multi-product integrated lot-sizing and pricing problem for an entity which produces and sells different products under a finite production capacity constraint. The demands for each product is a...
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This paper addresses a multi-product integrated lot-sizing and pricing problem for an entity which produces and sells different products under a finite production capacity constraint. The demands for each product is assumed to be linear and takes into account the complementarity or substitution characteristics of the products. The objective is to find prices and the production planning (productions quantities, inventory level, setups configuration) for each product during several time periods to maximize the profit. The problem is formulated as a mixed integer nonlinear model with the consideration of different constraints related to production capacity and setup costs. Some new theoretical properties regarding the convexity of the problem and its relaxation are established. Finally, numerical examples are presented to illustrate the obtained results. Copyright (C) 2022 The Authors.
Purpose Ensemble models that combine multiple base classifiers have been widely used to improve prediction performance in credit risk evaluation. However, an arbitrary selection of base classifiers is problematic. The...
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Purpose Ensemble models that combine multiple base classifiers have been widely used to improve prediction performance in credit risk evaluation. However, an arbitrary selection of base classifiers is problematic. The purpose of this paper is to develop a framework for selecting base classifiers to improve the overall classification performance of an ensemble model. Design/methodology/approach In this study, selecting base classifiers is treated as a feature selection problem, where the output from a base classifier can be considered a feature. The proposed correlation-based classifier selection using the maximum information coefficient (MIC-CCS), a correlation-based classifier selection under the maximum information coefficient method, selects the features (classifiers) using nonlinear optimization programming, which seeks to optimize the relationship between the accuracy and diversity of base classifiers, based on MIC. Findings The empirical results show that ensemble models perform better than stand-alone ones, whereas the ensemble model based on MIC-CCS outperforms the ensemble models with unselected base classifiers and other ensemble models based on traditional forward and backward selection methods. Additionally, the classification performance of the ensemble model in which correlation is measured with MIC is better than that measured with the Pearson correlation coefficient. Research limitations/implications The study provides an alternate solution to effectively select base classifiers that are significantly different, so that they can provide complementary information and, as these selected classifiers have good predictive capabilities, the classification performance of the ensemble model is improved. Originality/value This paper introduces MIC to the correlation-based selection process to better capture nonlinear and nonfunctional relationships in a complex credit data structure and construct a novel nonlinear programming model for base classifiers select
Dewatering is a major process in a wide range of manufacturing industries. One of the most commonly used technologies for dewatering is the screw press. The optimized setting of the screw press increases the amount of...
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Dewatering is a major process in a wide range of manufacturing industries. One of the most commonly used technologies for dewatering is the screw press. The optimized setting of the screw press increases the amount of recycled water for further production. Additionally, it reduces waste disposal costs by lowering the weight of discharged sludge. In this paper, we used the design of experiments to determine the parameters that affect the dryness of the final waste. Our study showed the significant parameters were the pump speed, the screw rotation speed, and the properties of inflowing sludge. Using the significant factors, a regression model was developed to predict the dryness of the final waste. Then, the regression model was used as the objective function of an optimization model to find the optimal settings of the screw press that maximizes the dryness of sludge. The optimum setting of the screw press increased the dryness of sludge by 2.3%, saving 387 metric tons of water annually. The financial effects of improving the dryness of the sludge leaving the screw press were calculated showing a reduction in disposal costs and reduction in water usage costs because the water extracted from the sludge is recycled. Further investigations showed that the amounts and types of chemicals used to pretreatment the inflowing sludge to the head box can affect the dryness of the sludge leaving the screw press.
The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with tr...
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The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered.
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