Robotic assembly lines are widely applied to process workflow, increase capacity, and easily produce a wide range of products because of their flexibility and multifunctionality. Robotic assembly line balancing proble...
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Robotic assembly lines are widely applied to process workflow, increase capacity, and easily produce a wide range of products because of their flexibility and multifunctionality. Robotic assembly line balancing problem (RALBP) refers to allocating the tasks and robots to workstations in order to maximize the line efficiency, which has become a popular research direction recently. In this paper, we propose a mixed-integer programming model to optimize the carbon footprint of the RALBP. Minimizing carbon footprint can reduce global greenhouse effect and atmospheric dust pollution, which is a very significant environmental topic in the world. We also investigate a realistic production process design in our model-cross-station task. In this design, a task can be operated by the station to which it is assigned as well as the adjacent stations. The model is solved by a commercial solver (Gurobi) and some results are presented. Copyright (C) 2022 The Authors.
This paper addresses the optimal power generation and load management problems in off-grid hybrid electric systems with renewable sources based on appropriately constructed optimization problems. In this venue, the ca...
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This paper addresses the optimal power generation and load management problems in off-grid hybrid electric systems with renewable sources based on appropriately constructed optimization problems. In this venue, the capacity and operating constraints for generating, storage and load units are first formulated as mixed-integer linear programming (MILP) models. In addition, we integrate the power curtailment strategies, such as temporary pause and multiple power supplies, for the load units in the MILP models to alleviate the peak power demands and power shortage without an adverse effect on the overall operation of the system. We subsequently consider the application of this framework for representative scenarios in the context of a residential power system with solar sources. Simulation results for the case of predetermined schedules with preset power requests, as well as for the case of varying schedules with updated power requests, are presented using the proposed optimization-based approach. (C) 2013 Elsevier Ltd. All rights reserved.
A computationally efficient algorithm for hinging hyperplane autoregressive exogenous (HHARX) model identification via mixed-integer programming technique is proposed in this paper. The HHARX model is attractive since...
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A computationally efficient algorithm for hinging hyperplane autoregressive exogenous (HHARX) model identification via mixed-integer programming technique is proposed in this paper. The HHARX model is attractive since it accurately approximates a general nonlinear process as a sum of hinge functions and preserves the continuity even in a piecewise affine form. Traditional mixed-integer programming-based method for HHARX model identification can only be applied on small-scale input/output datasets due to its significant computational demands. The contribution of this paper is to develop a sequential optimization approach to build accurate HHARX model more efficiently on a relatively large number of experimental data. Moreover, the proposed framework can handle more difficult and practical cases in piecewise model identification, such as: limited submodel switching, missing output data and specified steady state. Finally, the efficiency and accuracy of the proposed computational scheme are demonstrated through modeling of two simulated examples and a pilot-scale heat exchanger.
In the environment of peer competition and energy conservation, optimizing the deployment of application server clusters in real time according to actual workload conditions to reduce operating costs and energy consum...
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In the environment of peer competition and energy conservation, optimizing the deployment of application server clusters in real time according to actual workload conditions to reduce operating costs and energy consumption is an important issue that must be urgently addressed. In this paper, we propose a real-time power optimization strategy for application server clusters, and the optimization measures include CPU dynamic voltage/frequency scaling and server dynamic switching. First, the feasibility of defining variables for server types is proved, and appropriate variables are defined to describe the cluster power optimization as a mixed-integer programming (MIP) problem. Then, two solution methods are proposed: the exact method based on the Gurobi optimizer and the approximate method based on primary-secondary optimization and differential evolution with two mutations (PSODE). The former turns the MIP problem into a standard mixed-integer quadratic programming form by introducing intermediate variables and solves it using the Gurobi optimizer. The latter rewrites the MIP problem as a primary-secondary optimization problem and proposes a differential evolutionary-based solution algorithm for the primary optimization problem. The evolutionary process consists of two mutation operations, inter- and intraindividual mutations, which both use a heuristic policy to accelerate the evolution convergence. The test results reveal that the Gurobi-based method can quickly determine the global optimal deployment when the cluster size is small. The PSODE-based method can quickly determine the global optimal deployment or high-quality suboptimal deployment when applied to large-scale clusters. (C) 2022 Elsevier B.V. All rights reserved.
In this article, we propose a framework for the stability verification of mixed-integer linear programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an effic...
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In this article, we propose a framework for the stability verification of mixed-integer linear programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a mixed-integer quadratic program. In addition, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU neural networks (NNs), optimal solution maps of parametric quadratic programs, and model predictive control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a dc-dc power converter case study and investigate its computational complexity.
This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor spac...
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This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where the estimation data only seldom switches between the different submodels, we also suggest a way of trading off between optimality and complexity by using a change detection approach. (C) 2003 Elsevier Ltd. All rights reserved.
Plasma control systems (PCS) in tokamaks need to fulfill a number of control tasks to achieve the desired physics goals. In present-day devices, actuators are usually assigned to a single control task. However, in fut...
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Plasma control systems (PCS) in tokamaks need to fulfill a number of control tasks to achieve the desired physics goals. In present-day devices, actuators are usually assigned to a single control task. However, in future tokamaks, only a limited set of actuators is available for multiple control tasks at the same time. The priority to perform specific control tasks may change in real-time due to unforeseen plasma events and actuator availability may change due to failure. This requires the real-time allocation of available actuators to realize the requests by the control tasks, also known as actuator management. In this paper, we analyze possible architectures to interface the control tasks with the allocation of actuators inside the PCS. Additionally, we present an efficient actuator allocation algorithm for Heating and Current Drive (H&CD) actuators. The actuator allocation problem is formulated as a mixed-integer Quadratic programming optimization problem, allowing to quickly search for the best allocation option without the need to compute all allocation options. The algorithms performance is demonstrated in examples involving the full proposed ITER H&CD system, where the desired allocation behavior is successfully achieved. This work contributes to establishing integrated control routines with shared actuators on existing and future tokamaks.
This paper presents a mathematical programming based clustering approach that is applied to a digital platform company's customer segmentation problem involving demographic and transactional attributes related to ...
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This paper presents a mathematical programming based clustering approach that is applied to a digital platform company's customer segmentation problem involving demographic and transactional attributes related to the customers. The clustering problem is formulated as a mixed-integer programming problem with the objective of minimizing the maximum cluster diameter among all clusters. In order to overcome issues related to computational complexity of the problem, we developed a heuristic approach that improves computational times dramatically without compromising from optimality in most of the cases that we tested. The performance of this approach is tested on a real problem. The analysis of our results indicates that our approach is computationally efficient and creates meaningful segmentation of data. (c) 2005 Elsevier B.V. All rights reserved.
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We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent...
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We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived.
This paper proposes a solution to mixed-integer programming by using a gradient system and searching for multiple equilibrium points in the system. The method is available when the objective function of a problem is c...
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This paper proposes a solution to mixed-integer programming by using a gradient system and searching for multiple equilibrium points in the system. The method is available when the objective function of a problem is continuous and differentiable. In order to find feasible Solutions of a mixed-integer programming problem by gradient systems, discrete decision variables are treated as continuous ones. We demonstrate a systematic way to build the kind of gradient systems in which equilibrium points are embedded at feasible solutions of a mixed-integer problem. For numerical computation, the multiple equilibrium points search method we have already proposed is available and its adjustments to improve efficiency and certainly for mixed-integer programming are also proposed in this paper. Results for some problems show the effectiveness of our method: high ability of thorough search and high quality of derived solutions. (C) 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(8): 53-63, 2009;Published online in Wiley InterScience (***). DOI 10.1002/ecj.10037
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