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Strong mixed-integer programming Formulations for Trained Neural Networks 1

20th International Conference on integer programming and Combinatorial Optimization (IPCO)

作者： Anderson, Ross Huchette, Joey Tjandraatmadja, Christian Vielma, Juan Pablo Google Res Cambridge MA 02142 USA MIT Cambridge MA 02139 USA

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the input and output variables of the ReLU. We contrast it with an ideal "extended" formulation with a linear number of additional continuous variables, derived through standard techniques. An apparent drawback of our formulation is that it requires an exponential number of inequality constraints, but we provide a routine to separate the inequalities in linear time. We also prove that these exponentially-many constraints are facet-defining under mild conditions. Finally, we study network verification problems and observe that dynamically separating from the exponential inequalities (1) is much more computationally efficient and scalable than the extended formulation, (2) decreases the solve time of a state-of-the-art MIP solver by a factor of 7 on smaller instances, and (3) nearly matches the dual bounds of a state-of-the-art MIP solver on harder instances, after just a few rounds of separation and in orders of magnitude less time.

关键词： mixed-integer programming Formulations Deep learning

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Network expansion planning considering N-1 security criterion by iterative mixed-integer programming approach

Network expansion planning considering N-1 security criterio...

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IEEE-Power-and-Energy-Society General Meeting

作者： Hu, Zechun Li, Furong Univ Bath Dept Elect & Elect Engn Bath BA2 7AY Avon England

ISBN: (纸本)9781424483570

A methodology to solve the network expansion planning problem considering N-1 security criterion is proposed. The main idea to achieve the desired results is to separate the whole problem into two subproblems and solve them iteratively. The aim of upper level problem is to solve the mixed-integer programming model with all identified constraints. For the lower level problem, all N-1 contingencies are checked one by one and the corresponding constraints are added the upper level problem if line overload or network split is found. Each constraint is formed based on rigorous sensitivity or network topology analysis. The iteration between the two subproblems stops till a satisfactory planning solution is reached. Test results on two systems show effectiveness of the proposed method.

关键词： Iterative approach mixed-integer programming network planning N-1 security criterion

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Simultaneous Optimization of Task Allocation and Path Planning Using mixed-integer programming for Time and Capacity Constrained Multi-Agent Pickup and Delivery 22

Simultaneous Optimization of Task Allocation and Path Planni...

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22nd International Conference on Control, Automation and Systems (ICCAS)

作者： Okubo, Takuma Takahashi, Masaki Keio Univ Grad Sch Sci & Technol Kohoku Ku 3-14-1 Hiyoshi Yokohama Kanagawa 2238522 Japan Keio Univ Fac Sci & Technol Dept Syst Design Engn Kohoku Ku 3-14-1 Hiyoshi Yokohama Kanagawa 2238522 Japan

ISBN: (纸本)9788993215243

Lately, there has been a need to improve the efficiency of material movements within factories and multi-agents are required to perform these tasks. In this study, graphical representation and mixed-integer programming have been adopted for simultaneous optimization of task allocation and path planning for each agent to achieve the following three goals. First, this study realizes time and capacity constrained multi-agent pickup and delivery (TCMAPD) that simultaneously considers time constraints, capacity constraints, and collision avoidance. Previous studies have not considered these constraints simultaneously. Thus, we can solve the problems associated with using multi-agents in actual factories. Second, we achieved TCMAPD that optimizes the collision avoidance between multi-agents. In conventional research, only a single collision avoidance method can be used. However, an appropriate route was selected from a variety of avoidance methods in this study. Hence, we could achieve a more efficient task allocation and path planning with collision avoidance. Third, the proposed method simultaneously optimizes task allocation and path planning for each agent. Previous studies have separately considered the approach of optimizing task allocation and path planning or used the cost of path planning after task allocation to again perform task allocation and path planning. To simultaneously optimize them in a single plan, we have developed a solution-derivable formulation using mixed-integer programming to derive a globally optimal solution. This enables efficient planning with a reduced total time traveled by the agents.

关键词： task allocation path planning multi-agent path conflict mixed-integer programming

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New Ways in Municipal Flood Mitigation: a mixed-integer programming Approach and its Practical Application

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Operations Research Forum 2023年第4期4卷 86页

作者： Boeckmann, Jan Thielen, Clemens Weihenstephan-Triesdorf University of Applied Sciences Am Essigberg 3 TUM Campus Straubing for Biotechnology and Sustainability Straubing 94315 Germany Department of Mathematics School of Computation Information and Technology Technical University of Munich Boltzmannstr. 3 Garching bei München 85748 Germany

Adapting to the consequences of climate change is one of the central challenges faced by humanity in the next decades. One of these consequences are intense heavy rain events, which can cause severe damage to buildings due to flooding. In this paper, we present the first use of optimization techniques that scales well enough to be applicable for supporting decision-making in planning precautionary measures for flash floods caused by heavy rain events in realistic scenarios. Our mixed-integer programming model has been implemented as an innovative decision support tool in the form of a web application, which has already been used by more than 30 engineering offices, municipalities, universities, and other institutions. The model aims to minimize the damage caused in the case of a heavy rain event by taking best-possible actions subject to a limited budget and constraints on the cooperation of residents. We further present an efficient, graph-based representation and preprocessing of the surface terrain, a combinatorial algorithm for computing an initial solution of the mixed-integer program, and computational results obtained on real-word data from different municipalities. © 2023, The Author(s).

关键词： Flood mitigation Graph algorithms mixed-integer programming

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A mixed-integer programming Model for the Production-Inventory-Distribution-Routing Problem

A Mixed-Integer Programming Model for the Production-Invento...

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IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

作者： Mostafa, N. A. Eltawil, A. B. Egypt Japan Univ Sci & Technol Dept Ind Engn & Syst Management Alexandria Egypt

ISBN: (纸本)9781467380669

In this paper, an under development mixed-integer programming model is presented and used to solve the Production-Inventory-Distribution-Routing Problem (PIDRP), the main objective is to minimize the total cost of production, inventory, and transportation without violating the demand fulfillment policy. The proposed model deals with multiple products with different characteristics, split deliveries, a heterogeneous fleet of vehicles, and a route limitation for each vehicle. The main contribution of this work is the validation of the mathematical model and testing it for solving small-sized instances from literature.

关键词： lot sizing inventory distribution vehicle routing mixed-integer programming

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Training Experimentally Robust and Interpretable Binarized Regression Models Using mixed-integer programming

Training Experimentally Robust and Interpretable Binarized R...

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IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

作者： Tule, Sanjana Le, Nhi Ha Lan Say, Buser Monash Univ Melbourne Vic Australia

ISBN: (纸本)9781665487689

In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using mixed-integer programming (MIP). Our MIP model balances the optimization of prediction margin and model size by using a weighted objective that: minimizes the total margin of incorrectly classified training instances, maximizes the total margin of correctly classified training instances, and maximizes the overall model regularization. We conduct two sets of experiments to test the classification accuracy of our MIP model over standard and corrupted versions of multiple classification datasets, respectively. In the first set of experiments, we show that our MIP model outperforms an equivalent Pseudo-Boolean Optimization (PBO) model and achieves competitive results to Logistic Regression (LR) and Gradient Descent (GD) in terms of classification accuracy over the standard datasets. In the second set of experiments, we show that our MIP model outperforms the other models (i.e., GD and LR) in terms of classification accuracy over majority of the corrupted datasets. Finally, we visually demonstrate the interpretability of our MIP model in terms of its learned parameters over the MNIST dataset. Overall, we show the effectiveness of training robust and interpretable binarized regression models using MIP.

关键词： robust machine learning interpretable machine learning mixed-integer programming

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Load Matching Method Based on mixed-integer programming 5

Load Matching Method Based on Mixed-Integer Programming

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5th International Conference on Computer Engineering and Application (ICCEA)

作者： Zhang, Junwei Tan, Zhukui Gao, Jipu Liu, Bin Elect Power Res Inst Guizhou Power Grid Co Ltd Guiyang Guizhou Peoples R China

ISBN: (纸本)9798350386783;9798350386776

In recent years, load monitoring and analysis have played an increasingly important role in power system dispatch management. Although event-based non-intrusive load monitoring methods have made some progress in theory and practice, the increasing diversification and complexity of equipment types require enhanced recognition accuracy of existing methods. It is challenging to capture the power usage behavior of multi-state appliances. In this paper, a load matching method based on mixed-integer programming is proposed to assist in correcting the event detection identification results. This method involves constructing a matching matrix and solving it by considering event matching constraints, power matching constraints, and the number of matches constraints. The goal is to minimize the power error and the penalty terms associated with the number of matches constraints. Through arithmetic analysis of 546 real data in the public dataset PLAID, the method achieves an accuracy of 92.13%. This validates the effectiveness of mixed-integer programming modeling and demonstrates its potential as a supplementary tool for improving load identification results.

关键词： component load matching mixed-integer programming multi-state appliance identification

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Application of mixed-integer programming and Dispatching Rules on Parallel Machine Scheduling with Inserted Idle Time

Application of Mixed-Integer Programming and Dispatching Rul...

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2nd International Conference on Industrial Design and Mechanics Power (ICIDMP 2013)

作者： Tsai, Chi-Yang Wang, Yi-Chen Yuan Ze Univ Dept Ind Engn & Management Taoyuan Taiwan

ISBN: (纸本)9783037858967

This research considers the problem of scheduling jobs on unrelated parallel machines with inserted idle times to minimize the earliness and tardiness. The aims at investigating how particular objective value can be improved by allowing machine idle time and how quality solutions can be more effectively obtained. Two mixed-integer programming formulations combining with three dispatching rules are developed to solve such scheduling problems. They can easy provide the optimal solution to problem involving about nine jobs and four machines. From the results of experiments, it is found that: (1) the inserted idle times decreases objective values more effectively;(2) three dispatching rules are very competitive in terms of efficiency and quality of solutions.

关键词： Scheduling Unrelated parallel machine Inserted idle times Earliness and Tardiness mixed-integer programming

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A mixed-integer programming Approach for Scheduling Roadworks in Urban Regions 33rd

A Mixed-Integer Programming Approach for Scheduling Roadwork...

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33rd Australasian Joint Conference on Artificial Intelligence (AI)

作者： Vallati, Mauro Chrpa, Lukas Univ Huddersfield Huddersfield England Czech Tech Univ Fac Elect Engn Prague Czech Republic

ISBN: (纸本)9783030649838;9783030649845

In order to keep roads in acceptable condition, and to perform maintenance of essential infrastructure, roadworks are required. Due to the increasing traffic volumes and the increasing urbanisation, road agencies are currently facing the problem of effective planning frequent -and usually concurrent- roadworks in the controlled region. However, there is a lack of techniques that can support traffic authorities in this task. In fact, traffic authorities have usually to rely on human experts (and their intuition) to decide how to schedule and perform roadworks. In this paper, we introduce a mixed-integer programming approach that can be used by traffic authorities to plan a set of required roadworks, over a period of time, in a large urban region, by specifying constraints to be satisfied and suitable quality metrics.

关键词： mixed-integer programming Roadworks Urban traffic management

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Fast Non-Parametric Learning to Accelerate mixed-integer programming for Hybrid Model Predictive Control 21st

Fast Non-Parametric Learning to Accelerate Mixed-Integer Pro...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Zhu, Jia-Jie Martius, Georg Max Planck Inst Intelligent Syst Empir Inference Dept Tubingen Germany Max Planck Inst Intelligent Syst Autonomous Learning Grp Tubingen Germany

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e. g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement. Copyright (C) 2020 The Authors.

关键词： Model Predictive Control of Hybrid System Machine Learning Learning for Control Nonparametric learning mixed-integer programming

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