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The Journal of Machine Learning Research 2021年第1期22卷 6008-6054页

作者： Antoine Dedieu Hussein Hazimeh Rahul Mazumder Operations Research Center Massachusetts Institute of Technology Cambridge MA Sloan School of Management Operations Research Center MIT Center for Statistics Massachusetts Institute of Technology Cambridge MA

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to solve (to optimality) ℓ0-regularized regression problems at scales much larger than what was conventionally considered possible. Despite their usefulness, MIP-based global optimization approaches are significantly slower than the relatively mature algorithms for ℓ1-regularization and heuristics for nonconvex regularized problems. We aim to bridge this gap in computation times by developing new MIP-based algorithms for ℓ0-regularized classification. We propose two classes of scalable algorithms: an exact algorithm that can handle p ≈ 50; 000 features in a few minutes, and approximate algorithms that can address instances with p ≈ 106 in times comparable to the fast ℓ1-based algorithms. Our exact algorithm is based on the novel idea of integrality generation, which solves the original problem (with p binary variables) via a sequence of mixed integer programs that involve a small number of binary variables. Our approximate algorithms are based on coordinate descent and local combinatorial search. In addition, we present new estimation error bounds for a class of ℓ0-regularized estimators. Experiments on real and synthetic data demonstrate that our approach leads to models with considerably improved statistical performance (especially variable selection) compared to competing methods.

关键词： sparsity sparse classification l0 regularization mixed integer programming

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Local Self-optimizing Control with Input and Output Constraints

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IFAC Proceedings Volumes 2011年第1期44卷 9850-9855页

作者： Wuhua Hu Lia Maisarah Umar Vinay Kariwala Gaoxi Xiao School of Electrical and Electronic Engineering Nanyang Technological University Singapore 639798 School of Chemical and Biomedical Engineering Nanyang Technological University Singapore 637459

Abstract The available methods for selection of controlled variables (CVs) using the concept of self-optimizing control have been developed under the restrictive assumption that the set of active constraints remains unchanged for all the allowable disturbances. To keep the input and output variables within their allowable bounds, the use of cascade controllers, and to track the optimal set of active input constraints, the use of split-range controllers is suggested in literature. In this paper, we propose a different strategy, where CVs are selected as linear combinations of measurements to minimize local average loss, while ensuring that all the constraints are satisfied over the allowable set of disturbances. This result is extended to select a few of the available measurements, whose combinations are used as CVs. The proposed approach offers simpler implementation of operational policy for processes with tight operational constraints. We use the case study of forced-circulation evaporator to illustrate the usefulness of the proposed method.

关键词： Controlled variables Control system design mixed integer programming Process constraints Self-optimizing control

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Driver Shift Planning for an Online Store with Short Delivery Times

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Procedia Computer Science 2021年 180卷 517-524页

作者： Matthias Horn Nikolaus Frohner Günther R. Raidl Institute of Logic and Computation TU Wien Favoritenstrae 9-11/192-01 1040 Vienna Austria

In this work we derive daily driver shift plans for an online store which delivers goods to customers within short times. The goal is to minimize the total labor time (total shift lengths) over all shifts. Thereby orders must be assigned to shifts s.t. all orders are delivered in time. We model this optimization problem by means of a mixed integer linear program using a time-index based formulation. This model features strengthening inequalities that allow to solve it also reasonably well with an open source branch-and-cut solver. Furthermore we use a coarse-grained variant of the model to quickly derive high-quality heuristic solutions within one minute even for larger instances with up to two thousand orders. On a realistic benchmark instance set the overall approach is able to obtain solutions with remaining optimality gaps below 1%.

关键词： Shift Planning mixed integer programming Scheduling Problem

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A Broad Case-Based Distance Approach for Screening with Different Target Points

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2017年第4期34卷 1750013-1750013页

作者： Ma, Li-Ching Natl United Univ Dept Informat Management 1 Lienda Miaoli 36003 Taiwan

The case-based distance (CBD) methods for screening are helpful for assisting decision makers in filtering out alternatives that are unlikely to be chosen. However, most of these methods based on selected cases and distance measurements from a chosen target point can only solve screening problems with positive criteria weights. This study proposes a two-phase approach based on mixed integer programming to integrate the concept of Data Envelopment Analysis-Discriminant Analysis (DEA-DA) and the extended case-based distance (ECBD) method for screening problems involving uncertain signs of criteria weights and different target points. The results show that the proposed approach can reduce the misclassification rate and address multiple solution problems. In addition, because the proposed approach can solve problems involving negative weights directly, the influences of different target points can be reduced. Therefore, it is helpful for decision makers to conduct scenario analysis based on different chosen target points.

关键词： Case-based distance method DEA-DA mixed integer programming screening

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HYBRID SEARCH STRATEGIES FOR HETEROGENEOUS SEARCH SPACES

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International Journal on Artificial Intelligence Tools 2000年第1期9卷 45-57页

作者： CARLA GOMES BART SELMAN Dept. of Computer Science Cornell University Ithaca NY 14853 USA

Recently, there has been much interest in enhancing purely combinatorial formalisms with numerical information. For example, planning formalisms can be enriched by taking resource constraints and probabilistic information into account. The mixed integer programming (MIP) paradigm from operations research provides a natural tool for solving optimization problems that combine such numeric and non-numeric information. The MIP approach relies heavily on linear program relaxations and branch-and-bound search. This is in contrast with depth-first or iterative deepening strategies generally used in artificial intelligence. We provide a detailed characterization of the structure of the underlying search spaces as explored by these search strategies. Our analysis shows that much can be gained by combining different search strategies for solving hard MIP problems, thereby leveraging each strategy's strength in terms of the combinatorial and numeric information.

关键词： Search mixed integer programming randomization

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Batch delivery scheduling of trucks integrated with parallel machine schedule of job orders from multi-customers

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JOURNAL OF ADVANCED MECHANICAL DESIGN SYSTEMS AND MANUFACTURING 2018年第2期12卷

作者： Joo, Cheol Min Kim, Byung Soo Dongseo Univ Div Mechatron Engn 47 Jurye Ro Busan 47011 South Korea Incheon Natl Univ Dept Ind & Management Engn 119 Acad Ro Incheon 22012 South Korea

This article considers an integration of two-echelon supply chain management (SCM) problem between a manufacturing site and customers. In the first echelon, jobs ordered by a number of customers are arranged and manufactured by one of a number of identical parallel machines. In the second, jobs are grouped by customer in batches and then delivered via trucks with a limited capacity. The problem is to determine batch delivery schedule of identical trucks. The batch delivery schedule is integrated with a parallel machine schedule of job orders from multi-customers. So, the objective of the problem is to simultaneously determine machine scheduling, batching and truck delivery scheduling to the corresponding customer to minimize the delivery completion time of whole the batched jobs. To solve the problem, two approaches are addressed in this article. The first approach uses a mathematical model (mixed integer programming model) to obtain the optimal solution. Since the problem is NP-hard, three kinds of genetic algorithm-based heuristics are proposed to increase solution efficiency for the second approach. The performances of the algorithms are compared using computational experiments with randomly generated examples. The computational experiments illustrate that the one of the proposed algorithms is capable of near-optimal solutions within a reasonable computing time.

关键词： GA-based heuristics Supply chain optimization Scheduling Batching mixed integer programming

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Scheduling of maintenance windows in a mining supply chain rail network

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COMPUTERS & OPERATIONS RESEARCH 2020年 115卷 104670-000页

作者： Kalinowski, Thomas Matthews, Jason Waterer, Hamish Univ New England Sch Sci & Technol Armidale NSW Australia Univ Newcastle Sch Math & Phys Sci Callaghan NSW Australia

Rail infrastructure forms a critical part of the mining supply chain in Australia due to the high weight to volume ratio of the product and the long distances between the mines and the ports. Across Australia, rail infrastructure has been steadily expanding to account for the growth in export volumes and the movement of mining operations further inland, and so the efficient and effective management of this critical infrastructure is vitally important. Maintenance plays a crucial role in this management as it ensures that the infrastructure assets are in a condition that allows safe, reliable, and efficient transport. In this paper we consider the annual planning of maintenance for Australia's largest coal rail network, the Central Queensland Coal Network (CQCN), that is owned, operated, and managed, by Aurizon Holdings Pty Ltd. The current planning approach at Aurizon uses the concept of a maintenance access window (MAW) which provides a train-free time window across geographically contiguous track locations that define a maintenance zone. These train-free time windows facilitate the scheduling of specific maintenance tasks at specific track locations within zones closer to day of operation and forms the basis for a planning framework. A MIP model is introduced which facilitates the planning of different maintenance resources across this network to schedule MAWs. The model takes into account maintenance requirement forecasts as well as the availability of resources. Candidate solutions are compared using a proxy for network throughput capacity. Due to the long computation times required to solve the MIP model at the annual planning horizon a matheuristic is developed and two variants are tested. On average 80% less computational time is required to find a good solution (average gap of 5%) using the matheuristic compared to solving the MIP model directly (average gap of 1.5%). The MIP model and associated matheuristic provides a suitable framework for semi-automated

关键词： Rail infrastructure Maintenance scheduling Maintenance windows mixed integer programming Matheuristic

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A Graph-Based Approach for Relating integer Programs

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INFORMS JOURNAL ON COMPUTING 2024年第6期36卷 1359-1756, C2页

作者： Steever, Zachary Hunt, Kyle Karwan, Mark Yuan, Junsong Murray, Chase C. Philadelphia Eagles Philadelphia PA 19148 USA SUNY Buffalo Dept Management Sci & Syst Buffalo NY 14260 USA SUNY Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA SUNY Buffalo Dept Comp Sci & Engn Buffalo NY 14260 USA

This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques;those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph -based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph -structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is used to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph -based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs, namely, losslessness and permutation invariance, are also explored via computational experiments.

关键词： model structure combinatorial optimization mixed integer programming neural network

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Hybrid tabu search algorithm for unrelated parallel machine scheduling in semiconductor fabs with setup times, job release, and expired times

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 165卷

作者： Chen, Changyu Fathi, Mahdi Khakifirooz, Marzieh Wu, Kan Singapore Management Univ Singapore Singapore Univ North Texas G Brint Ryan Coll Business Dept Informat Technol & Decis Sci Denton TX 76203 USA Tecnol Monterrey Dept Ind Engn Monterrey NL Mexico Chang Gung Univ Business Analyt Res Ctr Taoyuan Taiwan

This research is motivated by a scheduling problem arising in the ion implantation process of wafer fabrication. The ion implementation scheduling problem is modeled as an unrelated parallel machine scheduling (UPMS) problem with sequence-dependent setup times that are subject to job release time and expiration time of allowing a job to be processed on a specific machine, defined as: R vertical bar r(j), e(ij), STsd vertical bar C-max. The objective is first to maximize the number of processed jobs, then minimize the maximum completion time (makespan), and finally minimize the maximum completion times of the non-bottleneck machines. A mixed-integer programming (MIP) model is proposed as a solution approach and adopts a hybrid tabu search (TS) algorithm to acquire approximate feasible solutions. The MIP model has two phases and attempts to achieve the first two objectives. The hybrid TS algorithm has three phases and attempts to achieve all three objectives. In a real setting, computational results demonstrate that the maximum number of processed jobs can be acquired within a short time utilizing the hybrid TS algorithm (average 8 s). By comparing the two approaches, the TS outperforms the MIP model regarding solution quality and computational time for the second objective, minimizing the makespan. Furthermore, the third phase of the hybrid TS algorithm shows the effectiveness further to enhance the utilization of the ion implantation equipment.

关键词： Scheduling Unrelated parallel machines Setup times Expired times Job release Wafer fabrication mixed integer programming Tabu search

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A multi-objective two-echelon vehicle routing problem with multiple delivery options

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Transportation Research Procedia 2024年 79卷 377-384页

作者： Amin Karimi Lele Zhang Mark Fackrell Russell Thompson School of Mathematics and Statistics The University of Melbourne ARC Training Centre in Optimisation Technologies Integrated Methodologies and Applications (OPTIMA) Australia The Department of Infrastructure Engineering The University of Melbourne Melbourne VIC Australia

The classical two-echelon vehicle routing problem (2E-VRP) has commodities transported from depots to intermediate facilities and then delivered to customers from these facilities. In this study, we consider another type of 2E-VRP, in which vehicles from both echelons can be used for home delivery. We also present a sustainable model, which considers customers' preferred delivery locations, economic and environmental costs. Also, we present a meta-heuristic algorithm to solve real-world size instances in a timely manner. The computational results demonstrate that the proposed solution method can effectively solve small instances with a minimal gap when compared to an exact solver, and it can also handle large instances in a timely manner.

关键词： Two-echelon vehicle routing problem Two-echelon logistics mixed integer programming multi-objective

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