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Reoptimization framework and policy analysis for maritime inventory routing under uncertainty

OPTIMIZATION AND ENGINEERING 2018年第4期19卷 937-976页

作者： Dong, Yachao Maravelias, Christos T. Jerome, Norman F. Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA BP Plc 150 West Warrenville Rd Naperville IL 60563 USA

We study a maritime inventory routing problem, in which shipments between production and consumption nodes are carried out by a fleet of vessels. The vessels have specific capacities and can be chartered under different agreements. The inventory levels of all consumption nodes and some production nodes should be maintained within specified bounds;for the remaining production nodes, orders should be picked up within pre-defined time windows. We propose a discrete-time mixed-integer programming model. In the face of new information and uncertainty, this optimization model has to be re-solved, as the horizon is rolled forward. We discuss how to account for different sources of uncertainty. We present a rolling-horizon reoptimization framework that allows us to study different policies that impact the quality of the implemented solution, so we can identify the optimal set of policies.

关键词： mixed-integer programming Optimization under uncertainty Inventory routing Rolling horizon approach

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A semidefinite programming method for integer convex quadratic minimization

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OPTIMIZATION LETTERS 2018年第3期12卷 499-518页

作者： Park, Jaehyun Boyd, Stephen Stanford Univ Packard BldgRoom 243350 Serra Mall Stanford CA 94305 USA Stanford Univ Packard BldgRoom 254350 Serra Mall Stanford CA 94305 USA

We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions, and thus an upper bound on the optimal value. The effectiveness of the method is shown for numerical problem instances of various sizes.

关键词： Convex optimization integer quadratic programming mixed-integer programming Semidefinite relaxation Branch-and-bound

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The Accessibility Vehicle Routing Problem

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JOURNAL OF CLEANER PRODUCTION 2018年 172卷 1514-1528页

作者： Ibarra-Rojas, O. J. Hernandez, L. Ozuna, L. Univ Autonoma Nuevo Leon Fac Ciencias Fisicomatemat San Nicolas De Los Garza Mexico Univ Autonoma Nuevo Leon Fac Ciencias Quim San Nicolas De Los Garza Mexico Univ Autonoma Nuevo Leon Fac Ingn Mecan & Elect San Nicolas De Los Garza Mexico

In a distribution process where the demand relates to essential products or services, is important to consider the access for people to fulfill their needs. In particular, for land use and urban transportation planning, accessibility relates to appropriately allocating opportunities to satisfy a demand or provide a service considering the cost of mobility. Measuring accessibility is a challenging task, indeed, it depends on the context of the study and has not been properly considered in the definition of vehicle routing problems, which are commonly used to represent distribution processes. In the study reported here, we addressed a vehicle routing problem to optimize accessibility based on six indicators: the number of zones with access to opportunities with delimited mobility, the number of zones covered by the route, the cost of travel, the distance to the nearest opportunity, the number of opportunities, and geographical disaggregation. We defined a mixed-integer linear formulation for the proposed problem that we used to show the potential benefits of our approach compared with a maximum coverage vehicle routing problem for small instances. In turn, we designed an iterated local search algorithm and analyzed its efficiency according to a benchmark of randomly generated instances. Numerical results show that we obtain high-quality solutions for acceptable computational times. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Accessibility Vehicle Routing Problem mixed-integer programming Iterated local search

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A dynamic reformulation heuristic for Generalized Interdiction Problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期267卷 40-51页

作者： Fischetti, Matteo Monaci, Michele Sinnl, Markus Univ Padua Dept Informat Engn Padua Italy Univ Bologna DEI Guglielmo Marconi Bologna Italy Univ Vienna Dept Stat & Operat Res Vienna Austria INRIA Lille Nord Europe INOCS F-59650 Villeneuve Dascq France

We consider a subfamily of mixed-integer linear bilevel problems that we call Generalized Interdiction Problems. This class of problems includes, among others, the widely-studied interdiction problems, i.e., zero-sum Stackelberg games where two players (called the leader and the follower) share a set of items, and the leader can interdict the usage of certain items by the follower: Problems of this type can be modeled as mixed-integer Nonlinear programming problems, whose exact solution can be very hard. In this paper we propose a new heuristic scheme based on a single-level and compact mixed-integer linear programming reformulation of the problem obtained by relaxing the integrality of the follower variables. A distinguished feature of our method is that general-purpose mixed-integer cutting planes for the follower problem are exploited, on the fly, to dynamically improve the reformulation. The resulting heuristic algorithm proved very effective on a large number of test instances, often providing an (almost) optimal solution within very short computing times. (C) 2017 Elsevier B.V. All rights reserved.

关键词： (O) Combinatorial optimization Bilevel optimization Interdiction problems mixed-integer programming Heuristics

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A Decomposition Method for Finding Optimal Container Stowage Plans

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TRANSPORTATION SCIENCE 2018年第6期52卷 1444-1462页

作者： Roberti, R. Pacino, D. Vrije Univ Amsterdam Dept Informat Logist & Innovat NL-1081 HV Amsterdam Netherlands Tech Univ Denmark Dept Engn Management DK-2800 Lyngby Denmark

In transportation of goods in large container ships, shipping industries need to minimize the time spent at ports to load/unload containers. An optimal stowage of containers on board minimizes unnecessary unloading/reloading movements, while satisfying many operational constraints. We address the basic container stowage planning problem (CSPP). Different heuristics and formulations have been proposed for the CSPP, but finding an optimal stowage plan remains an open problem even for small-sized instances. We introduce a novel formulation that decomposes CSPPs into two sets of decision variables: the first defining how single container stacks evolve over time and the second modeling port-dependent constraints. Its linear relaxation is solved through stabilized column generation and with different heuristic and exact pricing algorithms. The lower bound achieved is then used to find an optimal stowage plan by solving a mixed-integer programming model. The proposed solution method outperforms the methods from the literature and can solve to optimality instances with up to 10 ports and 5,000 containers in a few minutes of computing time.

关键词： column generation container stowage dynamic programming exact methods maritime logistics mixed-integer programming

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A Frank-Wolfe based branch-and-bound algorithm for mean-risk optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2018年第3期70卷 625-644页

作者： Buchheim, Christoph De Santis, Marianna Rinaldi, Francesco Trieu, Long TU Dortmund Fak Math Vogelpothsweg 87 D-44227 Dortmund Germany Univ Roma La Sapienza Dipartimento Ingn Informat Automat & Gest Via Ariosto 25 I-00185 Rome Italy Univ Padua Dipartimento Matemat Via Trieste 63 I-35121 Padua Italy

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems by designing a branch-and-bound algorithm, where at each node, the continuous relaxation is solved by a non-monotone Frank-Wolfe type algorithm with away-steps. Experimental results on portfolio optimization problems show that our approach can outperform the MISOCP solver of CPLEX 12.6 for instances where a linear risk-weighting function is considered.

关键词： mixed-integer programming Mean-risk optimization Global optimization

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Deep neural networks and mixed integer linear optimization

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CONSTRAINTS 2018年第3期23卷 296-309页

作者： Fischetti, Matteo Jo, Jason Univ Padua Dept Informat Engn DEI Padua Italy MILA Montreal PQ Canada Inst Data Valorizat IVADO Montreal PQ Canada

Deep Neural Networks (DNNs) are very popular these days, and are the subject of a very intense investigation. A DNN is made up of layers of internal units (or neurons), each of which computes an affine combination of the output of the units in the previous layer, applies a nonlinear operator, and outputs the corresponding value (also known as activation). A commonly-used nonlinear operator is the so-called rectified linear unit (ReLU), whose output is just the maximum between its input value and zero. In this (and other similar cases like max pooling, where the max operation involves more than one input value), for fixed parameters one can model the DNN as a 0-1 mixed integer Linear Program (0-1 MILP) where the continuous variables correspond to the output values of each unit, and a binary variable is associated with each ReLU to model its yes/no nature. In this paper we discuss the peculiarity of this kind of 0-1 MILP models, and describe an effective bound-tightening technique intended to ease its solution. We also present possible applications of the 0-1 MILP model arising in feature visualization and in the construction of adversarial examples. Computational results are reported, aimed at investigating (on small DNNs) the computational performance of a state-of-the-art MILP solver when applied to a known test case, namely, hand-written digit recognition.

关键词： Deep neural networks mixed-integer programming Deep learning Mathematical optimization Computational experiments

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Multiobjective Optimization of Multi-Carrier Energy System Using a Combination of ANFIS and Genetic Algorithms

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IEEE TRANSACTIONS ON SMART GRID 2018年第3期9卷 2276-2283页

作者： Kampouropoulos, Konstantinos Andrade, Fabio Sala, Enric Garcia Espinosa, Antonio Romeral, Luis Fundacio CTM Ctr Tecnol Manresa 08243 Spain Univ Puerto Rico Mayaguez PR 00681 USA Univ Politecn Cataluna MCIA Res Ctr Terrassa 08222 Spain

This paper presents a novel method for the energy optimization of multi-carrier energy systems. The presented method combines an adaptive neuro-fuzzy inference system, to model and forecast the power demand of a plant, and a genetic algorithm to optimize its energy flow taking into account the dynamics of the system and the equipment's thermal inertias. The objective of the optimization algorithm is to satisfy the total power demand of the plant and to minimize a set of optimization criteria, formulated as energy usage, monetary cost, and environmental cost. The presented method has been validated under real conditions in the car manufacturing plant of SEAT in Spain in the framework of an FP7 European research project.

关键词： Energy optimization multicarrier systems dynamic optimization mixed-integer programming multiobjective problem energy hub energy prediction optimal control manufacturing plants

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Remote-Controlled Switch Allocation Enabling Prompt Restoration of Distribution Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第3期33卷 3129-3142页

作者： Lei, Shunbo Wang, Jianhui Hou, Yunhe Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China Southern Methodist Univ Dept Elect Engn Dallas TX 75275 USA Argonne Natl Lab Energy Syst Div Argonne IL 60439 USA Univ Hong Kong Shenzhen Inst Res & Innovat Shenzhen 518057 Peoples R China

Remote-controlled switches (RCSs) play an important role in prompt service restoration of distribution systems (DSs). However, the cost of RCSs and the vast footprint of DSs limit widespread utilization of RCSs. In this paper, we present a new approach to RCS allocation for improving the performance of restoration and optimizing reliability benefits with reasonable RCS cost. Specifically, the optimal number and locations of to-be-upgraded switches can be determined with different objectives: maximizing the reduction of customer interruption cost;maximizing the reduction of system average interruption duration index;or maximizing the amount of loads that can be restored using the upgraded RCSs. We show that these models can actually be formulated as mixed-integer convex programming problems. We further introduce a novel method to equivalently transform and efficiently solve each of them. The global optimum can thus be computed within a reasonable amount of time. The IEEE 33-node and 123-node test systems are used to demonstrate the proposed models and algorithms.

关键词： Distribution system mixed-integer programming reliability remote-controlled switch service restoration

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Binary extended formulations of polyhedral mixed-integer sets

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MATHEMATICAL programming 2018年第1期170卷 207-236页

作者： Dash, Sanjeeb Gunluk, Oktay Hildebrand, Robert IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA Virginia Tech Grado Dept Ind & Syst Engn Blacksburg VA USA

We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables, what we call "unimodular" extended formulations are the strongest. We also compare the strength of some binary extended formulations from the literature. Finally, we study the behavior of branch-and-bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases.

关键词： mixed-integer programming Binarization Extended formulations Cutting planes Branch-and-bound

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