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Generalized Probabilistic Satisfiability

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2017年 332卷 39-56页

作者： Caleiro, Carlos Casal, Filipe Mordido, Andreia Univ Lisbon Inst Super Tecn Dept Math SQIG Inst Telecomunicacoes Lisbon Portugal Univ Lisbon Inst Super Tecn Dept Math Ctr Matemat Apllicacoes Fundamentais & Invest Ope Lisbon Portugal

We analyze a generalized probabilistic satisfiability problem (GenPSAT) which consists in deciding the satisfiability of linear inequalities involving probabilities of classical propositional formulas. GenPSAT is proved to be NP-complete and we present a polynomial reduction to mixed-integer programming. Capitalizing on this translation, we implement and test a solver for the GenPSAT problem. As previously observed for many other NP-complete problems, we are able to detect a phase transition behaviour for GenPSAT.

关键词： Probabilistic Satisfiability GenPSAT mixed-integer programming Phase Transition

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Location Optimization of Tower Crane and Allocation of Material Supply Points in a Construction Site Considering Operating and Rental Costs

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JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT 2017年第1期143卷 1-13页

作者： Nadoushani, Zahra Sadat Moussavi Hammad, Ahmed W. A. Akbarnezhad, Ali UNSW Australia Sch Civil & Environm Engn High St Kensington NSW 2052 Australia

The choice of a suitable tower crane along with its location may considerably affect the costs and duration of the construction process. The location of the tower crane determines the travel time of transporting material between the supply and demand points and thus the operation costs. On the other hand, the distance between the tower crane and supply points as well as the distance between the tower crane and demand points considerably affects the minimum required load moment capacity of the cranes and thus the cranes' rental and operating costs. Previous studies on optimizing the location of tower cranes on a construction site have focused mainly on minimizing the crane operation costs through minimizing their operation time, overlooking the effect of tower crane location on its required capacity and thus rental and operation costs. This paper presents a modified crane location optimization model that also accounts for the effects of crane location on its required capacity, on top of operating time, when minimizing the total costs of lifting operations. A mixed-integer programming model is developed and applied to an actual case study to illustrate the importance of accounting for the effect of crane location on its required capacity in crane location optimization. Furthermore, using a hypothetical case study, the presence of substantial differences between the weights of the elements required at different demand points is identified as an important project-specific parameter affecting the magnitude of the errors occurred by overlooking the capacity requirements and its effects on rental and operating costs in the crane location optimization problem. (C) 2016 American Society of Civil Engineers.

关键词： Tower crane Layout optimization Operating costs Rental costs mixed-integer programming Project planning and design

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Optimizing logistics operations in a country's currency supply network

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IISE TRANSACTIONS 2017年第2期49卷 223-237页

作者： Huang, Yiwei Geismar, H. Neil Rajamani, Divakar Sethi, Suresh Sriskandarajah, Chelliah Carlos, Marcelo Penn State Univ Smeal Coll Business University Pk PA 16802 USA Texas A&M Univ Mays Business Sch College Stn TX 77843 USA Univ Texas Dallas Naveen Jindal Sch Management Richardson TX 75083 USA Fiserv Cash & Logist Dallas TX USA

We optimize a large country's currency supply network for its central bank. The central bank provides currency to all branches (who in turn serve consumers and commerce) through its network of big vaults, regional vaults, and retail vaults. The central bank intends to reduce its total transportation cost by enlarging a few retail vaults to regional vaults. It seeks further reductions by optimizing the sourcing in the updated currency network. We develop an optimization model to select the retail vaults to upgrade, so that the total cost is minimized. Optimally choosing which retail vaults to upgrade is strongly NP-hard, so we develop an efficient heuristic that provides solutions whose costs average less than 3% above the optimum for realistic problem instances. An implementation of our methodology for a particular state has generated a total cost reduction of approximately 57% (equivalently, $2 million). To optimize the sourcing, we propose an alternative delivery process that further reduces the transportation cost by over 31% for the actual collected data and by over 38% for randomly generated data. This alternative optimizes the sourcing within the new currency network and requires significantly less computational effort.

关键词： Financial services currency network sourcing optimization mixed-integer programming minimum cost flow

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Solution methods for vehicle-based inventory routing problems

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COMPUTERS & CHEMICAL ENGINEERING 2017年 101卷 259-278页

作者： Dong, Yachao Maravelias, Christos T. Pinto, Jose M. Sundaramoorthy, Arul Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA Praxair Inc Business & Supply Chain Optimizat R&D Danbury CT 06810 USA Praxair Inc Business & Supply Chain Optimizat R&D Tonawanda NY 14150 USA

A novel method for solving vehicle-based inventory routing problems (IRPs) under realistic constraints is presented. First, we propose a preprocessing algorithm that reduces the problem size by eliminating customers and network arcs that are irrelevant for the current horizon. Second, we develop a decomposition method that divides the problem into two subproblems. The upper level subproblem considers a simplified vehicle routing problem to minimize the distribution cost while satisfying minimum demands, which are calculated based on consumption rate, initial inventory and safety stock. In the lower level, a detailed schedule with drivers is acquired using a continuous-time MILP model, by adopting the routes selected from the upper level. Finally, an iterative approach based on the upper and lower levels is presented, including the addition of different types of integer cuts and parameter updates. Different options of implementing this iterative approach are discussed, and computational results are presented. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Vendor managed inventory mixed-integer programming Network reduction algorithm Decomposition method

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Biogeography-based optimisation for road recovery problem considering value of delay after urban waterlog disaster

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INTERNATIONAL JOURNAL OF BIO-INSPIRED COMPUTATION 2017年第3期9卷 157-164页

作者： Meng, Lingpeng Kang, Qi Han, Chuanfeng Hu, Shaolong Tongji Univ Inst Urban Construct & Emergency Management Sch Elect & Informat Engn Shanghai Peoples R China Tongji Univ Sch Elect & Informat Engn Shanghai Peoples R China Tongji Univ Inst Urban Construct & Emergency Management Sch Econ & Management Shanghai Peoples R China

An urban waterlog disaster (UWD) is caused by a rainfall when the urban drainage system fails to drain off the water produced by the rainfall. To reduce the influence of the waterlog disaster on society, a road recovery planning approach is developed that performs water volume estimation, and pumps collection, assignment, and transportation after a waterlog disaster. A mixed-integer programming model that considers value of delay to travellers was formulated. A biogeography-based optimisation (BBO) algorithm was presented to solve the problem. A real-world example of waterlog (caused by torrential rain on August 12, 2011, in the Pudong district of Shanghai, China) was presented using numerical analysis. The proposed approach emerges as a decision-making tool to help decision makers evaluate diverse recovery strategies before an UWD occurs, with the aim of optimising trade-off between economic costs and value of delay.

关键词： urban waterlog disaster emergency logistics road recovery mixed-integer programming intelligent algorithm biogeography-based optimisation value of delay transportation

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PARTIAL OUTER CONVEXIFICATION FOR TRAFFIC LIGHT OPTIMIZATION IN ROAD NETWORKS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2017年第1期39卷 B53-B75页

作者： Goettlich, Simone Potschka, Andreas Ziegler, Ute Univ Mannheim Sch Business Informat & Math D-68131 Mannheim Germany Heidelberg Univ Interdisciplinary Ctr Sci Comp D-69120 Heidelberg Germany

We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a partial outer convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution heuristic. The two-stage approach consists of the solution of a (smoothed) nonlinear programming problem with dynamic constraints and a reconstruction mixed-integer linear program without dynamic constraints. The two-stage approach is founded on a discrete approximation lemma for partial outer convexification, whose grid-independence properties for (smoothed) conservation laws are investigated. We use the two-stage approach to compute traffic light programs for two scenarios on different discretizations and demonstrate that the solution candidates cannot be improved in a reasonable amount of time by global state-of-the-art mixed-integer nonlinear programming solvers. The two-stage solution candidates are not only better than results obtained by global optimization of piecewise linearized traffic flow models but also can be computed at a faster rate.

关键词： partial outer convexification traffic networks discretized conservation laws optimization mixed-integer programming

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The rescheduling arc routing problem

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2017年第6期24卷 1325-1346页

作者： Monroy-Licht, Marcela Alberto Amaya, Ciro Langevin, Andre Rousseau, Louis-Martin Ecole Polytech Montreal Dept Mathemat & Genie Ind Montreal PQ Canada CIRRELT Montreal PQ Canada Univ Los Andes Dept Ingn Ind Bogota Colombia

In this paper, the rescheduling arc routing problem is introduced. This is a dynamic routing and scheduling problem that considers adjustments to an initial routing itinerary when one or more vehicle failures occur during the execution stage and the original plan must be modified. We minimize the operational and schedule disruption costs. Formulations based on mixed-integer programming are presented to compare different policies in the rerouting phase. A solution strategy is developed when both costs are evaluated and it is necessary to find a solution quickly. Computational tests on a large set of instances compare the different decision-maker policies.

关键词： rescheduling disruption schedule costs mixed-integer programming arc routing problem

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Symmetry breaking for generalized disjunctive programming formulation of the strip packing problem

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ANNALS OF OPERATIONS RESEARCH 2017年第2期258卷 747-759页

作者： Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA

In this work we present a new generalized disjunctive programming (GDP) formulation for the strip packing problem. The new formulation helps to break some of the symmetry that arises in this problem. The new formulation is further improved for the case in which the heights and lengths of the rectangles are integer numbers. The GDP model can be formulated and solved as a mixed-integer linear programming (MILP) model, using different GDP-to-MILP reformulations. The results show that the MILP reformulations of the new GDP model (and its improvement for rectangles with integer heights and widths) can be solved faster than the previously proposed GDP formulation.

关键词： Strip packing Disjunctive programming mixed-integer programming

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New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem

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IEEE TRANSACTIONS ON POWER SYSTEMS 2017年第6期32卷 4161-4170页

作者： Kocuk, Burak Dey, Santanu S. Sun, Xu Andy Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that DC approximation may lead to inaccurate flow solutions and also overlook stability issues. In this paper, we focus on the optimal transmission switching problem with the full AC power flow model, abbreviated as AC optimal transmission switching (AC OTS). We propose a new exact formulation for ACOTS and its mixed-integer second-order cone programming relaxation. We improve this relaxation via several types of strong valid inequalities inspired by the recent development for the closely related AC optimal power flow problem [Kocuk et al., "Strong SOCP relaxations for the optimal power flow problem," Oper. Res., vol. 64, no. 6, pp. 1177-1196, 2016]. We also propose a practical algorithm to obtain high-quality feasible solutions for the AC OTS problem. Extensive computational experiments show that the proposed formulation and algorithms efficiently solve IEEE standard and congested instances and lead to significant cost benefits with provably tight bounds.

关键词： AC transmission switching cutting planes mixed-integer programming second order cone programming semidefinite programming valid inequalities

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Robust multicriteria risk-averse stochastic programming models

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ANNALS OF OPERATIONS RESEARCH 2017年第1-2期259卷 259-294页

作者： Liu, Xiao Kucukyavuz, Simge Noyan, Nilay Ohio State Univ Dept Integrated Syst Engn Columbus OH 43210 USA Univ Washington Ind & Syst Engn Seattle WA 98195 USA Sabanci Univ Ind Engn Program Istanbul Turkey

In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional value-at-risk (CVaR). First, we introduce a model that optimizes the worst-case multivariate CVaR and show that its optimal solution lies on a particular type of stochastic efficient frontier. To solve this model, we develop a finitely convergent delayed cut generation algorithm for finite probability spaces. We also show that the proposed model can be reformulated as a compact linear program under certain assumptions. In addition, for the cut generation problem, which is in general a mixed-integer program, we give a stronger formulation than the existing ones for the equiprobable case. Next, we observe that similar polyhedral enhancements are also useful for a related class of multivariate CVaR-constrained optimization problems that has attracted attention recently. In our computational study, we use a budget allocation application to benchmark our proposed maximin type risk-averse model against its risk-neutral counterpart and a related multivariate CVaR-constrained model. Finally, we illustrate the effectiveness of the proposed solution methods for both classes of models.

关键词： Stochastic programming Risk aversion Robust optimization Multicriteria optimization Stochastic Pareto optimality Conditional value-at-risk Cut generation mixed-integer programming McCormick envelopes RLT technique

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