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 prov...
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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.
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 mater...
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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.
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...
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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.
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 a...
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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.
作者:
Meng, LingpengKang, QiHan, ChuanfengHu, ShaolongTongji 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 recove...
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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.
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 succ...
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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.
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 du...
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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.
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 formulati...
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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.
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 reliab...
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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.
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 ...
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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.
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