作者:
Vielma, Juan PabloMIT
Sloan Sch Management 77 Massachusetts Ave Cambridge MA 02139 USA
There is often a significant trade-off between formulation strength and size in mixedintegerprogramming. When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variabl...
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There is often a significant trade-off between formulation strength and size in mixedintegerprogramming. When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes help resolve this trade-off. However, standard formulations that use such auxiliary continuous variables can have a worse-than-expected computational effectiveness, which is often attributed precisely to these auxiliary continuous variables. For this reason, there has been considerable interest in constructing strong formulations that do not use continuous auxiliary variables. We introduce a technique to construct formulations without these detrimental continuous auxiliary variables. To develop this technique we introduce a natural non-polyhedral generalization of the Cayley embedding of a family of polytopes and show it inherits many geometric properties of the original embedding. We then show how the associated formulation technique can be used to construct small and strong formulation for a wide range of disjunctive constraints. In particular, we show it can recover and generalize all known strong formulations without continuous auxiliary variables.
We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor The firm aims at finding the location and attractiv...
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We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit The competitor on the other hand can react by adjusting the attractiveness of its existing facilities with the objective of maximizing its own profit The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at predetermined candidate sites We employ Huff's gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and Inversely proportional to the distance between the facility site and demand point We formulate a bilevel mixed-integernonlinearprogramming model where the firm entering the market is the leader and the competitor is the follower In order to find the optimal solution of this model we convert It Into an equivalent one-level mixedintegernonlinear program so that it can be solved by global optimization methods Apart from reporting computational results obtained on a set of randomly generated instances we also compute the benefit the leader firm derives from anticipating the competitor s reaction of adjusting the attractiveness levels of its facilities The results on the test Instances indicate that the benefit is 58 33% on the average (C) 2010 Elsevier B V All rights reserved
An interval based superstructure approach for combining the synthesis of heat and mass exchanger networks is presented in this paper. The technique involves combining the interval based MINLP superstructure (IBMS) for...
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An interval based superstructure approach for combining the synthesis of heat and mass exchanger networks is presented in this paper. The technique involves combining the interval based MINLP superstructure (IBMS) for the synthesis of heat exchanger networks (HENS) with that of mass exchanger networks (MENs). The two networks are made to interact through the lean stream in the mass exchange network. The new approach involves the use of the lean substream concept to explore potential mass exchange temperatures. An example which involves a one-lean stream mass exchange problem alongside regeneration and hot and cold utilities is presented. (C) 2009 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates an...
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Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use mixed integer nonlinear programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.
Rapid global industrial development has led to a significant increase in waste generation, including wastewater. Improper disposal of wastewater leads to the degradation of water bodies, endangering marine life and po...
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Rapid global industrial development has led to a significant increase in waste generation, including wastewater. Improper disposal of wastewater leads to the degradation of water bodies, endangering marine life and posing health hazards to the nearby communities. This study addresses the current lack of integration in the design of wastewater treatment plants and the challenge presented by the conflicting criteria of economic impact and environmental cost. A multi-period and multi-criterion non-linear programming model for a wastewater treatment plant that simultaneously considers economic and environmental tradeoffs, alternative plant configurations, disposal and reuse options is then developed. The study considers the variability of inputs in the form of water quality and quantity in order to demonstrate the natural variations presented by wastewater sources across a planning horizon. The proposed model is applied to a case study of an actual water utility company in the Philippines. It was seen that the integration of disposal and reuse options had facilitated the realization of improved economic and environmental benefits as it was able to match the effluent water quality to the best suited option. The model enabled the improvement of the treatment process of wastewater inputs by considering alternative methods of entry such as series and parallel configurations instead of just having a mixed input configuration. This significantly improved relevant metrics such as processing time and operational costs. (C) 2019 Elsevier Ltd. All rights reserved.
In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective...
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In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of average zone pressure, while penalizing deviations from a target chlorine concentration. We propose a relax-tighten-round algorithm based on tightened polyhedral relaxations and a rounding scheme to compute feasible solutions, with bounds on their optimality gaps. This is because off-the-shelf global optimization solvers failed to compute feasible solutions for the considered non-convex mixedintegernonlinear program. The implemented algorithm is evaluated using three benchmarking water networks, and they are shown to outperform off-the-shelf solvers, for these case studies. The proposed heuristic has enabled the computation of good quality feasible solutions in most instances, with bounds on the optimality gaps that are comparable to the order of uncertainty observed in operational water network models. (c) 2021 Elsevier B.V. All rights reserved.
In this paper, a new global optimization approach for the synthesis of heat exchanger networks is presented. The Synheat model by [Comp. Chem. Eng. 1 (1990) 1165] uses a promising superstructure that includes the most...
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In this paper, a new global optimization approach for the synthesis of heat exchanger networks is presented. The Synheat model by [Comp. Chem. Eng. 1 (1990) 1165] uses a promising superstructure that includes the most common heat exchanger structures, and optimizes utility costs, the number of units and heat exchanger areas simultaneously. With some minor modifications of the model, it is possible to apply a new global optimization strategy to the problem. The heart of the strategy is to convexify signomial terms, and create approximate convexified subproblems. If the Synheat model is extended in an appropriate way, the isothermal mixing assumption can be removed. Applying the new global optimization strategy to the model allowing non-isothermal mixing makes it possible to find truly optimal network configurations for the case of constant heat-capacity flow rates and heat transfer coefficients. Some examples to illustrate the global optimization strategy and to illustrate that the Synheat model can exclude optimal configurations due to the isothermal mixing assumption are also given in this paper. (C) 2002 Elsevier Science Ltd. All rights reserved.
In this paper a new approach for the global solution of nonconvex MINLP (mixed integer nonlinear programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applyin...
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In this paper a new approach for the global solution of nonconvex MINLP (mixed integer nonlinear programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applying different variable transformation techniques and a discretization scheme a lower bounding convex MINLP problem can be derived. The convexified MINLP problem can be solved with standard methods. The key element in this approach is that all transformations are applied termwise. In this way all convex parts of the problem are left unaffected by the transformations. The method is illustrated by four example problems. (C) 2007 Elsevier B.V. All rights reserved.
We consider a hub-and-spoke network design problem with inter-hub economies-of-scale and hub congestion. We explicitly model the economies-of-scale as a concave piece-wise linear function and congestion as a convex fu...
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We consider a hub-and-spoke network design problem with inter-hub economies-of-scale and hub congestion. We explicitly model the economies-of-scale as a concave piece-wise linear function and congestion as a convex function. The problem is modeled as a nonlinearmixedinteger program that is difficult to solve directly since the objective function has both convex and concave nonlinear terms and hence finding an optimal solution may not be easy. A Lagrangian approach is proposed to obtain tight upper and lower bounds. The Lagrangian decomposition exploits the structure of the problem and decomposes it to convex and concave subproblems. Furthermore, we add some valid inequalities to accelerate the convergence rate of the Lagrangian heuristic. To tackle large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is developed. Both the Lagrangian heuristic and GRASP provide high-quality solutions within reasonable computational time. The optimal designs of hub-and-spoke networks with nonlinear inter-hub economies-of-scale and congestion at hub locations are analyzed in comparison with other models in the literature to demonstrate the significant impact of modeling nonlinearity in economies-of-scale and congestion simultaneously rather than independently.
Today's infrastructures are mainly designed heuristically using state-of-the-art simulation software and engineering approaches. However, due to complexity, only part of the restrictions and costs that show up dur...
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Today's infrastructures are mainly designed heuristically using state-of-the-art simulation software and engineering approaches. However, due to complexity, only part of the restrictions and costs that show up during the lifecycle can be taken into account. In this paper, we focus on a typical and important class of infrastructure problems, the design of high-pressure steam pipes in power plants, and describe a holistic approach taking all design, physical, and technical constraints and the costs over the full lifecycle into account. The problem leads to a large-scale mixed-integer optimization problem with partial differential equation (PDE) constraints which will be addressed hierarchically. The hierarchy consists of a combinatorial and a PDE-constrained optimization problem. The final design is evaluated with respect to damage, using beam models that are nonlinear with respect to kinematics as well as constitutive law. We demonstrate the success of our approach on a real-world instance from our industrial partner Bilfinger SE.
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