Providing a good formulation is an important part of solving a mixed-integer *** suggest measuring the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially...
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Providing a good formulation is an important part of solving a mixed-integer *** suggest measuring the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially strengthening coefficients can then be used as a tool for improving *** believe this method could be useful for analyzing and producing tight formulations of problems that arise in *** illustrate the use of the approach on a problem in production scheduling. We also prove that coefficient strengthening leads to formulations with a desirable property: if no coefficient can be strengthened, then no constraint can be replaced by an inequality that dominates it. The effect of coefficient strengthening is tested on a number of problems in computational experiments. The strengthened formulations are compared to reformulations obtained by the preprocessor of a commercial software package. For several test problems, the formulations obtained by coefficient strengthening are substantially stronger than the formulations obtained by the preprocessor. In particular, we use coefficient strengthening to solve two difficult problems to optimality that have only recently been solved.
Decisions regarding natural gas production, processing and transportation depend on each other, and knowledge about how partial changes in a gas transmission network influence the network capacity and flexibility is c...
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Decisions regarding natural gas production, processing and transportation depend on each other, and knowledge about how partial changes in a gas transmission network influence the network capacity and flexibility is crucial in ensuring efficient system operation. SINTEF has developed a decision support tool, GassOpt, which is based on mixed-integer optimisation. The model objective is to maximise the flow throughput or profit for a given technical state of a natural gas network. The objective of this work has been to develop extensions to the GassOpt model mainly related to modelling of gas processing and energy consumption related to compression, and to analyse their impact on network operation. The extended GassOpt model represents and analyses a gas transport network in more detail, in particular in discovering bottlenecks, related to gas quality, contaminants and energy efficiency, which have obtained increased focus in recent time. GassOpt is a general tool for gas network optimisation, but applied on the Norwegian gas transport network specifically. The GassOpt tool is used to evaluate the current network as well as possible network extensions. Our approach ensures optimal operation of the network by considering the complete system and provides valuable insights in the dependencies between the different parts of the system. Tests show that the model represents actual network operation in a very good way. (C) 2010 Elsevier B.V. All rights reserved.
We consider the problem of sequencing a set of jobs in a single machine to minimize the maximum of the total weighted completion time of the jobs over a number of scenarios, each corresponding to a set of job processi...
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We consider the problem of sequencing a set of jobs in a single machine to minimize the maximum of the total weighted completion time of the jobs over a number of scenarios, each corresponding to a set of job processing times. We give a large family of inequalities that are valid for the convex hull of the set of feasible schedules. We then present computational experience in which some of the inequalities are added to the original formulation. We demonstrate through the computational results that their addition to the formulation can substantially improve, among other things, the time required to solve difficult instances of the problem through branch-and-cut. (C) 2009 Elsevier Ltd. All rights reserved.
A mixed-integer knapsack problem solving method is suggested. With this purpose, first, the number of integer-valued variables and the domain of feasible solutions (containing the optimal solution) are decreased. Furt...
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A mixed-integer knapsack problem solving method is suggested. With this purpose, first, the number of integer-valued variables and the domain of feasible solutions (containing the optimal solution) are decreased. Further, the received problem is solved using the "branch and bound" type method, where the narrow intervals for the functional and variables are used while each is branching. The numerous computing experiments fulfilled have shown that the suggested method operates more rapidly than the known "branch and bound" method.
Lifting, tilting and fractional programming, though seemingly different, reduce to a common optimization problem. This connection allows us to revisit key properties of these three problems on mixedinteger linear set...
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Lifting, tilting and fractional programming, though seemingly different, reduce to a common optimization problem. This connection allows us to revisit key properties of these three problems on mixedinteger linear sets. We introduce a simple common framework for these problems, and extend known results from each to the other two. (C) 2010 Elsevier B.V. All rights reserved.
We consider mixed-integer sets defined by a linear system Ax >= b plus an integrality requirement on one variable, where A is a totally unimodular matrix with at most two nonzero entries per row. We give a complete...
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We consider mixed-integer sets defined by a linear system Ax >= b plus an integrality requirement on one variable, where A is a totally unimodular matrix with at most two nonzero entries per row. We give a complete linear-inequality description for the convex hull of any set of this type. (C) 2010 Elsevier B.V. All rights reserved.
We consider single-level uncapacitated and capacitated lot-sizing problems with product substitution, where products may be substituted by certain other products to satisfy demand. The models incorporate initial inven...
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We consider single-level uncapacitated and capacitated lot-sizing problems with product substitution, where products may be substituted by certain other products to satisfy demand. The models incorporate initial inventories and general substitution structures. We formulate the problems as mixed-integer linear programs and develop Simple Plant Location-based reformulations as well as new valid inequalities. Computational results on generated problem instances show that the reformulations are superior to the original formulations and those with valid inequalities added a priori, except for instances with multiple resources and downward substitution. In most cases, the running times of a mixed-integer programming solver on approximate extended formulations that only contain a subset of the disaggregated constraints were almost as good as on complete Simple Plant Location-based reformulations.
We consider mixed-integer sets of the form X {(s, y) is an element of R(+) x Z(n) : s + a(j)y(j) >= b(j), for all j is an element of N}. A polyhedral characterization for the case where X is defined by two inequali...
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We consider mixed-integer sets of the form X {(s, y) is an element of R(+) x Z(n) : s + a(j)y(j) >= b(j), for all j is an element of N}. A polyhedral characterization for the case where X is defined by two inequalities is provided. From that characterization we give a compact formulation for the particular case where the coefficients of the integer variables can take only two possible integer values a(1), a(2) is an element of Z(+) : X(n,m) = {(s, y) is an element of R(+) x Z(n+m) : s + a(1)y(j) >= b(j), for all j is an element of N(1), s + a(2)y(j) >= b(j), j is an element of N(2)} where N(1) = {1, ... , n}, N(2) = {n + 1, ... , n + m}. In addition, we discuss families of facet-defining inequalities for the convex hull of X(n,m).
We present an integerprogramming model for human leukocyte antigen (HLA) association studies based on the parsimony criterion. The model is simple, compact, easy to implement, and able to handle datasets containing u...
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We present an integerprogramming model for human leukocyte antigen (HLA) association studies based on the parsimony criterion. The model is simple, compact, easy to implement, and able to handle datasets containing up to 200 phenotypes. Computational experiments carried out on patients affected by psoriasis and severe alopecia areata show that the model is consistent with the experimental haplotype frequencies, showing, for the considered diseases at least, a high reliability of the predictions. These promising results provide perspective on computer-aided association studies and encourage the development of efficient exact computational approaches for haplotype estimation. (C) 2010 American Society for Histocompatibility and Immunogenetics. Published by Elsevier Inc. All rights reserved.
Energy systems are the major contributor to ever-increasing primary energy consumption and consequent greenhouse gas emissions. To tackle these critical problems, planning and design of energy systems needs to be impr...
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Energy systems are the major contributor to ever-increasing primary energy consumption and consequent greenhouse gas emissions. To tackle these critical problems, planning and design of energy systems needs to be improved towards a more efficient, cost-effective, and environmentally benign direction. However, although there are many technical choices available, they are often developed separately by their own technical communities and driven by their specific interest, thus methods and experience obtained in planning and design of a certain type of energy systems are usually not applicable to other types of energy systems. Energy systems engineering provides a generic methodological framework to facilitate the planning and design of energy systems and to produce integrated solutions to real-life complex energy problems via a systematic *** this paper, we present an overview of key methodologies of energy systems engineering, covering superstructure based modelling, mixed-integer programming, multi-objective optimization, optimization under uncertainty, and life-cycle assessment. Applications of these methodologies in polygeneration energy systems design, hydrogen infrastructure planning, and design of energy systems in commercial buildings are provided to demonstrate the capability of these methodologies.
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