Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 29 for “"Valid Inequalities"”.
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Discrete and Continuous Nonconvex Optimization: Decision Trees, Valid Inequalities, and Reduced Basis Techniques
… programming problems, through the generation of valid inequalities and reduced representations, along with the design and implementation of efficient algorithms. We first conduct a quantitative analysis for a strategic risk management problem that involves allocating certain available …
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Valid inequalities and algorithms for the network design problem with an application to LTL consolidation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 1985.
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The polyhedral structure of certain combinatorial optimization problems with application to a naval defense problem
… lifting procedures of minimal GUS cover inequalities. Second, we develop a new family of cutting planes for the set partitioning polytope for deleting any fractional basic feasible solutions to its underlying linear programming relaxation. We also show that all the known classes of valid …
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Network Design and Analysis Problems in Telecommunication, Location-Allocation, and Intelligent Transportation Systems
… p-median problem, we develop various valid inequalities, a separation routine for generating cutting planes via specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid …
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Distributionally Ambiguous Stackelberg Combinatorial Games for Submodular Optimization and Camera View-Frame Placement
… under any other, to derive a new class of valid inequalities. Since our algorithm repeatedly solves the defender's problem, placing p camera view frames to maximize the coverage, we also contribute efficient exact methods for p = 1 and novel heuristics for p ≥ 2, validated through …
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Contributions to Multiple Postmen Problems
… capacity constraints, an important class of valid inequalities, which could formerly only be separated heuristically. We achieve new best lower bounds with a cutting plane algorithm incorporating this new separation method. For the MM k-CPP we present the only existing heuristic found in the …
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Cutting Planes for Convex Objective Nonconvex Optimization
… over a nonconvex domain. A class of linear inequalities obtained by lifting easily obtained valid inequalities is introduced, and it is shown that this class of inequalities is sufficient to describe the epigraph of a convex and differentiable function over a general domain. In the special …
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A Demand Driven Re-fleeting Approach for Aircraft Assignment Under Uncertainty
… and for deriving certain classes of valid inequalities. Various approaches for implementing such reformulation techniques are investigated and tested. The best of these procedures for solving large-scale challenging instances of the problem turns out to be an integrated approach that …
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Polyhedra Study of Mixed Integer Programs With Variable Upper Bounds
… We introduce the flow cover inequality, which is valid for a projection. We also give conditions under which this inequality is facet defining. We use sequence independent lifting to obtain valid inequalities for the entire set. In general, computing the lifting function is NP-hard, but under an …
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Cutting plane algorithms for variational inference in graphical models
… in discrete Markov Random Fields (MRFs). Valid constraints are derived for the marginal polytope through a series of projections onto the cut polytope. Projecting onto a larger model gives an efficient separation algorithm for a large class of valid inequalities arising from each of the …
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Fair and Risk-Averse Resource Allocation in Transportation Systems under Uncertainties
… Additionally, we strengthen these models with valid inequalities. To efficiently solve these models, we design exact algorithms and approximation algorithms capable of obtaining near-optimal solutions. We numerically validate the effectiveness of our proposed models and demonstrate their …
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On the matrix cuts of Lovasz and Schrijver and their use in integer programming
… in a given polyhedron and to derive linear inequalities valid for these 0-1 vectors from a linear inequality system defining the polyhedron. Lovasz and Schrijver (1991) described a family of operators, called the matrix-cut operators, which generate strong valid inequalities, called matrix …
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An Airspace Planning and Collaborative Decision Making Model Under Safety, Workload, and Equity Considerations
… conflict analyses, the derivation of valid inequalities to tighten the conflict safety representation constraints, the development of workload metrics based on average (and its variance from) peak load measures, and the consideration of equity among airline carriers in absorbing the …
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Integrated Airline Operations: Schedule Design, Fleet Assignment, Aircraft Routing, and Crew Scheduling
… model is used to derive several classes of valid inequalities for tightening its representation. Solution approaches are developed by applying Benders decomposition method to the resulting lifted model, and computational experiments are conducted using real data obtained from a major U.S. …
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Studies of Complex Routing Problems with Synchronization and Stochastic Information
… problem with transfers, strengthened by novel valid inequalities, and extended to a novel branch-and-cut approach, which outperforms existing methods by solving 68 of 90 large benchmark instances and, for the first time, solves instances with up to 50 requests. The fourth chapter addresses a …
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A new hierarchy of relaxations for 0-1 mixed integer problems with application to some specially structured problems
… obtained using other methods. A new class of valid inequalities for the 3-index TSP is also presented. Finally, the dissertation concludes with comments concerning extensions and parallel implementations of RLT1.
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Advanced mixed-integer programming formulations : methodology, computation, and application
… and develop a new strong formulation and valid inequalities for this structure. We close the thesis by answering a speculative question: Given a disjunctive constraint, what can we reasonably sacrifice in order to construct MIP formulations with very few integer variables? We show that, if …
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Meal Delivery Optimisation for the Restaurant Chain
… solver and incorporating two categories of valid inequalities for exactly solving the SOCSS. The pandemic-induced surge in third-party Online Food Ordering and Delivery (OFOD) platforms has propelled them to a dominant position in the competitive environment compared with participating …
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Designing robust railroad blocking plans
… computational burden, such as adding a set of valid inequalities and using advanced start dual solutions. These enhancements help tighten the lower bounds and facilitate the generation of high quality feasible solutions. We test the proposed models and solution approaches using the data from a …
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Novel Approaches for Some Stochastic and Deterministic Scheduling Problems
… approach for its solution. Furthermore, a set of valid inequalities are incorporated to strengthen the relaxed master problem of this decomposition scheme. The proposed approach is demonstrated on the single machine total weighted tardiness scheduling problem. Our computational investigation …
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