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Showing 1 to 20 of 28 for “"reformulation linearization technique"”.
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Global Optimization of the Nonconvex Containership Design Problem Using the Reformulation-Linearization Technique
… modeling, approximation, and global optimization techniques for developing a multidisciplinary approach to the containership design problem. The problem involves five design variables, which prioritized according to their relative importance in the model are: design draft, depth at side, speed, …
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A new reformulation-linearization technique for the bilinear programming and related problems, with applications to risk management
… environments. The new algorithm develops a novel Reformulation-Linearization Technique (RlT) that uses an enumeration of variable factors to multiply constraints, and uses constraints to multiply constraints, to generate new nonlinear constraints which are subsequently linearized by defining new …
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A reformulation-linearization based implicit enumeration algorithm for the rectilinear distance location-allocation problem
… programming relaxations constructed via the Reformulation-Linearization Technique (RLT), the latter formulation is shown to provide stronger lower bounds and is therefore adopted for implementation. In addition, cutting planes are developed to further strengthen the linear programming …
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GPU accelerated Hungarian algorithm for traveling salesman problem
… function and constraints. This is referred to as Reformulation Linearization Technique at Level 2 (or RLT2). We apply dual ascent procedure for obtaining lower bounds that employs Linear Assignment Problem (LAP) solver recently developed by Date(2016). The solver is a parallelized Hungarian …
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Solving Factorable Programs with Applications to Cluster Analysis, Risk Management, and Control Systems Design
… This dissertation focuses on employing the Reformulation-Linearization Technique (RLT) to enhance model formulations and to design effective solution techniques for solving several practical instances of continuous nonconvex optimization problems, namely, the hard and fuzzy clustering …
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Development of Optimization and Simulation Models for the Analysis of Airfield Operations
… we develop a mathematical model and apply the Reformulation-Linearization-Technique (RLT) of Sherali and Adams to construct an enhanced tightened version of the proposed model. Since ASP is NP-Hard and in fact, it is a variation of the well-known Traveling Salesman Problem with time-windows, …
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A new hierarchy of relaxations for 0-1 mixed integer problems with application to some specially structured problems
… of relaxations is developed that extends the Reformulation-Linearization Technique (RLT) of Sherali and Adams (1989, 1990). This hierarchy referred to as (RLT1), provides a unifying framework for constructing a spectrum of continuous relaxations spanning from the linear programming relaxation …
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Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems
This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex …
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Algorithmic Approaches for Solving the Euclidean Distance Location and Location-Allocation Problems
… (EMFLP), two equivalent convex differentiable reformulations are proposed. The first of these is formulated directly in the primal space, and relationships between its Karush-Kuhn-Tucker (KKT) conditions and the necessary and sufficient optimality conditions for EMFLP are established in order …
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Enhanced intersection cutting plane and reformulation-linearization enumeration based approaches for linear complementarity problems
… a global optimization algorithm based on a novel Reformulation-Linearization Technique (RLT). We do not place any restrictions on the matrix M associated with LCP in this case. This RLT scheme provides an equivalent linear, mixed integer programming formulation of LCP, that possesses a tight …
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Network Design and Analysis Problems in Telecommunication, Location-Allocation, and Intelligent Transportation Systems
… problem, we develop a model and apply the Reformulation-Linearization Technique (RLT) to construct various enhanced tightened versions of the proposed model. We also design efficient Lagrangian dual schemes for solving the linear programming relaxation of the various enhanced models, and …
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A Discrete Optimization Approach to Solve a Reader Location Problem for Estimating Travel Times
… An optimization approach based on the Reformulation-Linearization Technique coupled with Semidefinite Programming concepts is designed to solve the formulated reader location problem. This approach can be used to derive alternative equivalent formulations of the problem that vary in the …
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Global Optimization of Nonconvex Factorable Programs with Applications to Engineering Design Problems
… polynomials, coordinated with a {em Reformulation-Linearization Technique} (RLT). The initial stage of the lower bounding step generates a tight, nonconvex polynomial programming relaxation for the given problem. Subsequently, an LP relaxation is constructed for the resulting …
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Optimization Models and Analysis of Routing, Location, Distribution, and Design Problems on Networks
… polyhedral outer approximations and applying the Reformulation-Linearization Technique (RLT), a tight linear lower bounding problem is derived. This problem provides an enhancement and a more precise representation of previous lower bounding relaxations that use similar approximations. …
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Polynomial and indefinite quadratic programming problems: algorithms and applications
… present a branch and bound algorithm that uses a Reformulation Linearization Technique (RLT) to generate tight linear programming relaxations. This bounding scheme involves an automatic reformulation of the problem via the addition of certain nonlinear implied constraints that are generated by …
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An optimal replacement-design model for a reliable water distribution network system
… optimal solutions. This procedure is based on a Reformulation-Linearization Technique that constructs tight linear programming relaxations for the nonlinear problem, and embeds these in a branch-and-bound algorithm. A suitable partitioning strategy is coordinated with this scheme to provably …
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Tight Discrete Formulations to Enhance Solvability with Applications to Production, Telecommunications, and Air Transportation Problems
… management problem. We first consider the Reformulation-Linearization Technique (RLT) of Sherali and Adams and explore the generation of reduced first-level representations for mixed-integer 0-1 programs that tend to retain the strength of the full first-level linear programming relaxation. …
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Integrated Aircraft Fleeting, Routing, and Crew Pairing Models and Algorithms for the Airline Industry
… which is then linearized and lifted using the Reformulation-Linearization Technique (RLT). The resulting formulation remains polynomial in size, and we show that it can be solved very efficiently by commercial software without complicated algorithmic implementations. Our numerical experiments …
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Enhanced Formulations for Minimax and Discrete Optimization Problems with Applications to Scheduling and Routing
… in order to tighten its representation using the Reformulation-Linearization/Convexification Technique (RLT), and demonstrate the benefits of the resulting lifted formulations for several classes of problems. Specifically, we investigate RLT-enhanced Lagrangian dual formulations for the class of …
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Tactical Network Flow and Discrete Optimization Models and Algorithms for the Empty Railcar Transportation Problem
… some partial convex hull constructions using the Reformulation-Linearization Technique (RLT). This tightening of the underlying linear programming relaxation is shown to permit the solution of larger problem sizes, and enables the exact solution of certain scenarios having 5,000 - 8,000 arcs. …
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