This work addresses the topic of constrained dynamic programming for problems involving multi-stage mixed-integerlinear formulations with a linear objective function. It is shown that such problems may be decomposed ...
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This work addresses the topic of constrained dynamic programming for problems involving multi-stage mixed-integerlinear formulations with a linear objective function. It is shown that such problems may be decomposed into a series of multi-parametric mixed-integerlinear problems, of lower dimensionality, that are sequentially solved to obtain the globally optimal solution of the original problem. At each stage, the dynamic programming recursion is reformulated as a convex multi-parametric programming problem, therefore avoiding the need for global optimisation that usually arises in hard constrained problems. The proposed methodology is applied to a problem of mixed-integerlinear nature that arises in the context of inventory scheduling. The example also highlights how the complexity of the original problem is reduced by using dynamic programming and multi-parametric programming. (C) 2014 Elsevier Ltd. All rights reserved.
This note concerns the problem of k-hop connectivity in a network of mobile agents, which is achieved if any pair of agents can communicate with each other through a link of k-1 or fewer intermediate nodes. We propose...
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This note concerns the problem of k-hop connectivity in a network of mobile agents, which is achieved if any pair of agents can communicate with each other through a link of k-1 or fewer intermediate nodes. We propose linear constraints involving binary optimization variables to ensure k-hop connectivity. Such constraints are then integrated into a mixed-integer linear programming (MILP) trajectory planning model. Simulation results illustrate the application of the proposed method and the effect of varying k in the context of a mission involving the visitation of multiple targets.
In this paper, we address the bin packing problem while minimizing the total loading cost of used bins. We focus on two different quantity discount schemes: the all-unit discount and the incremental discount. For both...
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Graph Neural Networks (GNNs) provide state-of-the-art graph learning performance, but their lack of transparency hinders our ability to understand and trust them, ultimately limiting the areas where they can be applie...
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This paper presents a non-intrusive load monitoring (NILM) model based on two-stage mixed-integer linear programming theory. Compared with other mixedinteger optimization-based models, this paper model introduces few...
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As the artificial intelligence community advances into the era of large models with billions of parameters, distributed training and inference have become essential. While various parallelism strategies—data, model, ...
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In mixed-integerprogramming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-cod...
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Hyperspectral unmixing is the analytical process of determining the pure materials and estimating the proportions of such materials composed within an observed mixed pixel spectrum. We can unmix mixed pixel spectra us...
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This research proposes a mixedintegerlinearprogramming model to assist structural engineers in the reinforcement detailing phase of circular foundations, with a specific focus on wind tower foundations, aiming to o...
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This research proposes a mixedintegerlinearprogramming model to assist structural engineers in the reinforcement detailing phase of circular foundations, with a specific focus on wind tower foundations, aiming to optimise the design process and, consequently, reduce the costs associated with constructing these elements. After analysing the internal forces in circular foundations, the designer must define the calculation sections to determine the required area of steel and select the diameter of the steel bars and their positioning in the base. This determination is often based on the designer's experience, which can lead to choices that unnecessarily increase costs, thus justifying the creation of a model to optimise this process. The proposed model consists of three phases: the first involves a non-linear regression to obtain an equation that represents the bending moments at any point in the foundation;the second applies a linear quadratic model to choose the ideal layout of the calculation sections;and the third uses a binary integerlinear model to determine the ideal diameter of the bars and their consequent positioning. This search for optimality must comply with the restrictions imposed by normative criteria, including maximum bar lengths and rebar lap splices, maintaining good constructability based on standardisation. Validation tests were conducted with confirmed cases using the proposed model, resulting in an average reduction of 10.72% in the value of the rebar weight due to the model's second stage and a decrease of 12.28% in the best case during the final step. It can, therefore, be concluded that the proposed model is viable for application in circular foundation projects, leading to savings in the total weight of steel used in the foundations.
Disjunctive cutting planes can tighten a relaxation of a mixed-integerlinear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose additional variables cause the procedu...
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Disjunctive cutting planes can tighten a relaxation of a mixed-integerlinear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose additional variables cause the procedure to be computationally prohibitive. Adopting a V-polyhedral perspective is a practical alternative that enables the separation of disjunctive cuts via a linear program with only as many variables as the original problem. The drawback is that the classical approach of monoidal strengthening cannot be directly employed without the values of the extra variables appearing in the extended formulation, which constitute a certificate of validity of the cut. We derive how to compute this certificate from a solution to the linear program generating V-polyhedral disjunctive cuts. We then present computational experiments with monoidal strengthening of cuts from disjunctions with as many as 64 terms. Some instances are dramatically impacted, with strengthening increasing the gap closed by the cuts from 0 to 100%. However, for larger disjunctions, monoidal strengthening appears to be less effective, for which we identify a potential cause. Lastly, the certificates of validity also enable us to verify which disjunctive cuts are equivalent to intersection cuts, which happens increasingly rarely for larger disjunctions.
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