Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting...
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Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous optimization problem over weights parametrizing families of valid inequalities. This problem can also be interpreted as optimizing a neural network to solve an optimization problem over subadditive functions, which we call the subadditive primal problem of the MILP. To do so, we propose a concrete two-step algorithm, and demonstrate empirical gains when optimizing generalized Gomory mixed-integer inequalities over various classes of MILPs. Code for reproducing the experiments can be found at https://github .com /dchetelat /subadditive.& COPY;2023 Elsevier B.V. All rights reserved.
Conferences are a key aspect of communicating knowledge, and their schedule plays a vital role in meeting the expectations of participants. Given that many conferences have different constraints and objectives, differ...
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Conferences are a key aspect of communicating knowledge, and their schedule plays a vital role in meeting the expectations of participants. Given that many conferences have different constraints and objectives, different mathematical models and heuristic methods have been designed to address rather specific requirements of the conferences being studied per se. We present a penalty system that allows organisers to set up scheduling preferences for tracks and submissions regarding sessions and rooms, and regarding the utilisation of rooms within sessions. In addition, we also consider hybrid and online conferences where submissions need to be scheduled in appropriate sessions based on timezone information. A generic scheduling tool is presented that schedules tracks into sessions and rooms, and submissions into sessions by minimising the penalties subject to certain hard constraints. Two integer programming models are presented: an exact model and an extended model. Both models were tested on five real instances and on two artificial instances which required the scheduling of several hundreds of time slots. The results showed that the exact model achieved optimal solutions for all instances except for one instance which resulted in 0.001% optimality gap, and the extended model handles more complex and additional constraints for some instances. Overall, this work demonstrates the suitability of the proposed generic approach to optimise schedules for in-person, hybrid, and online conferences.
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited 2-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary va...
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We consider the problem of mapping a logical quantum circuit onto a given hardware with limited 2-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized simultaneously without significant loss. We test our algorithm on a large number of quantum volume circuits, optimizing for error rate and depth;our algorithm significantly reduces the number of CNOTs compared to Qiskit's default transpiler SABRE [19] and produces circuits that, when executed on hardware, exhibit higher fidelity.
Origami architecture (OA) is a fascinating papercraft that involves only a piece of paper with cuts and folds. Interesting geometric structures 'pop up' when the paper is opened. However, manually designing su...
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In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-pr...
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In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-processing step to fix several variables. We design a exact iterativescheme algorithm based on a fast heuristic for the integer programming formulation (ISA-FH).Computational results show the effectiveness of the improved formulation and algorithm.
Two models and a heuristic algorithm to address the wind farm layout optimization problem are presented. The models are linear integer programming formulations where candidate locations of wind turbines are described ...
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Two models and a heuristic algorithm to address the wind farm layout optimization problem are presented. The models are linear integer programming formulations where candidate locations of wind turbines are described by binary variables. One formulation considers an approximation of the power curve by means of a stepwise constant function. The other model is based on a power-curve-free model where minimization of a measure closely related to total wind speed deficit is optimized. A special-purpose neighborhood search heuristic wraps these formulations with increasing tractability and effectiveness compared to the full model that is not contained in the heuristic. The heuristic iteratively searches for neighborhoods around the incumbent using a branch-and-cut algorithm. The number of candidate locations and neighborhood sizes are adjusted adaptively. Numerical results on a set of publicly available benchmark problems indicate that a proxy for total wind speed deficit as an objective is a functional approach, since high-quality solutions of the metric of annual energy production are obtained when using the latter function as an substitute objective. Furthermore, the proposed heuristic is able to provide good results compared to a large set of distinctive approaches that consider the turbine positions as continuous variables.
A crucial role of container shipping is maximizing container uptake onto vessels, optimizing the efficiency of a fundamental part of the global supply chain. In practice, liner shipping companies include block stowage...
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ISBN:
(纸本)9783031719929;9783031719936
A crucial role of container shipping is maximizing container uptake onto vessels, optimizing the efficiency of a fundamental part of the global supply chain. In practice, liner shipping companies include block stowage patterns that ensure that containers in above and below deck partitions of bays have the same destination. Despite preventing restows, increasing free space, and benefits for crane makespan and hydrostatics, this practical planning requirement is rarely included in stowage optimization models. In our paper, we introduce a novel 0-1 IP model that searches in the space of valid paired block stowage patterns, named template planning, which ensures sufficient vessel capacity and limits to crane makespan, trim, and bending moment. Our results show that template planning outperforms traditional allocation planning concerning optimality and runtime efficiency while preserving a sufficiently accurate representation of master planning constraints and objectives.
Key messageinteger programming was used as a novel approach for grapevine selection. Several selection criteria were considered using real data to test the method, which was successfully applied to polyclonal *** sele...
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Key messageinteger programming was used as a novel approach for grapevine selection. Several selection criteria were considered using real data to test the method, which was successfully applied to polyclonal *** selection (selecting a high-performing, balanced mixture of 7 to 20 clones) in ancient grapevine varieties is a selection method that is increasingly used in countries with ancient viticulture. However, to meet the needs of the vine and wine sector, polyclonal selection must take into account several target traits. Polyclonal selection is based on empirical best linear unbiased predictors of genotypic effects obtained by fitting appropriate linear mixed models. This work proposes a multicriteria method for polyclonal selection. A new approach based on integer programming is implemented to perform polyclonal selection considering multiple traits simultaneously. An algorithm that attempts to maximize the genetic gains of selection according to different selection criteria has been developed and tested on real data of important traits obtained in large field trials of four ancient grapevine varieties. Multiple selection criteria were used to perform polyclonal selection of groups of 7 to 20 clones of each variety based on multiple traits. The results showed that integer programming can be useful in polyclonal selection to obtain selected material with high genetic gains in the target traits, while avoiding losses in other equally important traits.
Wireless Sensor Networks (WSNs) are systems with great potential for applications in the most diverse areas such as industry, security, public health, and agriculture. In general, for a WSN to achieve high performance...
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ISBN:
(纸本)9783031232350;9783031232367
Wireless Sensor Networks (WSNs) are systems with great potential for applications in the most diverse areas such as industry, security, public health, and agriculture. In general, for a WSN to achieve high performance, multiple criteria must be considered, such as coverage area, connectivity, and energy consumption. In this work an integer programming (IP) model to solve a Sensor Allocation Problem (SAP) is presented. The IP model considers a heterogeneous WSN and deterministic locations to positioning of sensors. The proposed model was validated using the IBM ILOG CPLEX solver. A several computational experiments were performed, and an analysis through small and mediumsized instances of the problem under study are presented and discussed. The proposed model presents good results given the problem premises, constraints and considered objectives, achieving 0.0099% optimality gap for the best scenarios where networks are fully connected and are feasible to implement. Other suboptimal evaluated scenarios with denser distribution of sensor nodes depict about 0.04% of isolated node positioning, spite maintaining overall balance between energy consumption and coverage. Therefore, the proposed model shows promise for achieving practical solutions, i.e., those with implementation feasibility in most considered heterogeneous network scenarios.
Feasible solutions are crucial for integer programming (IP) since they can substantially speed up the solving process. In many applications, similar IP instances often exhibit similar structures and shared solution di...
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ISBN:
(纸本)9798400704901
Feasible solutions are crucial for integer programming (IP) since they can substantially speed up the solving process. In many applications, similar IP instances often exhibit similar structures and shared solution distributions, which can be potentially modeled by deep learning methods. Unfortunately, existing deep-learning-based algorithms, such as Neural Diving [21] and Predict-and-search framework [8], are limited to generating only partial feasible solutions, and they must rely on solvers like SCIP and Gurobi to complete the solutions for a given IP problem. In this paper, we propose a novel framework that generates complete feasible solutions end-to-end. Our framework leverages contrastive learning to characterize the relationship between IP instances and solutions, and learns latent embeddings for both IP instances and their solutions. Further, the framework employs diffusion models to learn the distribution of solution embeddings conditioned on IP representations, with a dedicated guided sampling strategy that accounts for both constraints and objectives. We empirically evaluate our framework on four typical datasets of IP problems, and show that it effectively generates complete feasible solutions with a high probability (> 89.7 %) without the reliance of Solvers and the quality of solutions is comparable to the best heuristic solutions from Gurobi. Furthermore, by integrating our method's sampled partial solutions with the CompleteSol heuristic from SCIP [19], the resulting feasible solutions outperform those from state-of-the-art methods across all datasets, exhibiting a 3.7 to 33.7% improvement in the gap to optimal values, and maintaining a feasible ratio of over 99.7% for all datasets.
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