139,798 research outputs found

    Cycle-based formulations in Distance Geometry

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    The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the edge weights. The problem is often modelled as a mathematical programming formulation involving decision variables that determine the position of the vertices in the given Euclidean space. Solution algorithms are generally constructed using local or global nonlinear optimization techniques. We present a new modelling technique for this problem where, instead of deciding vertex positions, formulations decide the length of the segments representing the edges in each cycle in the graph, projected in every dimension. We propose an exact formulation and a relaxation based on a Eulerian cycle. We then compare computational results from protein conformation instances obtained with stochastic global optimization techniques on the new cycle-based formulation and on the existing edge-based formulation. While edge-based formulations take less time to reach termination, cycle-based formulations are generally better on solution quality measures

    Cycle-based formulations in Distance Geometry

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    The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the edge weights. The problem is often modelled as a mathematical programming formulation involving decision variables that determine the position of the vertices in the given Euclidean space. Solution algorithms are generally constructed using local or global nonlinear optimization techniques. We present a new modelling technique for this problem where, instead of deciding vertex positions, formulations decide the length of the segments representing the edges in each cycle in the graph, projected in every dimension. We propose an exact formulation and a relaxation based on a Eulerian cycle. We then compare computational results from protein conformation instances obtained with stochastic global optimization techniques on the new cycle-based formulation and on the existing edge-based formulation. While edge-based formulations take less time to reach termination, cycle-based formulations are generally better on solution quality measures.Comment: 16 page

    New formulations and solutions for the strategic berth template problem

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    This paper develops new formulations for the Strategic Berth Template Problem, which combines strategic and operational decisions for medium-term berth planning of a given set of cyclically calling ships. The strategic decisions determine the ship calls that will be served, whereas the operational ones establish the berth template that will be applied in a cyclic fashion in the planning horizon. The proposed formulations use binary variables that classify served ships depending on whether or not their service starts in their arrival cycle or in the next one. This helps modeling the problem, since a closed linear expression can be obtained for the waiting times. Constraints imposing that the availability of the berths is respected at each time period can be derived by defining additional binary variables pointing to the starting service times of the served ships. Aggregating such variables over all berths leads to a relaxed formulation, which can be solved in remarkably small computing times. Furthermore, the solution of an auxiliary subproblem produces feasible solutions to the original problem as well as a simple optimality check. Disaggregating the initial service time variables for the different berths leads to a valid formulation. Numerical results from extensive computational tests over a set of benchmark instances from the literature are presented and analyzed. The obtained results assess the excellent performance of the proposed formulations, which outperform existing ones. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )This research was partially funded by the Spanish Ministry of Economy and Competitiveness and ERDF funds [Grant PID2019-105824GB-I0 0 (MINECO/FEDER) ] . This support is gratefully ac-knowledged. The authors are thankful to Eduardo Lalla-Ruiz who kindly made available to us the set of benchmark instances

    Computational methods for finding long simple cycles in complex networks

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    © 2017 Elsevier B.V. Detection of long simple cycles in real-world complex networks finds many applications in layout algorithms, information flow modelling, as well as in bioinformatics. In this paper, we propose two computational methods for finding long cycles in real-world networks. The first method is an exact approach based on our own integer linear programming formulation of the problem and a data mining pipeline. This pipeline ensures that the problem is solved as a sequence of integer linear programs. The second method is a multi-start local search heuristic, which combines an initial construction of a long cycle using depth-first search with four different perturbation operators. Our experimental results are presented for social network samples, graphs studied in the network science field, graphs from DIMACS series, and protein-protein interaction networks. These results show that our formulation leads to a significantly more efficient exact approach to solve the problem than a previous formulation. For 14 out of 22 networks, we have found the optimal solutions. The potential of heuristics in this problem is also demonstrated, especially in the context of large-scale problem instances

    New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem

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    As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that DC approximation may lead to inaccurate flow solutions and also overlook stability issues. In this paper, we focus on the optimal transmission switching problem with the full AC power flow model, abbreviated as AC OTS. We propose a new exact formulation for AC OTS and its mixed-integer second-order conic programming (MISOCP) relaxation. We improve this relaxation via several types of strong valid inequalities inspired by the recent development for the closely related AC Optimal Power Flow (AC OPF) problem. We also propose a practical algorithm to obtain high quality feasible solutions for the AC OTS problem. Extensive computational experiments show that the proposed formulation and algorithms efficiently solve IEEE standard and congested instances and lead to significant cost benefits with provably tight bounds
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