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  • 1
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    New Conjectures For Union-Closed Families (2015)
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    Publication Date: 2020-08-05
    Description: The Frankl conjecture, also known as the union-closed sets conjecture, states that there exists an element in at least half of the sets of any (non-empty) union-closed family. From an optimization point of view, one could instead prove that 2a is an upper bound to the number of sets in a union-closed family with n elements where each element is in at most a sets, where a and n are non-negative integers. Formulating these problems as integer programs we observe that computed optimal values do not vary with n. We formalize these observations as conjectures, and show that they are not equivalent to the Frankl conjecture while still having wide-reaching implications if proven true. Finally, we partially prove the new conjectures and discuss possible approaches to solve them completely.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 2
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    A fast hybrid primal heuristic for multiband robust capacitated network design with multiple time periods (2014)
    Details
    Publication Date: 2020-08-05
    Description: We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (Büsing and D'Andreagiovanni, 2012), a refinement of classical Gamma-Robustness by Bertsimas and Sim (2004) that uses a system of multiple deviation bands. Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib (2010) show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 3
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    A Fast Hybrid Primal Heuristic for Multiband Robust Capacitated Network Design with Multiple Time Periods (2014)
    Details
    Publication Date: 2020-08-05
    Description: We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (Büsing and D'Andreagiovanni, 2012), a refinement of classical Gamma-Robustness by Bertsimas and Sim (2004) that uses a system of multiple deviation bands. Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib (2010) show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 4
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    An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design (2016)
    Details
    Publication Date: 2020-08-05
    Description: We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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    OPUS
  • 5
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    Cutting Planes for Families Implying Frankl's Conjecture (2016)
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    Publication Date: 2020-08-05
    Description: We find previously unknown families which imply Frankl’s conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non–Frankl-Complete (Non–FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non–FC-families.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
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    OPUS
  • 6
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    The Multiperiod Network Design Problem: Lagrangian-based Solution Approaches (2011)
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    Publication Date: 2020-08-05
    Description: We present and prove a theorem which gives the optimal dual vector for which a Lagrangian dual problem in the Single Period Design Problem (SPDP) is maximized. Furthermore we give a straightforward generalization to the Multi-Period Design Problem (MPDP). Based on the optimal dual values derived we compute the solution of the Lagrangian relaxation and compare it with the linear relaxation and optimal IP values.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 7
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    A hybrid primal heuristic for Robust Multiperiod Network Design (2013)
    Details
    Publication Date: 2020-08-05
    Description: We investigate the Robust Multiperiod Network Design Problem, a generalization of the classical Capacitated Network Design Problem that additionally considers multiple design periods and provides solutions protected against traffic uncertainty. Given the intrinsic difficulty of the problem, which proves challenging even for state-of-the art commercial solvers, we propose a hybrid primal heuristic based on the combination of ant colony optimization and an exact large neighborhood search. Computational experiments on a set of realistic instances from the SNDlib show that our heuristic can find solutions of extremely good quality with low optimality gap.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 8
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    A hybrid primal heuristic for Robust Multiperiod Network Design (2014)
    Details
    Publication Date: 2020-08-05
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 9
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    An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design (2015)
    Details
    Publication Date: 2020-08-05
    Description: We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
  • 10
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    Cutting Planes for Union-Closed Families (2017)
    Details
    Publication Date: 2020-08-05
    Description: Frankl’s (union-closed sets) conjecture states that for any nonempty finite union-closed (UC) family of distinct sets there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given UC family ensures Frankl’s conjecture holds for all UC families which contain it. The weight systems are nontrivial to identify for a given UC family, and methods to determine such weight systems have led to several other open questions and conjectures regarding structures in UC families. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem using computational integer programming coupled with redundant verification routines that ensure correctness. We find over one hundred previously unknown families of sets which ensure Frankl’s conjecture holds for all families that contain any of them. This improves significantly on all previous results of the kind. Our framework allows us to answer several open questions and conjectures regarding structural properties of UC families, including proving the 3-sets conjecture of Morris from 2006 which characterizes the minimum number of 3-sets that ensure Frankl’s conjecture holds for all families that contain them. Furthermore, our method provides a general algorithmic road-map for improving other known results and uncovering structures in UC families.
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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