@masterthesis{Hendel2011, type = {Bachelor Thesis}, author = {Hendel, Gregor}, title = {New Rounding and Propagation Heuristics for Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13322}, school = {Zuse Institute Berlin (ZIB)}, pages = {95}, year = {2011}, abstract = {Die vorliegende Arbeit befasst sich mit Primalheuristiken f{\"u}r gemischt-ganzzahlige, lineare Optimierungsprobleme (engl.: mixed integer program MIP). Zahlreiche Optimierungsprobleme aus der Praxis lassen sich als MIP modellieren, Beispiele hierf{\"u}r sind u. a. Optimierungsprobleme im {\"o}ffentlichen Nah- und Fernverkehr, bei logistischen Fragestellungen oder im Bereich der Chip-Verifikation. Das L{\"o}sen von MIP ist NP-schwer und wird heutzutage meistens mit Hilfe von Branch-and-Bound-basierenden Algorithmen versucht. Das Branch-and-Bound-Ver\-fah\-ren profitiert unter Umst{\"a}nden von bereits fr{\"u}hzeitig zur Verf{\"u}gung stehenden L{\"o}sungen, daher sind wir sehr an heuristischen Verfahren interessiert, die in der Praxis schnell eine gute L{\"o}sung f{\"u}r eine große Zahl an MIPs liefern und somit die L{\"o}sezeit des Branch-and-Bound-Verfahrens erheblich beschleunigen k{\"o}nnen. Primalheuristiken sind Suchverfahren zum Auffinden zul{\"a}ssiger L{\"o}sungen eines MIP. Verschiedene Typen von Primalheuristiken sollen dabei den jeweiligen Bedarf des Anwenders zu unterschiedlichen Zeiten w{\"a}hrend der Branch-and-Bound-Suche decken. W{\"a}hrend Start- und Rundeheuristiken zu Beginn des L{\"o}seprozesses eine große Rolle bei der Suche nach der ersten zul{\"a}ssigen L{\"o}sung haben, arbeiten Verbesserungs-heuristiken auf schon bekannten L{\"o}sungen, um neue, bessere L{\"o}sungen zu produzieren. Diese Arbeit besch{\"a}ftigt sich mit Primalheuristiken, welche Teil des MIP-L{\"o}sers SCIP sind. Im ersten Kapitel werden nach der Erarbeitung grundlegender Definitionen viele der durch Tobias Achterberg und Timo Berthold in SCIP integrierten heuristischen Verfahren vorgestellt und kategorisiert. Auf dieser Grundlage bauen dann die Kapitel 2-4 der Arbeit auf. In diesen werden drei zus{\"a}tzliche Heuristiken vorgestellt, im Einzelnen sind dies ZI Round, eine Rundeheuristik, welche zuerst von Wallace beschrieben wurde, außerdem eine 2-Opt-Heuristik f{\"u}r MIP und eine neue Startheuristik, Shift-And-Propagate. Großer Wert wird in jedem Kapitel auf die algorithmische Beschreibung der Heuristiken gelegt, die stets anhand von motivierenden Beispielen eingef{\"u}hrt und anhand von Pseudocode-Algorithmen begleitet werden. Zus{\"a}tzlich enth{\"a}lt jedes Kapitel Auswertungen der mit den neuen Heuristiken gemessenen Ergebnisse von SCIP. Eine kurze Zusammenfassung in Kapitel 5 schließt diese Arbeit ab.}, language = {en} } @misc{AchterbergBertholdHendel2011, author = {Achterberg, Tobias and Berthold, Timo and Hendel, Gregor}, title = {Rounding and Propagation Heuristics for Mixed Integer Programming}, doi = {10.1007/978-3-642-29210-1_12}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13255}, number = {11-29}, year = {2011}, abstract = {Primal heuristics are an important component of state-of-the-art codes for mixed integer programming. In this paper, we focus on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation). We give an overview of eight different approaches. To assess the impact of these primal heuristics on the ability to find feasible solutions, in particular early during search, we introduce a new performance measure, the primal integral. Computational experiments evaluate this and other measures on MIPLIB~2010 benchmark instances.}, language = {en} } @article{BertholdHendelKoch2017, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {From feasibility to improvement to proof: three phases of solving mixed-integer programs}, volume = {33}, journal = {Optimization Methods and Software}, number = {3}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2017.1392519}, pages = {499 -- 517}, year = {2017}, abstract = {Modern mixed-integer programming (MIP) solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three distinct phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behaviour of the non-commercial MIP solver Scip at the predicted phase transition points.}, language = {en} } @article{BertholdHendel2014, author = {Berthold, Timo and Hendel, Gregor}, title = {Shift-and-Propagate}, volume = {21}, journal = {Journal of Heuristics}, number = {1}, doi = {10.1007/s10732-014-9271-0}, pages = {73 -- 106}, year = {2014}, abstract = {In recent years, there has been a growing interest in the design of general purpose primal heuristics for use inside complete mixed integer programming solvers. Many of these heuristics rely on an optimal LP solution, which may take a significant amount of time to find. In this paper, we address this issue by introducing a pre-root primal heuristic that does not require a previously found LP solution. This heuristic, named Shift-and-Propagate , applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement to existing rounding and propagation heuristics.}, language = {en} } @misc{Hendel2015, author = {Hendel, Gregor}, title = {Exploiting Solving Phases for Mixed-Integer Programs}, issn = {1438-0064}, doi = {10.1007/978-3-319-42902-1_1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57098}, year = {2015}, abstract = {Modern MIP solving software incorporates dozens of auxiliary algorithmic components for supporting the branch-and-bound search in finding and improving solutions and in strengthening the relaxation. Intuitively, a dynamic solving strategy with an appropriate emphasis on different solving components and strategies is desirable during the search process. We propose an adaptive solver behavior that dynamically reacts on transitions between the three typical phases of a MIP solving process: The first phase objective is to find a feasible solution. During the second phase, a sequence of incumbent solutions gets constructed until the incumbent is eventually optimal. Proving optimality is the central objective of the remaining third phase. Based on the MIP-solver SCIP, we demonstrate the usefulness of the phase concept both with an exact recognition of the optimality of a solution, and provide heuristic alternatives to make use of the concept in practice.}, language = {en} } @misc{BertholdHendelKoch2016, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {The Three Phases of MIP Solving}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1392519}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61607}, year = {2016}, abstract = {Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points.}, language = {en} }