TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Shift-and-Propagate JF - Journal of Heuristics N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1007/s10732-014-9271-0 VL - 21 IS - 1 SP - 73 EP - 106 ER - TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor A1 - Koch, Thorsten T1 - From feasibility to improvement to proof: three phases of solving mixed-integer programs JF - Optimization Methods and Software N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2017.1392519 VL - 33 IS - 3 SP - 499 EP - 517 PB - Taylor & Francis ER - TY - JOUR A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Gamrath, Gerald A1 - Achterberg, Tobias A1 - Bastubbe, Michael A1 - Berthold, Timo A1 - Christophel, Philipp M. A1 - Jarck, Kati A1 - Koch, Thorsten A1 - Linderoth, Jeff A1 - Lübbecke, Marco A1 - Mittelmann, Hans A1 - Ozyurt, Derya A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Shinano, Yuji T1 - MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library JF - Mathematical Programming Computation N2 - We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data. Y1 - 2021 U6 - https://doi.org/10.1007/s12532-020-00194-3 VL - 13 IS - 3 SP - 443 EP - 490 ER - TY - CHAP A1 - Hendel, Gregor T1 - Exploiting Solving Phases for Mixed-Integer Programs T2 - Operations Research Proceedings 2015 N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-42902-1_1 SP - 3 EP - 9 ER - TY - CHAP A1 - Hendel, Gregor T1 - Enhancing MIP Branching Decisions by Using the Sample Variance of Pseudo Costs T2 - Integration of AI and OR Techniques in Constraint Programming N2 - The selection of a good branching variable is crucial for small search trees in Mixed Integer Programming. Most modern solvers employ a strategy guided by history information, mainly the variable pseudo-costs, which are used to estimate the objective gain. At the beginning of the search, such information is usually collected via an expensive look-ahead strategy called strong branching until variables are considered reliable. The reliability notion is thereby mostly based on fixed-number thresholds, which may lead to ineffective branching decisions on problems with highly varying objective gains. We suggest two new notions of reliability motivated by mathematical statistics that take into account the sample variance of the past observations on each variable individually. The first method prioritizes additional strong branching look-aheads on variables whose pseudo-costs show a large variance by measuring the relative error of a pseudo-cost confidence interval. The second method performs a specialized version of a two-sample Student’s t -test for filtering branching candidates with a high probability to be better than the best history candidate. Both methods were implemented in the MIP-solver SCIP and computational results on standard MIP test sets are presented. Y1 - 2015 U6 - https://doi.org/10.1007/978-3-319-18008-3_14 VL - 9075 SP - 199 EP - 214 ER - TY - JOUR A1 - Hendel, Gregor T1 - Adaptive Large Neighborhood Search for Mixed Integer Programming JF - Mathematical Programming Computation N2 - Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search domains, which we call neighborhoods. The decision which neighborhood should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available neighborhoods based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing priorization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some neighborhoods which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP. Y1 - 2018 ER - TY - JOUR A1 - Hendel, Gregor A1 - Anderson, Daniel A1 - Le Bodic, Pierre A1 - Pfetsch, Marc T1 - Estimating the Size of Branch-And-Bound Trees JF - INFORMS Journal on Computing N2 - This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP. Y1 - 2021 U6 - https://doi.org/10.1287/ijoc.2021.1103 ER - TY - CHAP A1 - Hendel, Gregor A1 - Berthold, Timo A1 - Achterberg, Tobias T1 - Rounding and Propagation Heuristics for Mixed Integer Programming T2 - Operations Research Proceedings 2011 N2 - 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. Y1 - 2011 SP - 71 EP - 76 ER - TY - CHAP A1 - Hendel, Gregor A1 - Miltenberger, Matthias A1 - Witzig, Jakob T1 - Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms T2 - OR 2018: International Conference on Operations Research N2 - State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics as well as Simplex pricing strategies. For each class we propose a selection strategy that is updated based on the observed runtime behavior, aiming to ultimately select only the best algorithms for a given instance. We review several common strategies for such a selection scenario under uncertainty, also known as Multi Armed Bandit Problem. In order to apply those bandit strategies, we carefully design reward functions to rank and compare each individual heuristic or pricing algorithm within its respective class. Finally, we discuss the computational benefits of using the proposed adaptive selection within the SCIP Optimization Suite on publicly available MIP instances. Y1 - 2018 ER -