Primal Heuristics for Wasserstein Barycenters

2020 ◽  
pp. 239-255
Author(s):  
Pierre-Yves Bouchet ◽  
Stefano Gualandi ◽  
Louis-Martin Rousseau
Keyword(s):  
Primal Heuristics

Column generation based primal heuristics for routing and loading problems

2018 ◽  
Vol 64 ◽  
pp. 135-144 ◽  
Author(s):  
Telmo Pinto ◽  
Cláudio Alves ◽  
José Valério de Carvalho
Keyword(s):  
Column Generation ◽  
Primal Heuristics

Measuring the impact of primal heuristics

2013 ◽  
Vol 41 (6) ◽  
pp. 611-614 ◽  
Author(s):  
Timo Berthold
Keyword(s):  
Primal Heuristics ◽  
The Impact

scholarly journals Learning to Run Heuristics in Tree Search

2017 ◽  
Author(s):  
Elias B. Khalil ◽  
Bistra Dilkina ◽  
George L. Nemhauser ◽  
Shabbir Ahmed ◽  
Yufen Shao
Keyword(s):  
Integer Programming ◽  
State Of The Art ◽  
Independent Set ◽  
Search Tree ◽  
Mixed Integer ◽  
Tree Search ◽  
Trial And Error ◽  
Benchmark Instances ◽  
Primal Heuristics ◽  
Improved Performance

``Primal heuristics'' are a key contributor to the improved performance of exact branch-and-bound solvers for combinatorial optimization and integer programming. Perhaps the most crucial question concerning primal heuristics is that of at which nodes they should run, to which the typical answer is via hard-coded rules or fixed solver parameters tuned, offline, by trial-and-error. Alternatively, a heuristic should be run when it is most likely to succeed, based on the problem instance's characteristics, the state of the search, etc. In this work, we study the problem of deciding at which node a heuristic should be run, such that the overall (primal) performance of the solver is optimized. To our knowledge, this is the first attempt at formalizing and systematically addressing this problem. Central to our approach is the use of Machine Learning (ML) for predicting whether a heuristic will succeed at a given node. We give a theoretical framework for analyzing this decision-making process in a simplified setting, propose a ML approach for modeling heuristic success likelihood, and design practical rules that leverage the ML models to dynamically decide whether to run a heuristic at each node of the search tree. Experimentally, our approach improves the primal performance of a state-of-the-art Mixed Integer Programming solver by up to 6% on a set of benchmark instances, and by up to 60% on a family of hard Independent Set instances.

scholarly journals Learning Primal Heuristics for Mixed Integer Programs

2021 ◽  
Author(s):  
Yunzhuang Shen ◽  
Yuan Sun ◽  
Andrew Eberhard ◽  
Xiaodong Li
Keyword(s):  
Mixed Integer ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Primal Heuristics

Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

2020 ◽  
Author(s):  
Thomas Kleinert ◽  
Martin Schmidt
Keyword(s):  
Optimization Problems ◽  
Mathematical Optimization ◽  
Alternating Direction Method ◽  
Convergence Theory ◽  
Mixed Integer ◽  
Solution Quality ◽  
Alternating Direction ◽  
Bilevel Problems ◽  
Primal Heuristics ◽  
Feasible Points

Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, and so on. Often these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization, one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper, we develop such a primal heuristic for bilevel problems with a mixed-integer linear or quadratic upper level and a linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem and extensively test the method on a test set of more than 2,800 instances—which is one of the largest computational test sets ever used in bilevel programming. The study illustrates the very good performance of the proposed method in terms of both running times and solution quality. This renders the method a suitable subroutine in global bilevel solvers as well as a reasonable standalone approach. Summary of Contribution: Bilevel optimization problems form a very important class of optimization problems in the field of operations research, which is mainly due to their capability of modeling hierarchical decision processes. However, real-world bilevel problems are usually very hard to solve—especially in the case in which additional mixed-integer aspects are included in the modeling. Hence, the development of fast and reliable primal heuristics for this class of problems is very important. This paper presents such a method.

scholarly journals An exploratory computational analysis of dual degeneracy in mixed-integer programming

2020 ◽  
Vol 8 (3-4) ◽  
pp. 241-261 ◽  
Author(s):  
Gerald Gamrath ◽  
Timo Berthold ◽  
Domenico Salvagnin
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Computational Study ◽  
Solution Process ◽  
Mixed Integer ◽  
Different Types ◽  
Primal Heuristics ◽  
Individual Variables ◽  
The Individual ◽  
Constraint Ratio

Abstract Dual degeneracy, i.e., the presence of multiple optimal bases to a linear programming (LP) problem, heavily affects the solution process of mixed integer programming (MIP) solvers. Different optimal bases lead to different cuts being generated, different branching decisions being taken and different solutions being found by primal heuristics. Nevertheless, only a few methods have been published that either avoid or exploit dual degeneracy. The aim of the present paper is to conduct a thorough computational study on the presence of dual degeneracy for the instances of well-known public MIP instance collections. How many instances are affected by dual degeneracy? How degenerate are the affected models? How does branching affect degeneracy: Does it increase or decrease by fixing variables? Can we identify different types of degenerate MIPs? As a tool to answer these questions, we introduce a new measure for dual degeneracy: the variable–constraint ratio of the optimal face. It provides an estimate for the likelihood that a basic variable can be pivoted out of the basis. Furthermore, we study how the so-called cloud intervals—the projections of the optimal face of the LP relaxations onto the individual variables—evolve during tree search and the implications for reducing the set of branching candidates.

Sign in / Sign up

Export Citation Format

Share Document