A computational study of primal heuristics inside an MI(NL)P solver

2018 ◽  
Vol 70 (1) ◽  
pp. 189-206 ◽  
Author(s):  
Timo Berthold
Keyword(s):  
Computational Study ◽  
Primal Heuristics

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.

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