The positive edge criterion within COIN-OR׳s CLP

Abstract

This paper presents the first direct implementation of the positive edge criterion using COIN-OR׳s CLP, where it has been combined with the Devex pivot rule. Positive edge is designed to take advantage of degeneracy in linear programming. The original implementation, while yielding strong computational results, suffers from significant overhead caused by CPLEX not allowing modification of its standard pivot rules. We test the method over the same set of highly degenerate problems used by the original authors of positive edge. To test its robustness, we solve a set of linear problems from Mittelmann׳s library which contains instances with a wide range of degeneracy levels. These computational results show that below a degeneracy level of 25%, the positive edge criterion is on average neutral while above this threshold, it reaches an average run time speedup of 2.3, with a maximum at 4.2 on an instance with a 75% degeneracy level.