Performance evaluation of a family of criss-cross algorithms for linear programming

In this article we evaluate a family of criss-cross algorithms for linear programming problems, comparing the results obtained by these algorithms over a set of test problems with those obtained by the simplex algorithms implemented in the XPRESS¹ commercial package. We describe the known criss-cross variants existing in the literature and introduce new versions obtained with a slight modification based on the original criss-cross algorithm. Moreover, we consider some computational details of our implementation and describe the set of test problems used.