On generation of test problems for linear programming codes

Abstract

Users of linear programming computer codes have realized the necessity of evaluating the capacity, effectiveness, and accuracy of the solutions provided by such codes. Large scale linear programming codes at most installations are assumed to be generating correct solutions without ever having been *'bench-marked*' by test problems with known solutions. The reason for tbis failure to adequately test tbe codes is tbat rarely are tbere large problems with known solutions readily available. This paper presents a tbeoretical justification and an illustrative implementation of a method for generating linear programming test problems with known solutions. The method permits tbe generation of test problems tbat are of arbitrary size and have a wide range of numerical characteristics.

Primal and dual algorithms for optimization over the efficient set

“…If any of these points is non-dominated a lower bound is found. Then solving problem (18), a relaxation of (7), finds an upper bound.…”

“…In this section, we use randomly generated instances to compare some of the algorithms for solving (8). The method proposed by [7] is used to generate instances the coefficients of which are uniformly distributed between -10 and 10. All of the algorithms were implemented in Matlab R2013b using CPLEX 12.5 as linear programming solver.…”

“…In this section, we use randomly generated instances to compare some of the algorithms discussed in Section 4 and the primal and the dual algorithms for (10). The method proposed by [7] is used to generate convex polyhedra as feasible sets of the underlying CMOP. Quadratic functions are generated as the objective functions, which are in the form f (x) = x T H x + a T x, where H is a positive semi-definite matrix and a is a column vector.…”

A Mathematical Program Generator MPGENR

“…This approach was proposed by Rosen and Suzuki [14], although the legacy of this paper has been the sample problem they generated rather than implementation of the procedure. An LP generator has been developed by Charnes et al [1] and a network generator had been developed by Klingman, Napier, and Stutz [7]. The two approaches in many ways complement each other.…”

Development of a Parametric Generating Procedure for Integer Programming Test Problems

“…In particular several authors have reported parametric problem generators which produce test problems having particular properties of research interest to the experimenter. Such a linear programming (LP) generator has been developed by Charnes, Raike, Stutz, and Waiters [1]; a network generator was reported by Khngman, Napier, and Stutz [8]; and a nonlinear programming generator was proposed by Michaels and O'Neill [9]. The avadabdity of the network generator seems to have made possible an extensive computational study on transportation problems by Glover, Karney, Klingman, and Napier [2] In this paper the development of a parametric generator for all-integer ILP test problems is reported.…”