Fast Heuristics for the Maximum Feasible Subsystem Problem

Branch-and-Cut for the Maximum Feasible Subsystem Problem

This paper presents a branch-and-cut algorithm for the NPhard maximum feasible subsystem problem: For a given infeasible linear inequality system, determine a feasible subsystem containing as many inequalities as possible. The complementary problem, where one has to remove as few inequalities as possible in order to make the system feasible, can be formulated as a set covering problem. The rows...

A two-phase relaxation-based heuristic for the maximum feasible subsystem problem

We consider the maximum feasible subsystem problem in which, given an infeasible system of linear inequalities, one wishes to determine a largest feasible subsystem. The focus is on the version with bounded variables that naturally arises in several fields of application. To tackle this NP-hard problem, we propose a simple but efficient two-phase relaxation-based heuristic. First a feasible sub...

Exact and Approximate Sparse Solutions of Underdetermined Linear Equations

In this paper, we empirically investigate the NP-hard problem of finding sparsest solutions to linear equation systems, i.e., solutions with as few nonzeros as possible. This problem has received considerable interest in the sparse approximation and signal processing literature, recently. We use a branch-and-cut approach via the maximum feasible subsystem problem to compute optimal solutions fo...

Minimizing the bicriteria of makespan and maximum tardiness with an upper bound on maximum tardiness

This paper studies the flowshop scheduling problem with a complex bicriteria objective function. A weighted sum of makespan and maximum tardiness subject to a maximum tardiness threshold value is to be optimized. This problem, with interesting potential applications in practice, has been sparsely studied in the literature. We propose global and local dominance relationships for the three machin...

The Maximum Feasible Subsystem Problem and Vertex-Facet Incidences of Polyhedra