Given an infeasible set of linear constraints, finding the maximum cardinality feasible subsystem is known as the maximum feasible subsystem problem. This problem is known to be NP-hard, but has many practical applications. This paper presents improved heuristics for solving the maximum feasible subsystem problem that are significantly faster than the original, but still highly accurate.

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INFORMS Journal on Computing
Department of Systems and Computer Engineering

Chinneck, J. (2001). Fast Heuristics for the Maximum Feasible Subsystem Problem. INFORMS Journal on Computing, 13(3), 210–223.