Incorporating Simplex Method into Guided Complete Search: An Application to the Nurse Rostering Problem

Guided Complete Search (GCS) is a generic framework for combining and coordinating a tree search solver and a secondary solver to yield a complete and efficient CSP solver. The primary solver of GCS is systematic tree search augmented with constraint propagation algorithm, which is used to maintain the completeness of the GCS solver. The secondary solver of GCS can either be a complete or incomplete solver, which mainly produces guidance to the primary solver for solution searching by providing value ordering suggestions. In this paper, we describe our newly defined GCS/Simplex solver, which incorporates Simplex method into the GCS framework. To demonstrate the efficiency, we apply the GCS/Simplex to the nurse rostering problem, and its general form, namely, cardinality matrix problem. The nurse rostering problem is one of the most difficult scheduling problems in artificial intelligence and operations research. And the cardinality matrix problem is the underlying structure of several real-life problems such as rostering, scheduling and time-tabling problem. Both are shown to be computational intractable. Experimental results show that the GCS/Simplex solver is efficient in solving this kind of scheduling problems in terms of both computation time and number of fails.