A hospital facility layout problem finally solved

This paper presents a history of a difficulty facility layout problem that falls into the category of the Koopmans–Beckmann variant of the quadratic assignment problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German University Hospital, Klinikum Regensburg. This problem, known as the Krarup 30a upon its inclusion in the QAP library of QAP instances, has remained an important example of one of the most difficult to solve. In 1999, two approaches provided multiple optimum solutions. The first was Thomas Stützle's analysis of fitness–distance correlation that resulted in the discovery of 256 global optima. The second was a new branch-and-bound enumeration that confirmed 133 of the 256 global optima found and proved that Stützle's 256 solutions were indeed optimum solutions. We report here on the steps taken to provide in-time heuristic solutions and the methods used to finally prove the optimum.