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General hospitals consist of several sections such as the internal medicine department and the pediatrics department, etc. About fifty to thirty nursing staffs belong in each section. A section manager constitutes a roster, or a shift schedule, of all nurses of her/his section every month. In our interviewing research to several real hospitals, we found that the manager considers more than fifteen requirements for the scheduling. Such the schedule arrangement, in other words, the nurse scheduling, is a very complex task. We call such the problem Nurse Scheduling Problem (NSP). In the interview, even a veteran manager has to spend one or two weeks to complete the nurse scheduling. This means a great loss of work force. Therefore, computer software for solving NSP has recently come to be required in the general hospitals (Goto, 1993; Berrada, 1996; Takaba, 1998; Ikegami, 2001; Burke, 2001a; Kawanaka, 2002; Inoue, 2002; Itoga, 2003; Cheang, 2003; Burke, 2004a; Ernst, 2004; Burke, 2004b; Li, 2004; Bard, 2005; Oezcan, 2005; Burke, 2006; Bard, 2007).