Strong valid inequality constraints for architectural layout design optimization

Abstract

In the past decades, many attempts have been made to solve the challenging architectural layout design problem such as non-linear programming and evolutionary algorithm (Michalek and Papalambros, 2002). The Mixed Integer Programming (MIP) (Kamol and Krung, 2005) was recently developed to find the global optimal solution. However, the problem can be shown to belong to the class of NP-hard problem (Michalek and Papalambros, 2002). Hence, only the small instances of the problem can be solved in a reasonable time. In order to deal with large problem sizes, this paper utilizes the strong valid inequalities (George and Laurence). It cut off the infeasible points in the integral search space by formulated the disconnected constraints involved with line configurations of three rooms. It is shown to significantly increase the computational speed to more than thirty percents. This exhibits the practical use of the MIP formulation to solve the medium size architectural layout design problems.