Mixed integer programming model with non-circular and guided constraints for architectural layout design optimization

Various techniques have been used to solve a challenging architecturallayout design problem for more than a decade, such as an expert system, an evolutionary algorithm, a simulated annealing and a mathematical programming method. This paper concentrates on the mathematical programming technique that formulates an architectural layout design optimization as the mixed integer programming model using the state-of-the art optimization solver to determine the optimal solution. All non-linear relationships among design components are captured using the corresponding linear equalities and linear in- equalities. Due to the combinatorial nature of the MIP solutions, the MIP can be solved for small problem sizes, 2-6 rooms, within a reasonable time limit. To remedy this situation, the valid inequality of non-circular connections has been adopted that reduces the computational time significantly. Moreover, the guided constraints based on the architect’s preferences of a specific room have been embraced. This helps abandon some alternative solutions and reduced the search space considerably. The computational time and iterations gain of more than 80% is now achievable for the architectural layout design for 7-10 rooms.