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

Abstract

Various techniques have been used to solve a challenging architectural layout 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 inequalities. 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 reduces 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.