Optimizing Architectural Layout Design via Mixed Integer Programming

Abstract

For many decades, solving the optimal architectural layout design is unattainable for the reasonable problem sizes. Architects have to settle for acceptable layouts instead of the favourable optimal solution. With today technologies, various optimization techniques have been used to alleviate the optimal search according to diversified goals. This paper formulates the optimal architectural layout design as the multiobjective mixed integer programming model solved by the MIP solver. The main idea is to capture functional constraints, dimensional constraints and the objective function using only linear formulae with binary variables. Functional constraints are the connectivities, the unused grid cells, the fixed room location, the boundary and the fixed border location while dimension constraints are the non-intersecting, the overlapping, the length and the ratio constraints. The objective function is designed to minimize the absolute distance among rooms and maximize room spaces. Due to the nonlinearity of area computation, the linear approximation of width and height constraints have been utilized. Architects can control these different objectives within the model. By specifying the rigid restriction and the time limits, the problem can be solved within a reasonable amount of time.