Learning binary variables selections to improve the mip solution time in architectural layout design optimization

Abstract

Varieties of optimization techniques have been used to solve an architectural layout design optimization for more than a decade such as an expert system, an evolutionary algorithm, a simulated annealing and a mathematical programming method. This thesis will concentrate on the mathematical programming technique that formulates an architectural layout design optimization as the architectural layout Mixed Integer Programming (MIP) model called AL-MIP. All non-linear relationship among design components will be captured using the corresponding linear equalities and linear inequalities. Due to the combinatorial nature of the MIP solutions, the AL-MIP can be solved optimally for a small size, (2-5 rooms), within a reasonable time limit. To remedy this situation, both valid inequality constraints called AL-MIP+ from non-circular connectivity of consecutive room connections and the architect’s preference constraints have been adopted that reduces the computational time significantly. Moreover, to speed up the computational time of AL-MIP+, the machine learning using Genetic Algorithm (GA) has been applied to determine the best sequences of branching variables, the Special Order Set (SOS) called AL-MIP+GA. The search space reduction comes from the better candidate solution used to prune the search tree. These combinations of speeding up technique illustrate the computational MIP iterations and time reduction more than 80% that is now achievable for a medium size (5-10 rooms). The global solutions from 10 room patterns have been solved within a few minute. Indeed, both valid inequality MIP and learning methodology present a novel mathematical concept to optimize MIP for an architectural layout design problem.