Solving multi-objective rational placement of load-bearing walls problem via genetic algorithm

The rational placement of load-bearing walls remains a complex and poorly studied problem, despite the existence of numerous algorithms and models for solving the similar problem of column placement. The main complexity factors are the large number of alternative solutions, the significant time required to calculate deformations for a given wall placement, and the multi-objective nature of the problem. In addition to the nonlinear criterion for estimating deformations, it is necessary to minimize the length of load-bearing walls and the number of their unique lengths. A model for the rational placement of load-bearing walls is proposed, which divides the walls into functional parts with a specific step and considers all the required target criteria. Adjacent wall parts with the same functionality are combined into segments. The combinatorial formulation applied in the model of the problem allows the use of genetic algorithms as a solution tool. Therefore, a new approach to multi-objective genetic algorithm is proposed, containing metrics for calculating population diversity at the phenotype and genotype levels. Modifications of crossover, mutation, and selection operators, considering the segmental structure of the wall's genotype, are presented. A comparative analysis of the developed algorithm with other known multi-objective genetic algorithms showed that the developed algorithm finds, on average, three times more non-dominated solutions, particularly more plans with a lower deformation estimates, despite the twice-longer execution time. The proposed model differs significantly from previous models in terms of handling deformations in slab-support systems, comparing placement plans with each other rather than calculating precise reinforcement estimates, which is often unnecessary at the early stages. The proposed genetic algorithm scheme increases the number of found nondominated solutions without losing their diversity, and can be used to solve other multi-objective problems, taking into account the specified features. The developed algorithm was easily integrated into the CAD-based decision support software and can be used in practice by building designers.