Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation

Graphical abstractDisplay Omitted HighlightsA surrogate based on radial basis function networks is adapted for mixed-type variables, multiple objectives and constraints and integrated into NSGA-II.A deterministic method to include infeasible solutions in the population is proposed.Variants of NSGA-II including these changes are applied to a typical building optimisation problem, with improvements in solution quality and convergence speed.Analysis of the constraint handling and fitness landscape of the problem is also conducted. Reducing building energy demand is a crucial part of the global response to climate change, and evolutionary algorithms (EAs) coupled to building performance simulation (BPS) are an increasingly popular tool for this task. Further uptake of EAs in this industry is hindered by BPS being computationally intensive: optimisation runs taking days or longer are impractical in a time-competitive environment. Surrogate fitness models are a possible solution to this problem, but few approaches have been demonstrated for multi-objective, constrained or discrete problems, typical of the optimisation problems in building design. This paper presents a modified version of a surrogate based on radial basis function networks, combined with a deterministic scheme to deal with approximation error in the constraints by allowing some infeasible solutions in the population. Different combinations of these are integrated with Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and applied to three instances of a typical building optimisation problem. The comparisons show that the surrogate and constraint handling combined offer improved run-time and final solution quality. The paper concludes with detailed investigations of the constraint handling and fitness landscape to explain differences in performance.