Binary equilibrium optimizer: Theory and application in building optimal control problems

This study proposes a binary version of the recently developed Equilibrium Optimizer (EO) widely used in various applications. The performance of the proposed Binary Equilibrium Optimizer (BiEO) is evaluated against three classes of mathematical benchmark functions, including unimodal, multimodal, and composition functions. The results of BiEO are also compared to other binary optimizers, including Binary Particle Swarm Optimization with S-shape (BPSO/S) and V-shape (BPSO/V) transfer functions, Binary Dragonfly Algorithm (BDA), and Genetic Algorithm (GA). This study employs an advanced post-hoc analysis of Bonferroni–Dunn test to reveal the significant difference between BiEO and its competitors from the statistical point of view. BiEO has implications for various applications, specifically optimal control problems in buildings due to its rapid convergence rate and simplicity. To assess BiEO efficiency in the building and construction industry, three different test cases are selected: (i) control of switchable Ethylene tetrafluoroethylene (ETFE) cushions, (ii) operation of motorized shades, and (iii) schedule of window opening during natural ventilation. The results from the optimal control problems are analyzed from two perspectives of optimization and building energy performance. The proposed BiEO method shows a fast rate of convergence compared to its competitors in most mathematical and construction case studies (i.e., on average 5 times). This characteristic highlights the merits of BiEO and makes it a powerful binary optimizer specially when there are limited budget of time and iterations for solving an optimization problem and specifically for building applications it allows deploying it to real-time control of building systems and components. The source code of BiEO is publicly available at: https://github.com/afshinfaramarzi/Binary-Equilibrium-Optimizer, https://built-envi.com/portfolio/equilibrium-optimizer/, and https://seyedalimirjalili.com/eo.