## 1 Introduction  
The constructal theory is the view that the design of any finite-size flow system is ruled by a physical principle named the constructal law of design and evolution. This law states that the geometrical patterns in the flow system result from its evolution in such a way as to facilitate the access of its internal currents (fluid flow, heat flux, stress flow, people, goods) [1,2]. The method used for the application of constructal theory is named constructal design (CD) and it is based on the definition of constraints, degrees of freedom, and performance indicators [3,4]. Constructal design is not an optimization method, but a method for geometrical investigation of flow systems seeking to comprehend the design evolution and effects of degrees of freedom over the performance of the system and other geometrical parameters. For geometrical optimization, the constructal design is used to define the search space of investigation and the performance indicator, while an optimization method is associated to define the sweep of the search space to obtain the optimal configurations [5,6]. The heat transfer field has been a prolific field for the investigation of the design of flow systems subjected to streams of high/low resistance, generating patterns similar to those seen in many natural flow systems, e.g., trees, rivers, and vascular systems. In this sense, the study of cavities inserted into heat generation walls has been widely investigated to comprehend the generation of design in this kind of system: I, T, Y, X, H, and \(\psi\)-shaped cavities [7, 8, 9, 10, 11, 12, 13]. Most of the investigations performed in the literature used the exhaustive search method to perform the geometrical optimization. Although the exhaustive search is a benchmark solution, mainly for the representation of the effect of degrees of freedom over the performance indicators, for the investigation of geometries with a high level of complexity, the number of required simulations can become prohibitive. As a consequence, some meta-heuristic methods have been employed jointly with the constructal design in the recent literature, such as genetic algorithm (GA), simulated annealing (SA), and Luus-Jakola (LJ) [6,14, 15, 16, 17, 18, 19]. The metaheuristic parameters were also investigated to adequate the computational intelligence strategy to solve other optimization problems in engineering, as can be seen in [PERSON] et al. [20]. The authors analyzed the parameters of particle swarm optimization and the ant colony optimization algorithm, and as a result, a new version of PSO emerges. Concerning the association between computational intelligence and constructal design, [PERSON] et al. [14,15] performed the first studies that associate evolutionary computation with the CD method for geometric optimization of a Y-shaped cavity. The GA was used to reduce the computational effort during the geometric optimization process, as well as allow the study of other conditions as different fraction areas of the cavity and the convection heat transfer coefficient imposed at the cavity's surfaces, and also its effect over the design of the cavities. Later, [PERSON] et al. [16] investigated different functions of the cooling schedule (CS) of the simulated annealing (SA) algorithm over the effect of degrees of freedom on the thermal performance of the Y-shaped cavity previously studied in [PERSON] et al. [14]. The results revealed a more suitable reproduction of the geometry effects over the thermal performance of the system for specific conditions of CS parameters. In [PERSON] et al. [17] the SA algorithm was compared with the Luus-Jakola (LJ) heuristic to optimize a double T-shaped cavity. Results demonstrated that the SA algorithm showed better performance to reach the optimal geometries with more regularity than the LJ method. The results of this study were the base for the use of SA associated with the CD method for the complete optimization and geometric evaluation of the double T-shaped cavity in [PERSON] et al. [6].