The total heating cost of residential buildings corresponds to a significant part of the energy consumption of countries. Designing cost-efficient residential buildings in terms of energy gains importance. In the current study, it is targeted to take a beneficial step that will contribute to this issue. In this respect, the decisive components for the calculation of the total heating cost of insulated buildings (i.e. the fuel type, insulation material, and insulation thickness) are determined optimally. For this aim, an optimization model is utilized in which the total heating cost based on life cycle cost analysis is considered as the objective function. The design variables are selected from both continuous and discrete spaces and they are dependent on each other. For solving the problem with such a complex search domain, different well-established non-gradient and population-based optimization techniques are utilized. These methods do not require the information of the objective functions so they can be used widely in solving different optimization problems. In addition, multivariable thermo-economic optimization for minimizing the total heating cost of the insulated building with the selected methods presents the effect and power of the population-based methods in solving different engineering optimization problems. The considered methods are tested on unconstrained mathematical functions and thermo-economic optimization of five distinct locations in the Aegean region of Turkey. The comparative assessments are reported and discussed in detail. Different analyses are employed for evaluating the performance of the optimization techniques. According to the archived outcomes, the utilized optimization techniques present acceptable performance in handling both discrete and continuous design variables.