## 1 Introduction  
Interference is a fundamental optical phenomenon that emerges when two or more waves, whether mechanical or electromagnetic, overlap within the same spatial plane. The scientific discipline tasked with measuring and harnessing this interference is known as interferometry. Interferometry plays a pivotal role in various domains, ranging from the precise assessment of aberrations, deformations, and flatness to addressing challenges posed by disturbances and temperature gradients [1]. The methodologies that are usually preferred to demodulated interferograms are the phase-shift algorithms and the Fourier method for single linear carrier fringe patterns [2]. However, these techniques often struggle in the case of rapidly changing events because the phase difference between consecutive interferograms is not a constant. In this situation, a large linear carrier interferogram can be recorded but at the cost of a reduced dynamic range of the phase that can be measured. Attempts to record a fringe pattern in the described situation would lead to infringing the sampling theorem. A solution to measure a dynamic event with a high dynamic phase range is to analyze a single interferogram with closed fringes. A unique interferogram with closed fringes can be examined to recover the phase information associated with the physical phenomena being measured. The measurement accuracy from a unique closed fringe pattern is thus closely dependent on the phase distribution of the interferogram being measured. Several phase demodulation methods from a single fringe pattern have been proposed. Each one of the proposed solutions has strengths and drawbacks. There are methods that use different computational strategies, such as the combination of genetic algorithms and parametric methods [3; 4; 5]; soft computing techniques applied to Zernike polynomials [6]; a combination of genetic algorithms and frequency-guided sequential demodulation [7]; combined harmony search optimization and frequency-guided sequential demodulation [1]; demodulate directly with Particle Swarm Optimization [8]; unwrapping of phase maps with sign changes [9]; demodulation with symmetric wavefront and tilt [10]; two-dimensional regularized phase-tracking technique [11]; different techniques of deep learning [12; 13]; convolutional neural network [14]; and Lissajous ellipse fitting [15], among others. While each of these methods demonstrates efficacy in specific contexts and scenarios, no universal approach exists capable of reliably extracting phase information from any given interferogram. Some of the mentioned methods have a slow convergence rate, require a specific path determination method to avoid critical points, and need a large training set of known solutions to the demodulation problem, besides a high computational complexity. Rather, these techniques are optimized for particular characteristics of fringe patterns, thus limiting their applicability in broader contexts. All techniques are susceptible to be improved. In particular, the optical phase demodulation has been expressed as an optimization problem, where computational intelligence algorithms can be applied to find the best phase solution that matches with the closed fringe patterns called interferogram. In 2007 [PERSON] and [PERSON] proposed a frequency-guided sequential demodulation (FSD) technique suggesting a single fringe pattern demodulation by estimating the local frequencies of the interferogram, where the phase sign determination is guided by the frequency or fringe density [16]. Harmony search optimization (HSO) is a soft computing technique inspired by the observation of musical composition to search for perfect harmony and was introduced in 2001 by [PERSON] et al. [17]. In 1995, [PERSON] and [PERSON] proposed an evolutionary algorithm that consists of the optimization of the data using a cloud of particles in order to model social problems; this algorithm is known as Particle Swarm Optimization (PSO) [18].