## 1 Introduction
In mechanical correction techniques, the compensation algorithm synthesizes the radiation pattern by adaptively changing the contour of the array surface and the location of the radiating elements with the help of mechanical beam steering conformal transmitarray [6], mechanical translation of the parasitic elements [7], driving mechanism, dielectric elastomer actuator [8], tuning of antennas with mechanical action [9], and employing electro-active polymers to adjust the antenna pattern [10]. However, these techniques demand sophisticated control strategies, micro servos, additional mounting space, sustainable power supply, and have a limited accuracy for the adjustment of radiation pattern with slow reaction time. Compared to the mechanical techniques, the electrical correction techniques correct the radiation pattern with high accuracy, in lesser time, and without the need of mechanical adjustments in the array. To compensate the field distortion, a variety of numerical methods and optimization algorithms has been used to optimize the field pattern in phased array antennas owing to the computer hardware limitations. These optimization methods include several evolutionary and probabilistic techniques that iteratively look-up and adjust the parameters determining the best-fitted results. For example: Method of moments [11]: This is a numerical method that solves Maxwell's equations to compute the antenna's radiation pattern. The method involves discretizing the antenna's surface into small segments and solving for the electric and magnetic fields at each segment. The resulting system of equations is then solved to obtain the current distribution on the antenna surface, which is used to compute the radiation pattern. Geometric optimization [12]: This technique involves optimizing the shape and size of the antenna elements in the array to achieve the desired field patterns. Genetic algorithms [13]: These are optimization algorithms that use a population-based approach to search for the optimal antenna design. The algorithm generates a population of potential antenna designs, evaluates their radiation patterns, and then selects the best designs for further iteration. The algorithm continues until the best radiation pattern is achieved. Particle swarm optimization [14]: This is another optimization algorithm that simulates the behavior of a group of particles in a search space. The particles move through the search space to evaluate the optimum solutions, guided by their own experience and the experience of the other particles in the swarm. The algorithm continues until the best radiation pattern is achieved. Finite element method [15]: This numerical method solves the partial differential equations of electromagnetics to compute the antenna's radiation pattern. The method involves discretizing the antenna's volume into small cells and solving for the electric and magnetic fields at each cell. The resulting system of equations is then resolved to acquire the current distribution on the surface of antenna, which is used to calculate the field patterns. Once the optimal radiation pattern has been synthesized, the antenna elements are positioned and oriented to achieve the desired pattern. This involves selecting the appropriate phase and amplitude for each antenna element to create constructive and destructive interference, shaping the radiation pattern in the desired direction. Simulated annealing [16]: This technique is a stochastic optimization method that involves iteratively searching for the global minimum of a cost function by randomly changing the antenna element positions. The algorithm accepts moves that increase the cost function with a probability that decreases over time. This technique has been used successfully in conformal array synthesis, but it can be computationally expensive. Neural networks [17]: This technique involves training a neural network to obtain the relationship between the antenna element positions and the radiation pattern.