<p>Squirrel Search Algorithm (SSA), inspired by the behavior of flying squirrels, belongs to the strategy of Swarm Intelligence. As it suffers from early convergence, to rectify it two variants of SSA, namely, Memory and Threshold based Squirrel Search Algorithms (MTSSA1 and MTSSA2) have been proposed here. In MTSSA1 and MTSSA2, a Memory has been introduced to store the good squirrels having same or nearly same fitness based on some Threshold value (TH). From the Memory the top k squirrels are randomly selected and considered for the next operation. This strategy balances the exploration and exploitation capacity of the search process. MTSSA1 and MTSSA2 have been applied to 26 benchmark test functions and the results show that they outperform the state-of-the-art of SSA variants and other algorithms in most of the functions. Furthermore, MTSSA1 and MTSSA2 have been applied to some complex real-life problems including Gene Selection. Gene selection by sample classification involves identifying specific genes from a large gene expression dataset to differentiate between distinct biological conditions, such as normal and diseased states. Given that the dataset contains tens of thousands of genes, while the number of critical disease-related genes is much smaller, the primary goal is to select a subset of genes from the gene expression dataset. The selected gene will be considered as biomarkers. The performance of MTSSA1 algorithm is observed to be better than other methods in constrained real-life optimization (optimum cost: 0.010314) and Gene selection problem (classification accuracy: 85.7143% to 100%), and on the other hand the MTSSA2 performs better in unconstrained real-life optimization problems (optimum cost: 2.7009e-12 and 2.1719e-05 for two problems).</p>