One of the phases in the Software Development Life Cycle is planning the software project. Estimating the software effort is another task in this project planning phase. Software effort estimation is the method of determining how many workers are required to create a software project. To increase the precision of software effort estimation, many researchers have focused on this field and used both algorithmic and non-algorithmic techniques. The most widely used method is the Constructive Cost Model (COCOMO). However, the COCOMO model has a limitation, which is related to the precision of the software effort estimation. Meta-heuristic algorithms are preferred with parameter optimization because they can provide solutions that are nearly optimal at a reasonable cost. This study aims to enhance the precision of effort estimation by modifying the three COCOMO-based models' coefficients and assess the efficiency of Grey Wolf Optimization (GWO) in finding the optimal value of effort estimation through applying four other algorithms, including Zebra Optimization(ZOA), Moth-Flame Optimization(MFO), Prairie Dog Optimization(PDO), and White Shark Optimization(WSO) with NASA18 dataset. These models include the basic COCOMO model, and another two models were also suggested in the published research as a modification of the basic COCOMO model. To assess the performance of the proposed models, the six most used software effort estimation metrics are used. The results demonstrated that the GWO outperformed other algorithms based on high accuracy and significant error minimization, involving ZOA, MFO, PDO, WSO, and other existing models.