Manufacturing microscale textures can reduce friction and wear compared with smooth surfaces. In laser surface texturing, the resulting texture geometry is directly affected by laser parameters such as laser power, scanning speed and overlap rate. Therefore, finding the optimal parameter settings to improve the process performance is crucial. One of the biggest challenges encountered during the optimization stage is accurately determining the functional relationship between surface quality and process parameters. Another significant problem is solving the nonlinear equation system. This study aims to investigate the effect of laser-textured surfaces on the tribological behavior of titanium Ti6Al4V. Optimization of laser texture process parameters using metaheuristic algorithms is a hot topic. The first contribution of this study is the modeling of the contact angle, kurtosis and skewness quality parameters of Ti6Al4V titanium alloy based on the polynomial curve fitting method as a function of laser power, laser speed and overlap rate. Another significant contribution is to optimize the proposed nonlinear regression models using metaheuristic approaches such as genetic algorithm, particle swarm optimization, whale optimization algorithm, gray wolf optimization, equilibrium optimizer, teaching-learning-based optimization, student psychology-based optimization (SPBO), slime mould algorithm and social network search. The reason for using many metaheuristics is to test the effectiveness of different metaheuristic methods in solving this problem. Analysis of variance was performed to evaluate experimental data and compare the success of optimization methods. The results revealed that the proposed metaheuristic methods can be applied to the related problem. It has been observed that the methods give identical results. Among these methods, the SPBO method provided the best performance in the optimization of all laser output parameters.