The prediction of critical points of thermodynamic systems is an important tool for modeling many high-pressure processes of theoretical and practical interest. In this article, the calculation of critical points of multicomponent mixtures is treated as a global minimization problem of a modified merit function associated with the criticality conditions obtained from the Gibbs tangent plane criterion, designed to discriminate the scale of the problem. The methodology used to solve the optimization problem is based on two versions of the Particle Swarm Optimization (PSO), equipped with Lowdiscrepancy sequences to prevent the sensitivity of the swarm with respect to the location of the initial population. To avoid a rapid decrease of the weight inertia, and to prevent stagnations near undesirable local minimizers, we present a modification of the PSO method which uses different search cycles with the same inertia weight. This new version developed here is a fast and robust algorithm for solving the critical-point problem, via global optimization.