Goal directed agent navigation in crowd simulations involves a complex decision making process. An agent must avoid all collisions with static or dynamic obstacles (such as other agents) and keep a trajectory faithful to its target at the same time. This seemingly global optimization problem can be broken down into smaller local optimization problems by looking at a concept of criticality. Our method resolves critical agents - agents that are likely to come within collision range of each other - in order of priority using a Particle Swarm Optimization scheme. The resolution involves altering the velocities of agents to avoid criticality. Results from our method show that the navigation problem can be solved in several important test cases with minimal number of collisions and minimal deviation to the target direction. We prove the efficiency and correctness of our method by comparing it to four other well-known algorithms, and performing evaluations on them based on various quality measures.