The molecular docking problem is to find a good position and orientation for docking a small molecule ( ligand) to a larger receptor molecule. In the first part of this paper we propose a new algorithm for solving the docking problem. This algorithm-called ClustMPSO-is based on Particle Swarm Optimization (PSO) and follows a multi-objective approach for comparing the quality of solutions. For the energy evaluation the algorithm uses the binding free energy function that is provided by the Autodock 3.05 tool. The experimental results show that ClustMPSO computes a more diverse set of possible docking conformations than the standard Simulated Annealing and Lamarckian Genetic Algorithm that are incorporated into Autodock. Moreover, ClustMPSO is significantly faster and more reliable in finding good solutions. In the second part of this paper a new approach for the prediction of a docking trajectory is proposed. In this approach the ligand is "un-docked'' via a controlled random walk that can be biased into a given direction and where only positions are accepted that have an energy level that is below a given threshold.