This paper presents the solution of the inverse kinematics problem of a 6-Degrees-of-Freedoom (6 DOF) industrial robot manipulator using two bio-inspired multiobjective optimization techniques: The Fast and Elitists NonDominated Sorting Genetic Algorithm (NSGA-II) and the recently developed Bacterial Chemotaxis Multi-Objective Algorithm (BCMOA). The optimization problem described establishes reaching a desired set of position and orientation for the robot end effector (EF). The desired set to be solved is taken from the surface of a Computer Aided Design (CAD) based workpiece model. Once forward kinematics of the studied robot MOTOMAN MH6 is modeled, the workpiece is placed inside the known robot workspace based on its operational standing. Then, the objective functions that minimize the position and orientation errors are defined and the techniques are implemented. Finally, the performance to solve the inverse kinematics problem of both techniques is compared.