Multiobjective Particle Swarm Optimization With Preference-Based Sort and Its Application to Path Following Footstep Optimization for Humanoid Robots

This paper proposes multiobjective particle swarm optimization with preference-based sort (MOPSO-PS), in which the user´s preference is incorporated into the particle swarm optimization (PSO) update process to determine the relative merits of nondominated solutions while handling the mutual dependences and priorities of objectives. In MOPSO-PS, the user´s preference is represented as the degree of consideration for each objective using the fuzzy measure. The global evaluation of a particle, which represents the quality of the particle according to the user´s preference, is carried out by the fuzzy integral, which integrates the partial evaluation value of each objective with respect to the degree of consideration. Since the global best attractor of each particle in the population is randomly chosen among the nondominated particles having a relatively higher global evaluation value in each PSO update iteration, the optimization is gradually guided by the user´s preference. After the optimization, the most preferable particle can be chosen for practical use by selecting the particle with the highest global evaluation value. The effectiveness of the proposed MOPSO-PS is demonstrated by the application of path, following footstep optimization for humanoid robots in addition to empirical comparison with the other algorithms. The footsteps optimized by the MOPSO-PS were verified by simulation. The results indicate that the user´s preference is properly reflected in optimized solutions without any loss of overall solution quality or diversity.