This paper presents a new optimization algorithm based on particle swarm optimization (PSO). The new contribution relates to the introduction of a new momentum term' which is known to influence the convergence properties of the original PSO algorithm. It is shown that the new algorithm structure, named nPSO, can solve the problem of premature convergence, widely experienced in the original PSO algorithm, and also can make the particles' optimal search process truly' adaptive. The proposed algorithm is validated via well-known challenging functions and is found to be more efficient than the original PSO algorithm. Furthermore, the algorithm is extended to include the multiobjective case via dynamic weighted aggregation (DWA) and the maintaining of an archive to preserve the Pareto optimal solutions. The new algorithm, named new multiobjective PSO (nMPSO), it also compared to well-known evolutionary multiobjective algorithms based on a series of challenging benchmark multiobjective functions. Results obtained hitherto suggest that nMPSO can locate the Pareto-optimal front and performs better than other salient optimization algorithms.