There are two ultimate goals in multiobjective optimization. The primary goal is to obtain a set of Pareto-optimal solutions while the secondary goal is to obtain evenly distributed solutions to characterize the efficient frontier. In this paper, a collaborative neurodynamic approach to multiobjective optimization is presented to attain both goals of Pareto optimality and solution diversity. The multiple objectives are first scalarized using a weighted Chebyshev function. Multiple projection neural networks are employed to search for Pareto-optimal solutions with the help of a particle swarm optimization (PSO) algorithm in reintialization. To diversify the Pareto-optimal solutions, a holistic approach is proposed by maximizing the hypervolume (HV) using again a PSO algorithm. The experimental results show that the proposed approach outperforms three other state-of-the-art multiobjective algorithms (i.e., HMOEA/D, MOEA/DD, and NSGAIII) most of times on 37 benchmark datasets in terms of HV and inverted generational distance.