Restricted Velocity Particle Swarm Optimization (RVPSO) and Self-Adaptive Velocity Particle Swarm Optimization (SAVPSO) are two recently proposed Particle Swarm Optimization (PSO) algorithms specially for solving Constrained Optimization Problem (COP), but to our knowledge, no research has been done on the applications of the two algorithms to Unconstrained Optimizations Problem (UOP). To this end, the effectiveness and performance characteristics of the two algorithms in UOP were investigated. Moreover, in view of their relatively strong conservativeness, the algorithms were improved by combining chaos factor and random strategy respectively with the search mechanism to enhance their global exploration ability. Also, the effects of different parameter settings on the performance of all these algorithms were studied. The performance of all these algorithms was evaluated on 5 typical benchmark functions. Experimental and comparison results show that the improved RVPSO is better than RVPSO in terms of robustness and global exploration ability, but it may easily get trapped into local optima when solving high-dimensional multi-modal functions; the improved SAVPSO has stronger exploration ability and faster convergence rate than improved RVPSO, and it can achieve more accurate solutions when applied to high-dimensional multi-modal functions. Therefore, the improved SAVPSO has competitive ability of global optimization, and thus is an effective algorithm for solving unconstrained optimization problems.