•A constrained optimization algorithm abbreviated as CMPSOWV is proposed.•Two evolution phases are designed into CMPSOWV to solve different COPs robustly.•Two schemes are embedded into CMPSOWV to address the premature convergence issue.•The proposed CMPSOWV outperforms its peers in terms of searching accuracy. The original particle swarm optimization (PSO) is not able to tackle constrained optimization problems (COPs) due to the absence of constraint handling techniques. Furthermore, most existing PSO variants can only perform well in certain types of optimization problem and tend to suffer with premature convergence due to the limited search operator and directional information used to guide the search process. An improved PSO variant known as the constrained multi-swarm particle swarm optimization without velocity (CMPSOWV) is proposed in this paper to overcome the aforementioned drawbacks. Particularly, a constraint handling technique is first incorporated into CMPSOWV to guide population searching towards the feasible regions of search space before optimizing the objective function within the feasible regions. Two evolution phases known as the current swarm evolution and memory swarm evolution are also introduced to offer the multiple search operators for each CMPSOWV particle, aiming to improve the robustness of algorithm in solving different types of COPs. Finally, two diversity maintenance schemes of multi-swarm technique and probabilistic mutation operator are incorporated to prevent the premature convergence of CMPSOWV. The overall optimization performances of CMPSOWV in solving the CEC 2006 and CEC 2017 benchmark functions and real-world engineering design problems are compared with selected constrained optimization algorithms. Extensive simulation results report that the proposed CMPSOWV has demonstrated the best search accuracy among all compared methods in solving majority of problems.