Constrained multi-objective optimization problems (CMOPs) involve both conflicting objective functions and various complex constraints. Artificial Physical Optimization is susceptible to local optimality and it is challenging to identify a solution that simultaneously achieves constrained feasibility and objective optimization. To address this problem, we propose a two-population algorithm called BiACMOAPO. In BiACMOAPO, the main population is made to search for the optimal Pareto front that satisfies the constraints within the identified feasible region by clustering and angle-based screening and by calculating the correlation between individuals using the APO force rule to attract the good particles to the poor ones. The auxiliary population enables particles to traverse the infeasible region by initially disregarding the constraints entirely, and subsequently addressing the constraints through separate cases, and guides the individuals of the main population toward the constrained optimal frontier. For the complex situation of multiple constrained regions, a fitness evaluation model based on DBSCAN clustering and angle is introduced, which divides the space into multiple regions through DBSCAN clustering disassembly and adjusts the individual fitness values by using the angle information to effectively maintain the search diversity and to prevent different feasible regions from interfering with the current region. Finally, the promising particles searched are deposited into the archive set by the update strategy of clustering and angle. In the experiments, the MW series and DTLZ series are selected as the benchmark test functions to compare the proposed algorithm with some state-of-the-art algorithms, and the experimental results suggest that the BiACMOAPO algorithm can obtain quite competitive performance in comparison to other algorithms on both IGD and HV test problems.