Containerization has transformed application deployment by offering a lightweight, scalable, and portable architecture for the deployment of container applications and their dependencies. In contemporary cloud computing data centers, where virtual machines (VMs) are frequently utilized to host containerized applications, the challenge of effective placement of the container has garnered significant attention. Container placement (CP) involves placing a container over the VM to execute a container. CP is a nontrivial problem in the container cloud data center (CCDC). Poor placement decisions can lead to decreased service performance or wastage of cloud resources. Efficient placement of containers within a virtual environment is critical while optimizing resource utilization and performance. This paper proposes a penalty-based particle swarm optimization (PB-PSO) CP algorithm. In the proposed algorithm, we have considered the makespan, cost, and load of the VM while making the CP decisions. We have proposed the concept of a load-balancing penalty to prevent a VM from becoming overloaded. This algorithm solves various CP challenges by varying container application sizes in heterogeneous cloud environments. The primary goal of the proposed algorithm is to minimize the makespan and computational cost of containers through efficient resource utilization. We have performed extensive simulation studies to verify the efficacy of the proposed algorithm using the CloudSim 4.0 simulator. The proposed optimization algorithm (PB-PSO) aims to minimize both the makespan and the execution monetary costs and maximize the resource utilization simultaneously. During the simulation, we observed a reduction of 10% to 15% in both execution cost and makespan. Furthermore, our algorithm achieved the most optimal cost-makespan trade-offs compared to other competing algorithms.