Fog computing has recently emerged as a new infrastructure composed of three layers: node levels, cloud services, and companies (clients). In general, node levels deliver services to cloud computing layers which in turn serve to in-situ processes at companies. This kind of framework has gained popularity in the Internet of Things (IoT) networks context. The main purpose of node layers is to deliver inexpensive and highly responsive services, and as a consequence, cloud layers are reserved for expensive processes. Thus, the optimal load balancing is a major concern between cloud and fog nodes as well as the efficient use of memory resources on those layers. We propose a simple Tabu Search method for optimal load balancing between cloud and fog nodes which accounts for resource constraints. The main motivation for using Tabu Search is that on-line computations are a must in those layers and as tasks are received they should be processed. We consider a biobjective cost function for such purpose; the first one denotes the computational cost of processing tasks in fog nodes while the last one stands for that in cloud nodes. During the optimization process, convex combinations of the objective functions are employed to reduce the optimization problem to mono-objective cases. Experimental tests are performed by using synthetic scenarios of tasks to be executed. The results reveal that, by using the proposed method the memory usage can be minimized as well as the computational costs of load balancing methods.