## 1 Introduction  
Distributed computing platforms are becoming increasingly important as cost-effective options to conventional high-performance computing platforms. The distributed systems keep going to expand in size, heterogeneity, and diversity of network resources [1, 2]. In such complicated platforms, workload management and load balancing become critical factors in keeping business activities float. Workload management has reached the top of business and management engineering research priorities [3, 4]. One of the most complex concerns in real-time optimization problems is the robust management of a wide range of workload patterns. Robust management includes a resilient load balancing system [5]. Load balancing is an important element in distributed and parallel environments [6, 7], as it is used to achieve maximum use of resources, to avoid node overload, to reduce response time, to avoid network bottlenecks, and to ensure system scalability. The challenge of dynamic load balancing persists as a difficult issue of global optimization because of system structure heterogeneity, requisitions of Quality of Service (QoS) per application and administration of computational resources [8, 9]. There are several algorithmic methods for optimizing load balancing problems [10, 11, 12]. These optimization algorithms were based on a metaheuristic (or stochastic) nature-inspired paradigm. Most metaheuristic algorithms generate random possible solutions at each iteration to enhance the chances of exploring the whole search space [13]. The first feasible solution can be improved using mechanisms as movement, mutation, exchange, and cooperative perception. The improvement process is then repeated many times until the best solution is discovered, and the optimization is completed using termination conditions. The stochastic methods use a cost function (or fitness function) [14]. The cost function is a set of agents passing through the solution space. The position of an agents in the solution space represents a set of parameters in the cost function. Thus, the aim of the metaheuristic algorithm is to find the global minimum or global maximum of the cost function and to supply high-quality solutions within a feasible lead time [15]. The swarmintelligence-based (SI-based) algorithms belong to the category of stochastic population-based bioinspired algorithms [16]. SI-based algorithms covered algorithms that are based on the behavior of different animal species, chemical processes, or even other natural processes [17]. Several nature-inspired metaheuristic algorithms have been presented to handle optimization problems in different applications. The ant colony optimization (ACO) [18], genetic algorithm (GA) [19], and particle swarm optimization (PSO) [20] are some examples of algorithms inspired by nature. ACO imitates the behavior of a colony of real foraging ants to find the most cost-effective path. The shortest or optimal path is found via the stigmergy process. It is a social network mechanism where pheromones push agents toward promising solutions. ACO is designed to solve the most challenging concern of combinatorial optimization problems, as well as of network applications, such as routing and load balancing. ACO algorithms can be applied to solve different problems, such as the traveling salesman problem (TSP) [21], vehicle routing [22], sequential ordering [23], and scheduling [24]. GA is a search algorithm based on the concepts of natural selection and natural genetics (crossover and mutation). The GA is employed in real-world optimization problems, for example, manufacturing [25], warehouses [26], robotics [27], and automatic control [28]. PSO mimics the behavior of a swarm of birds or fish in search of food. In PSO, each particle in a swarm does not exchange materials with other particles. A particle is impacted by its current position, the best position in the swarm, and its velocity.