The widespread use of mobile devices has led to the emergence of mobile cloud technology. Mobile users want several applications on their mobiles, and they need cloud services to carry out storage and computation due to limited mobile resources like battery life, storage, and computation. Resource limitations lead to the offloading of mobile data to the cloud to carry out remote computation and then send back the computational result to the mobile device. The mobile cloud computing (MCC) concept introduced in 2010 [1] is a combination of three technologies: Cloud Computing (CC), Mobile Computing (MC), and Mobile Internet [2,3]. The epitome of MCC is to let the user access and compute accurate and real-time information at any time and any place.

Cloud computing has brought a new era of development to the internet. It has removed all limitations regarding computer applications. Cloud is the interconnected assemblage of high-performance servers with extensive storage and computational power accessible through the internet. Cloud resources are available to users on pay per use basis [4]. The proliferation of wireless mobile communication, new web technologies, and the evolution of mobile internet business are driving forces for the development of the internet. Internet technology is a way of communication by using the internet, which is to provide real-time network resources and services to the users. Mobile internet gives convenience and the facility to provide various new business opportunities, computational services, and quality assurance [5]. MC is about sharing different resources and exchanging data among intelligent devices like mobile phones, laptops, and computers. [6].

Although, MCC has eliminated all limitations of mobile devices related to storage, computation, and battery life. However, connecting mobile devices to the cloud undergoes high network latency and high power consumption while data are offloading specifically through 4G/LTE networks [7]. To overcome these problems concept of the cloudlet framework was introduced by M. Satyanarayanan in 2009 [8]. Cloudlets are trusted, resource-rich computer or a cluster of computers that is well connected to the internet and available for use by nearby mobile devices [8]. Cloudlets provide physical proximity to mobile users. They are deployed just one hop distance compared to the cloud, resulting in the offloading of tasks to the nearest cloudlet [9]. Mobile devices use Wi-Fi to connect to the proximate cloudlet [10]. Cloudlet is the middle layer of the 3-tier architecture, as shown in Fig. 1. Low latency, high bandwidth, and one-hop distance provide mobile devices with real-time interactive services. For large applications requiring high computational and processing capabilities or when cloudlets are already busy, the cloud is used for data offloading and computational purposes [11]. Due to the proliferation of MCC nowadays, it is essential to balance the load on cloudlet and cloud.

A hybrid meta-heuristic load balancing technique, named fuzzy firefly-based algorithm with levy flight (LF), is introduced in this paper. Firefly algorithm (FA) is a powerful nature-inspired optimization technique used widely by researchers. The essence of the FA is to maintain the proper balance between solution diversification and speed. FA may fall in local optimum and leads to premature convergence. To overcome this issue, LF is used to enhance the exploration of global search space. Levy distribution provides the random movement by generating a random direction and a step length. Fuzzy logic is used to make cloudlet selection. Fuzzy logic provides evenness among true and false values without using any mathematical model. Optimization using fuzzy logic is simple, fast, and adaptive, leading to system stability.

In recent times, MCC has turned out to be a significant research area as it enhances mobile devices’ capabilities by integrating them with cloud computing technologies and cloudlet. The major highlights of this paper are as follows:

Study of existing load balancing techniques in MCC.

The remnants of this paper are organized as follows: Section 2 presents existing work on load balancing in MCC. Section 3 drafts the mathematical model of the load balancing problem. The proposed methodology presents a novel hybrid Fuzzy Firefly algorithm with Levy Flight to address the load balancing in Section 5. The results of the proposed technique are discussed in Section 6. Finally, Section7 concludes the paper with some future directions.

Many researchers have proposed different load balancing and scheduling techniques [12]. Job scheduling in a mobile cloud environment is challenging as there are numerous processors, and all have numerous different or same instances of virtual machines (VM). Assigning jobs to the correct VM and improving the performance and cost is a significant issue in the mobile cloud environment. Job scheduling should also consider allocating the load to all the VMs to achieve load balancing while minimizing the makespan [13]. Many works have been carried out using a few legacy algorithms used for scheduling and load balancing purposes.

In some existing works, scheduling is performed based on the size of tasks like the Min-Min algorithm chose the job with small tasks [14] and came out to be better as it reduced the makespan while balancing the load. An improved min-min scheduling algorithm with load balancing [15] had been proposed, but execution cost was not considered in this paper. It showed an increase in resource utilization and decreasing the makespan. The max-min algorithm chose the maximum size task after selecting the task [16]. Many research works exist on priority-based scheduling [17] to perform fair scheduling to prioritize the jobs. However, these legacy algorithms were not good enough for complex, uncertain, and real-time user demand. None of these works had considered utility-based prioritization.

On the other hand, meta-heuristic and nature-inspired algorithms like Genetic algorithm (GA), Ant colony optimization (ACO), FA, and Bees colony optimization attempt to provide near-optimal solutions for the scheduling and load balancing problem. In [18], ACO is used and compared the makespan with the First Come First Serve (FCFS) and Round Robin (RR) algorithms. Cost and job interdependency were not considered in this work. ACO concentrated on makespan and cost reduction. Its performance depended on the initial solution, and it also had a more extended convergence than several algorithms. Bees’ colony algorithm also had a restriction as it converged only in its local optima. Most of the previous works focused only on the execution time [19].

Guo et al. in [20] used Particle swarm optimization (PSO) to reduce processing time. A multi-objective scheduling algorithm was proposed to reduce the cost and execution time of jobs using the Pareto frontier method. The Pareto frontier method was also used in one more multi-objective PSO algorithm [21] to reduce the execution time of jobs. Here, attention was given to reducing data transfer time. However, load balancing was not considered in any of the abovementioned work. A layered mobile cloud resource scheduling algorithm was proposed for mobile devices in the mobile cloud environment. An energy-efficient and cost-aware mobile service provisioning scheme for the mobile cloud was proposed in [22]. Chunlin et al. [23] studied the composition of mobile device services to enhance user utility within the capacity of physical resources and other restrictions in the mobile grid. The authors of the paper [24] proposed an algorithm for task assignment in a mobile cloud environment while balancing the load. Cloudlets are used for the execution of tasks leading to reduced makespan. However, this algorithm has the highest energy consumption rate. This paper [25] proposed a distributed scheduling algorithm for resource-intensive mobile applications using the Lagrangian method. A bargaining protocol to maximize resource utilization and profit was introduced in [26]. It balanced the load by distributing jobs to reliable VMs using FA. Wang et al. [27,28] provide task-centered resource allocation in mobile edge computing. Gu et al. [29,30] proposed a secure framework for data queries in fog and cloud environments. Liao et al. proposed [31,32,33] task offloading algorithms in edge computing, providing cost savings related to data transmission, latency, and bandwidth usage, among other benefits.

From the above discussion, we observe that less work is done on cloudlet selection and load balancing on the cloudlet and cloud. Cloudlet selection based on remaining capacity is rarely found. Hence, we propose an intelligent hybrid meta-heuristic Fuzzy Firefly Algorithm with Levy Flight for Load Balancing using capacity and waiting time for cloudlet selection to increase resource reliability while reducing the makespan and maintaining load balancing.

For formulating the problem mathematically, Let us consider n mobile users, each submitting a task set at any time t in the system. This submitted task set is represented by vector D={D1,D2,D3……Dn}. Tasks are offloaded to cloudlet or public cloud in MCC for execution. Assume p cloudlets in close vicinity of the mobile user represented by vector C={C1,C2,C3……..Cp} and m VMs on each cloudlet or cloud represented by vector VM= {VM1,VM2,VM3……..VMm}. The user request can be offloaded either on cloudlet or public cloud as the user request arrives. Cloudlets have limited resources and computing power as compared to the cloud. If cloudlets are full and refuse to process the tasks, then tasks can be offloaded to the public cloud. We have assumed an assignment matrix A to show the assignment of tasks to VMs on cloudlets. In this matrix, rows represent the tasks, and columns represent the VMs, as shown by Eq. (1). Entry Aij in matrix A will be 1, if task Di is assigned to VMj, otherwise it will be 0.

(1)A=[A11A12A13……A1mA21A22A23……A2m………………An1An2An3……Anm]

Similarly, a matrix CT represents the completion time of tasks on VMs. Here also, matrix rows represent the tasks, and columns represent the VMs, as shown by Eq. (2).

(2)CT=[CT11CT12CT13……CT1mCT21CT22CT23……CT2m………………CTn1CTn2CTn3……CTnm]

In this paper, makespan and Degree of imbalance are used for performance analysis of the system. These metrics are defined as follows:

The ultimate goal of this hybrid load balancing technique is to minimize makespan and Degree of imbalance while balancing the load. So, the fitness function can be represented as follows by Eq. (17) using Eqs. (8) and (16) [35,36]:

(17)Fitnessfunction,F(x)=w1∗ef1+w2∗ef2where f1 and f2, are objective functions for makespan and Degree of imbalance. Here, e is the exponential function and w1 and w2 are weights corresponding to the f1 and f2 s.t. w1+w2=1 and w1,w2∈{0,1}. Weights may be assigned on the basis of the choice or preference of a particular parameter. In the case of equal preference, each weight can be assigned a value of 0.5, so their total should be equal to 1. Hence, the proposed hybrid load balancing technique efficiently balances the mobile cloud load based on the above fitness function.

This section presents the concept of Fuzzy, firefly with levy flight, and their hybridization to achieve load balancing on the mobile cloud.

In this section, we discuss simulation setup and results obtained in different scenarios using a simulated mobile cloud network.

A novel intelligent hybrid meta-heuristic algorithm for better assignment of offloaded tasks in an MCC environment is proposed in this paper. The proposed technique implicitly acts intelligently as the fuzzy system is an integral part of artificial intelligence, automatically deciding based on input values and rule base. Secondly, Fireflies use swarm intelligence in terms of specific rules derived from their swarm behavior, ensuring interaction between various flies. Thirdly, the proposed algorithm automatically adjusts its behavior or converges depending on the information gathered and provides balance in underloaded and overloaded situations. The simulation was carried out in Cloud Analyst, and performance is compared with UFA, DSOA, and ACOQDM on two different datasets, NASA and CLARKNET. The results show that the FFALF excels in UFA, DSOA, and ACOQDM at about 17.39%, 10.20%, and 20%, respectively, on the CLARKNET dataset and 20.42%, 10.98%, and 17.91% on the NASA dataset while balancing the load. In this algorithm, the mobility of users is not considered, so this algorithm can be best applied in indoor environments like shopping marts, supermarkets, malls, and hospitals, where users are considered stationary. Secondly, this algorithm cannot partition large tasks, which can be distributed among multiple cloudlets simultaneously to achieve parallelism. Hence, in the future, this work can be extended by considering the mobility of users and task partitioning.