1. Introduction

Optimization is a part of the nature of human works, in which almost all of the human decisions go through an optimal process [1]. Optimization is embedded in the essence of the many branches of science, for example, a system with minimal energy in physics, the maximum profit in business, survival of the best organism in biology, and designing an engineering system that satisfies a set of constraints [2, 3]. Almost all of the engineering problems contain several nonlinear and complex constraints depending on the design criteria and safety rules.

Over the last decades, various types of methods have been developed to solve constrained engineering problems. Two well-known groups of these methods are mathematical and metaheuristic methods. The idea of mathematical methods can be attributed to the development of the calculus of variations [4]. These methods employ the gradient of the objective function and constraints of the problem to find the optimal solution. The results of these methods are exact. However, these approaches search in a space near the starting point, which makes them sensitive to the initial starting point. In other words, just a correct starting point can lead to the global optima. In dealing with complex optimization problems, these methods are not suitable and frequently reach local solutions, and in some real applications, the gradient of the objective function and constraints is impossible to be calculated [5]. These drawbacks encourage researchers towards metaheuristic methods. Metaheuristic methods try to combine basic heuristic methods with randomization and rule-based theories, which are usually taken from natural phenomena such as evolution, swarm intelligence, and governing laws in different physics theories. Metaheuristic algorithms are approximate, but their results have high accuracy and are very close to the global optimum solution [6]. These methods are problem-independent, and the starting point does not determine the quality of the final solutions. Besides, these methods employ different operators to perform a global search in the space of the problem at an appropriate speed. These features have made them popular in recent decades. Also, these types of algorithms are among the most popular techniques that are employed for solving optimization problems in different fields, such as computer and electrical engineering [7], water, geotechnical and transport engineering [8], structure and infrastructures engineering [9], robotic [10], project and construction management [11], feature selection and data mining [12, 13], industrial and manufacturing [14], and medicine and biology [15].

Glover [16] introduced the term metaheuristic firstly. The word metaheuristic is a combination of two old Greek words: meta and heuristic. The word heuristic has its origin in the old Greek work heuriskein, which means the art of discovering new strategies (rules) to solve problems. The suffix meta also is a Greek word that means “upper-level methodology” [17]. Almost every metaheuristic algorithm follows the general process shown in Figure 1. Algorithm steps cause fundamental differences in the performance of algorithms when faced with different problems. In the other words, algorithm steps represent the unique operators of each algorithm in which new solutions are generated. The operators of each algorithm refer to the optimal process of a particular phenomenon that those algorithms have imitated.

According to the type of basic phenomena of each method, metaheuristic algorithms can be classified into four main categories: (1) evolutionary, (2) swarm intelligence, (3) physics-based, and (4) human-based algorithms. Evolutionary algorithms are motivated by natural evolution. Swarm intelligence algorithms model the natural behavior of animals in teamwork such as foraging and hunting. Physical phenomena and laws of science inspire physics-based algorithms, and finally, human-based algorithms mimic various optimal behaviors of humans in different conditions. Some of the most popular and novel algorithms are presented in Table 1.

Each of these algorithms can behave differently when dealing with different problems, so that one particular algorithm may not solve some problems. Therefore, it is necessary to create a new high-performance optimization algorithm that is able to solve more types of problems. Novel metaheuristic methods are developed to find the optimal solution for complex and large-scale problems in less time than previous ones, with higher accuracy. These aims are satisfied by developing more robust algorithms that have a better ability to search the space of problems to find a better solution. In addition, this property arises from the right balance between exploration and exploitation of the proposed algorithm. Exploitation means searching around the current best solutions, while exploration tries to explore the search space more efficiently, often by randomization [42].

In addition to inventing novel algorithms based on natural phenomena, developing new algorithms using hybridizing the operators of the current methods or modifying them is a hot topic in the field of metaheuristic algorithms. Firefly algorithm with chaos [43], hybrid particle swarm optimizer, ant colony strategy and harmony search scheme (HPSACO) [44], island-based cuckoo search with highly disruptive polynomial mutation (iCSPM) [45], quantum-behaved developed swarm optimizer (QDSO) [46], hybrid self-assembly with particle swarm optimization (SAPSO) [47], upgraded whale optimization algorithm (UWOA) [48], fuzzy controllers with slime mould algorithm (SMAF) [49], and hybrid invasive weed optimization-shuffled frog-leaping (SFLA-IWO) [50, 51] are some the newly developed hybrid or modified optimization algorithms.

Social network search (SNS) algorithm is a robust metaheuristic algorithm that was innovated as a novel method for solving optimization problems, and its results showed that it is capable of outperforming various methods in dealing with different optimization problems [42]. The SNS algorithm simulates human behavior as users of a social network. Social network users can influence the opinions of other users on the network by sharing their views, opinions, and thoughts. Each of the users can also share their thoughts on the network and affect other people’s opinions. In other words, the SNS simulates particular moods where the views and opinions of users are influenced under their communications. This paper investigates the performance of the SNS algorithm using 14 constrained engineering optimization problems and a real application in the field of satellite image segmentation. The obtained results are compared with other optimizers in terms of best function value and number of function evaluations, and in most cases, the solutions of the SNS are better than the other methods.

The rest of this paper is organized as follows. Section 2 describes the SNS algorithm and constraint-handling technique. The performance of the SNS algorithm in solving optimization problems is evaluated against other methods in Section 3. Finally, conclusions are given in Section 4.

2. Materials and Methods

This section presents the general framework of the SNS algorithm and the utilized constraint-handling technique for solving engineering optimization problems.

2.1. Social Network Search (SNS)

Human beings are social species, which always try to communicate with each other. Social networks are virtual tools that were created for this goal with the advent of technology. The proposed SNS algorithm simulates the interactive behavior among users in social networks to achieve more popularity. Social networks are platforms where users can interact virtually with other users. Interacting with other users of the network may affect their opinions. The process of interacting with and influencing other users of the network goes through an optimal process so that users are always trying to increase their level of popularity on the network.

The main property of social networks is that users can follow other persons, as shown in Figure 2. If a user shares a new post, that person’s followers may be informed about the shared topic. This feature (fast propagation of views) has turned networks into a powerful tool for promoting information and ideas, which is due to having high connectivity of users in the social networks, as demonstrated in Figure 2.

In social networks, users’ viewpoint can be affected by other views in different moods containing imitation, conversation, disputation, and innovation. One of these moods that look like real-world social behavior creates the new solution in the SNS algorithm. Description and mathematical modeling of these moods are as follows [42].

2.1.1. Mood 1: Imitation

Imitation means that the views of other users are attractive, and usually, users try to imitate each other in expressing their opinions as follows:

()

where X_j represents the vector of the jth user’s view, which is selected randomly (i ≠ j), X_i is the view vector of the ith user, and rand(−1,1) and rand (0,1) are two random vectors in intervals [−1, 1] and [0, 1], respectively. In this mood, the new solution will be generated according to imitation space (Figure 3(a)), and this space is created using the radii of shock and popularity. The shock radius (R) reflects the amount of influence of the jth user, and its magnitude is considered as a multiple of r. The value of r shows the popularity radius of the jth user, which is calculated based on the difference in the opinions of the ith and jth users. Also, the final effect of the shock radius is reflected by multiplying its value to a random vector in the interval of [−1, 1], in which if the components of the random vector are positive, the shared view will be agreed with the jth opinion and vice versa. The process of the imitation mood is illustrated in Figure 3(a). As can be seen, using equation (1), the space of imitation will be formed, and then a point as a new view will be shared on the network.