# Multi-Robot Exploration Based on Multi-Objective Grey Wolf Optimizer
## 2 Related Work  
In the last two decades, many techniques have been proposed for robot exploration. Among them, there are novel fundamental, hybridized, and modified methods. In this section, studies on the different algorithms and the impact of the evolutionary optimization techniques in exploration are discussed. Considering exploration as one of the branches in robotics, [PERSON] et al. 's frontier-based method is the pioneering work in this field [26]. From that time up to now, many frontier-based studies have appeared, most of which were hybridized or modified with success. The coordinated multi-robot exploration (CME) is frontier-based with the emphasis on the cooperative work with a team of robots [22]. The robot's mission is to search for maximum utility with the minimum cost that diverges the robots from each other keeping the direction to search unexplored space. The alternative coordinated method is the randomized graph approach [27; 28]. It builds a roadmap in an explored area that navigates robots to move through safe paths. Recently, [PERSON] et al. [29] introduced the efficient backtracking concept to the random exploration graph, preventing the same robot in visiting the same place more than once. These above-mentioned methods have the common idea of using frontier-based control. Another approach in exploration that is completely different in theory and practice is artificial intelligence (AI). Reinforcement Learning (RL) and convolutional neural network (CNN) are such attempts, which have been proposed in previous studies [30; 31; 32]. The exploration-based approach on neural networks differs considerably from the frontier-based approach in terms of environment perception and control system. Visual sensors (cameras) scan a place for further computation using image-processing algorithms [33]. The output of the calculation is the interaction of the robot with the environment. [PERSON] et al. [34] conducted a survey of leading studies in mobile robotics using deep learning from perception to control systems. Recently, a novel branch of exploration that employs nature-inspired optimization techniques has appeared. The approaches seek to enhance existing solutions to exploration. [PERSON] et al. [35] applied clustering-based distribution and bio-inspired algorithms such as PSO, Bacteria Foraging Optimization, and Bat algorithm. The clustering provides a direction of robot motion, while the nature-inspired approaches involve exploring the unknown area. The study of [36] applied a combination of PSO, fractional calculus, and fuzzy inference system. They compared their results with other six other PSO variations that showed effective multi-robot exploration. A similar waypoint concept in our study was performed in [37]. The artificial pheromone and fuzzy controllers help the multi-robot systems to navigate efficiently by distributing the search between robots and avoiding repeated visits in explored regions. Figure 1: The proposed Multi-Objective Grey Wolf Optimizer (MOGWO) exploration in two stages: (**a**) selecting the waypoints in unexplored space with high probability values of occupancy grid map; (**b**) selecting the closest waypoints in explored space with high probability values proportional to the distance; (**c**) the next position is one of the frontier points, which is the nearest to the selected waypoint. The study of [38] involved more than one optimization problem in the exploration, which is important to highlight here. The optimal solution seeks to minimize two objective functions: the variance of path lengths and the sum of the path lengths of all robots. Compared to our research, they applied the K-Means clustering algorithm instead of the bio-inspired technique used in our study. The study of [39] presented the auto-adaptive multi-objective strategy for multi-robot exploration, where the multi-objective concept consisted of two missions: a search of uncertainties and stable communication.