# Multi-Robot Exploration Based on Multi-Objective Grey Wolf Optimizer
## 1 Introduction  
In robotics, exploration pertains to the process of scanning and mapping out an environment to produce a map, which can be used by a robot or group of robots for further work. Based on the type of environment, exploration can be one of the following: outdoor, indoor, or underwater, using a mobile-robot or multi-robot systems [1; 2]. In this study, we focused on indoor exploration by robots, which are equipped with ranging sensors. It can be assumed that these robots with onboard sensors can scan an environment without any difficulties by walking randomly around. However, their motion is not efficient, which can result in an incomplete map coverage. As a solution to this issue, this paper proposes an algorithm that enhances the efficiency of the multi-robot exploration by using a multi-objective optimization strategy. Naturally, all real-world optimization problems in engineering pursue multiple goals. They may differ from each other in various fields. However, it is common for all to optimize problems by maximization or minimization functions. In the past, multiple optimization problems were solved by one function because of the lack of suitable solution methodologies for solving a multi-objective optimization problem (MOOP) as a single-objective optimization problem. With the development of evolutionary algorithms, new techniques, which seek to optimize two or more conflicting objectives in one simulation run, have been applied to MOOPs. This new research area is named multi-objective optimization (MOO) [3]. In robotics, studies related to optimization have been gaining wide attention [4]. If we consider multi-robot systems [5], optimization is popularly applied in path planning [6], formation [7], exploration [8], and other fields where decision-making control needs to be optimized. Previous research conventionally found the optimal solutions as separated single-objective tasks: short path, obstacle-free motion, smoothest route, and constant search of uncertain terrain. The new impact of optimization in robotics is obtained due to the metaheuristics and its nature-inspired optimization techniques [9]. The nature-inspired algorithms are not only restricted to robotics but also have significant applications in different fields. Due to this, they have attracted the attention of scholars [10; 11]. Metaheuristic algorithms are optimization approaches, which emulate the intelligence of various species of animals in nature. The number of agents classifies the metaheuristic algorithms into single-solution-based and population-based algorithms. In both classes, the solutions improve over the course of iterations with one single agent or an entire swarm of agents, respectively. The main advantage of population-based approaches is their ability to avoid stagnation in the local optima due to the number of agents. The swarm can explore search space more and faster than a single agent. Regardless of this, the benefit of one class over the other depends on its application in a certain problem. However, it is important to mention the No-Free-Lunch (NFL) theorem for optimization, which assures that there is no algorithm with universal optimal solution by all criteria and in all domains [12]. Despite the number of agents, the metaheuristic algorithms can be classified into single and multi-objective optimization techniques according to the number of objective functions. A multi-objective optimization is an extended approach to single optimization. It allows finding an optimal solution of two independent objectives simultaneously. In order to select just one best solution from the available ones, a trade-off should be considered among them. The Pareto-optimal front helps pick up one of the suitable solutions satisfying two objective functions.