This paper proposes stochastic exploration algorithms for mobile robot exploration problems. Navigation with uncertain conditions in the absence of initial parameters is a situation wherein precomputation and prediction are impossible for a robot. Therefore, stochastic optimization techniques were applied to find the optimal solution for the robot exploration problem. Driving to the unknown areas, the robot updates the frontier line of sensor visibility during the exploration mission. The points of the frontier line are assumed as the swarm population with their own positions and costs, which allows the computation of the next global waypoint. The calculation of global waypoints is carried out by a nature-inspired optimization algorithm that can place a waypoint in uncertainties. This study offers to apply three metaheuristic algorithms individually, such as Whale Optimization, Grey Wolf Optimizer, and Particle Swarm Optimization algorithms, for comparison and testing their performances in the mobile robotics. At first, the simulations based on the proposed exploration algorithms were implemented and evaluated in a created environment. The results were compared in a single and average cases. Then, the real-world experiments using Grey Wolf Optimizer exploration algorithm were conducted in the different types of environments using MATLAB-ROS integration tool. These results proved the effectiveness and applicability of the bio-inspired optimization algorithm in the mobile robotics.