# An Approach to Multi-Objective Path Planning Optimization for Underwater Gliders
## 1 Introduction
### Multi-Objective Path Planning  
One area in which multi-objective optimization is important is in path planning. Multi-objective path planning (MOPP) problems will be introduced here, including different techniques and applications discussed in the scientific literature. MOPP is the way of finding a feasible path for a vehicle that requires travelling from a staring point A to a final point B, and accomplishes all the objectives planned for the mission. Considering the most common objective--reaching a target--other objectives for the mission might include (but are not limited to), verifying several path properties, limiting battery consumption, and crossing or avoiding specified areas [10]. Previous studies solved MOPP in different ways, for diverse types of vehicles and different environments. In [27; 28], the authors used genetic algorithms (GA) to optimize both length and difficulty of the path, adding a basic path repair mechanism to make non-valid paths usable, on a 2D realm. The genetic algorithm NSGA-II was used by [PERSON] and [PERSON] [29] to perform offline path planning for an unmanned aerial vehicle, with the fitness functions being avoid collisions, no abrupt changes to the path, and not flying above a specified altitude. Also, [PERSON] et al. [30], worked on path planning optimization for unmanned aerial vehicles, using NSGA-II combined with Nash-equilibrium to decrease the time for searching one global solution, showing that a hybridization with game theory is a valid choice to solve MOPP. The usage of particle swarm optimization (PSO) to solve a MOPP was proposed in [31], to find smooth and shorter paths, with parameter tuning, using a 2D map. Another work using PSO was carried out by [PERSON] et al. [32] to solve path planning on a 2D environment, incorporating previously known danger locations, and similarly in [33], where path planning in a 2D uncertain environment, with danger sources and obstacles were concurrently being considered also using PSO. A spline approach is discussed in [34], to perform MOPP with fitness functions being \"path length and potential\", \"obstacle hindrance\", and \"visibility\" of the robot. [PERSON] et al. [17] described a MOPP accounting for length and clearance of the path, using path refiner operators based on geometry parameters. Later, [PERSON] et al. [20] tried to find a path that minimizes a primary cost function subject to a bound on a secondary cost function, handling collision avoidance in all the vertexes along the path. The same work described planning in belief space, with collision probability and multi-objective, proposing one algorithm that is more accurate but with higher computation costs and another that sacrifices accuracy but is more efficient. Using the Mars Rover scenario (3D), [PERSON] [35] developed a MOPP using A* search with real objectives (minimize difficulty, danger, elevation, and length). Usageof the Pareto front and the Pareto optimal in every step of A* was proposed by [36; 37] using memetic algorithms in order to optimize both path length and smoothness. A survey of 2016 [38], about applying nature inspired algorithms to solve MOPP, analysed the usage of particle swarm optimization, ant colony optimization, and artificial bee colony. In addition, [PERSON] et al. [39] presented a firefly-based approach to pursue MOPP considering path safety, length, and smoothness, pointing to the path planning as one of the most researched topics in robotics. One year later, in 2017 another publication [40] reviews robot path planning techniques, with soft computing and heuristic approaches (artificial neural networks, fuzzy logic, wavelets, and genetic algorithms) replacing the classical methods (potential fields, roadmap, and cell decomposition). In same year, another work [41] addressed the path planning for the problem of an aircraft climbing using PSO and a two-level optimization scheme, in order to improve search performance, with results showing 15% faster climbs saving 20% more fuel. Later, in 2018, and also using PSO, [PERSON].