# An Approach to Multi-Objective Path Planning Optimization for Underwater Gliders
## 1 Introduction
### Multi-Objective Path Planning
[42] compared their improved PSO algorithm against other evolutionary algorithms, showing better results finding collision free and feasible paths along with minimum length and terrain roughness for a car-like mobile robot. Using an adapted version of NSGA-II, Ref. [43] was able to optimize three objectives and study the influence of the input parameters, when applying it to mobile robots on a 2D plane, obtaining fast optimization speeds and a good convergence of solutions. Also applied to mobile robotics, Ref. [44] proposed a multi-objective evolutionary algorithm, tested using five scenarios and quality metrics. Using a combination of ant colony and PSO on different optimization levels was studied by [45], to find the best energy-efficient path for underwater vehicles on an eddy field, using uncertainty levels. An algorithm to do multi-objective path planning using PSO was proposed by [46] applied to mobile sink in wireless sensor networks, employing the concept of Pareto front to select the global and local best solutions, outperforming other algorithms in several performance metrics. Considering aerial vehicles, Ref. [47] used a genetic algorithm to do collision-free shortest path planning, testing their proposal with and without restrictions to the path of aerial vehicles, stating that their solution can be applied to 3D environments. Another solution for multi-objective path planning for aerial vehicles was proposed by [48], combining a genetic algorithm with ant colony and using maps of height, risk, quantity, and value of sensing information. Authors used small population sizes and generations and were able to obtain dynamic environmental adaptability and high utility paths. Ref. [49] used an improved genetic algorithm to do multi-objective path planning, applied to a free-form surface milling, with three fitness functions (efficiency, energy, and carbon footprint) being converted to one single fitness function and replicating the travelling salesman problem. Another approach to multi-objective path planning using a genetic algorithm was done by [50], by using both dynamic and static 2D environments and concluding that their matrix-binary codes approach is more efficient and robust than random search algorithms. The usage of hybrid algorithms, was detailed later in [51], applying hybrid particle-swarm optimization-modified frequency bat optimization algorithm to tackle 2D path planning. The fitness functions were collision-free path, path-smoothness, and shortest-distance, assuming some simplifications to ease the process, such as no kinematic constraints, circular obstacles, and the addition of the robot size to the obstacle size. More recently, in 2019, [PERSON]. [52] combined the concepts of robust optimization and the integration of multiple scenarios as a multi-objective function, in order to investigate the relation between dominance and robustness. Using a parallel genetic approach, [PERSON]. [53] tackled optimal path planning for single and multiple underwater vehicles, avoiding upstream currents in multi-objective optimizations by developing a new crossover operator in order to raise the diversity of the solution. Authors state two aspects when dealing with underwater vehicles: the importance of path planning tools and the usage of simulations to validate solutions before real tests. The usage of a multi-objective firefly algorithm was proposed by [54], which saves elite particles obtained on each generation to ensure a higher ability to escape local optima results, increases the convergence speed and precision of the solution, being suitable for high-complexity multi-objective optimization problems.