## 4 Review of Existing Methods and Capabilities
### Path Planning
#### 4.1.1 Fixed Target
[PERSON] _et al._[34] used an RHC method in conjunction with a virtual force method to improve the performance of the RHC. [PERSON] _et al._[35] developed a cooperative search algorithm utilizing RHC with a rapidly exploring random-tree path-planning algorithm. [PERSON] _et al._ proposed a multiple aircraft trajectory planning algorithm utilizing a RHC strategy with a mixed integer linear programming basis [36]. There have been multiple efforts utilizing RHC methods in conjunction with Partially Observable Markov Decision Processes [37; 38; 39; 27]. In 1995, [PERSON] and [PERSON] [40] proposed a methodology of nonlinear function optimization using particle swarm optimization (PSO). This method provides a simple and computationally useful algorithm for optimizing a wide range of functions. The use of PSOs as part of a UAS path-planning algorithm has been employed successfully by numerous researchers [30; 35; 41; 42; 43; 44]. [PERSON] _et al._[45] provided a comparison of GAs and PSOs for UAS path planning. The resultant of the comparison shows that the GA produces superior trajectories to the PSO. An approach that has shown good results is the use of Genetic Algorithms (GA). A GA provides a heuristic method based on natural evolution by defining the decision variable as a chromosome. The chromosomes defined by the problem give the resultant population and an algorithm is utilized that generates an evolution process until a satisfactory solution results. [PERSON] [46; 47] and colleagues [48; 49] have performed significant work in using GAs for both single and multiple UAS path planning which has shown satisfactory results. [PERSON] _et al._[50] developed an immune genetic algorithm that provided an \"immune operator and concentration mechanism\" that improved convergence of existing GA algorithms. GAs can, under certain circumstances, suffer from premature convergence. [PERSON] and [PERSON] [51] used a GA design for self-organized search and attack of UAS swarms. [PERSON] [52] proposed a vibrational GA algorithm enhanced with a Voronoi Diagramin an effort to improve the convergence problem. Research is continuing in the use of GAs for path planning of UASs [53; 54]. An algorithm based upon the annealing of metal [55; 56] can be utilized to find global minimum of an objective. Drawing upon the annealing process, a Simulated Annealing (SA) algorithm will search randomly in the area of an initial guess. If an improvement is found, the new value is kept. If deterioration is noted, the result may be discarded or kept depending upon a temperature-dependent probability. A cooling schedule is used to determine when the temperature has been sufficiently cooled from the initial value. [PERSON] _et al._[57] presented a method for 2D path planning in a radar threat constrained environment using a simulated annealing algorithm. [PERSON] _et al._[26] evaluated five algorithms including SA, Consensus Based Bundle Algorithm (CBBA), greedy allocation, optimal Mixed Integer Linear Programming (MILP), and suboptimal MILP. The results showed that the SA algorithm provided the best solutions for path generation but required the longest computation time of the five algorithms; however, the growth in computation time with increased parameters was the lowest. In 1992, [PERSON] proposed an approach for finding an optimal path that drew upon the behavior of a colony of ants [58]. The ant colony optimization (ACO) approach has been adopted as a method to optimize UAS path planning. [PERSON] _et al._[59] proposed a method that integrated ACO and an analytic hierarchy process that showed good results for path planning using the ACO algorithm. An adaptive ant colony optimization approach for multiple UASs for coordinated trajectory re-planning was proposed by [PERSON] _et al._[60]. An extension of ACO looks more generically at digital pheromone responses and has been used to improve target search methods [61; 62; 63].