1 Introduction
UAVs have the capability of autonomous navigation which allows them to move towards the goal location in the most optimal fashion, and simultaneously ensure that they do not suffer any collisions with other UAVs or the obstacles present in the environment. The most compelling ability of the UAVs is to operate in complex environments where human operations tend to be very difficult. The time needed to solve the route planning problem is exponential and substantially grows with the increasing complexity of environment since it is an NPhard problem.
There are two different methods for route planning refa : offline (or global) route planning
– in which the UAV estimates the complete route even before starting any movement; and
online (or local) route planning – in which the vehicle simultaneously updates the route and moves towards the destination.Route planning can be applied to land, air or water – while the vehicle in land corresponds to a 2D environment; in the latter two, the UAV can move in all the three dimensions and corresponds to a 3D environment. This paper considers the problem of global route planning for multiple UAVs in 3D environment.
As shown in Figure 1, the underlying architecture of route planning can be divided into four components:

Perception: Vehicle utilizes the sensors to devise meaningful information of the surroundings. If the agent/robot possesses full knowledge of the environment at all time then the route planning is global otherwise it is local.

Localization: Vehicle identifies its location in the operating environment.

Cognition and path planning: Vehicles decide in which direction it should steer to reach to the goal location in accordance with the deterministic or metaheuristic algorithm used.

Motion control: Vehicle regulates its motion in order to achieve the desired trajectory.
Metaheuristic algorithms can be termed as stochastic algorithms with randomization and local search refa . The main reason to choose a metaheuristic based SSA algorithm for route planning is that these algorithms generate nearoptimal routes in significantly less time in complex environments which can not be achieved by deterministic algorithms. Metaheuristic algorithms are very efficient and have a wide range of applications since they can achieve practical solutions for various problems.
Metaheuristic algorithms are classified as
Evolutionary and Swarm Intelligence. The former algorithm tries to mimic the approach of evolution in nature; and the latter tries to mimic the intelligence of herds, swarms, flocks in nature. The primary source of inspiration for these techniques emerge from the collective behavior of creatures. Some of the evolutionary algorithms include Genetic Algorithm, Differential evolution, BiogeographyBased Optimization (BBO), Evolution strategy; while swarm intelligence includes Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Dragonfly Algorithm (DA), Cuckoo Search (CS), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Salp Swarm Algorithm (SSA) among others.
2 Related Work
The problem of route planning by autonomous UAVs in a 2D environment has been solved by many approaches like cell decomposition method refb , Voronoi diagram, visibility graph refc , potential field approach, and rapidly exploring random trees (RRTs) refd , deterministic search algorithm Dijkstra refe and heuristic based algorithms (A* and D*) reff . The algorithms mentioned above are proactive, so they are not effective solutions for route planning and suffer from local minima stagnation and considerable time complexity.
In a 3D environment various metaheuristics algorithms like Genetic Algorithm (GA) refg , PredatorPrey Pigeon Inspired Optimization (PPPIO) refh , Whale Optimization Algorithm (WOA) refi , BiogeographyBased Optimization (BBO) refj , Particle Swarm Optimization (PSO) refk , Invasive Weed Optimization (IWO) refl , Glowworm Swarm Optimization (GSO) refm etc. have been applied. Md. Arafat refn presented Bacterial Foraging Optimization (BFO) to compute the shortest path in a dynamic unknown environment and used Gaussian cost function. Similarly, Edin Dolicanin refo , applied a modification of BrainStorm Optimization (BSO) Algorithm for finding the optimal path of an unmanned combat aerial vehicle (UCAV) while considering fuel consumption and safety degree as a metric. Zhang et al. refp applied Grey Wolf Optimizer (GWO) to path planning issue on the battlefield. Phung et al. refq improved discrete PSO technique. He devised it to path planning for surface inspection using UAV vision. Yaoming Zhou refr proposed a bioinspired computing algorithm that is inspired from plant growth mechanism and applied it to the problem of path planning.
In general, natureinspired algorithms have displayed excellent performance in solving intricate realworld problems like route planning. In this paper, the extension of some abovelisted algorithms for finding routes for multiple UAVs in a 3D environment is presented. This paper proposes the use of Salp Swarm Algorithm(SSA) which is a metaheuristic optimization algorithm and proposed by Mirjalili et al. refs to solve the route planning problem. SSA is influenced by swarming behavior of salps while foraging and navigating in oceans. In refs , it was shown that SSA significantly outperforms other popular metaheuristic algorithms. By using several stochastic operators, the problem of local optima stagnation is avoided in multimodal search landscapes. The algorithm is applicable for single as well as multiobjective optimization tasks.
The further structure of the paper is formulated into following sections. Section 3 illustrates the methodology of multiple autonomous UAV route planning and a description of the environment. Section 4 gives a thorough explanation of the SSA. Section 5 illustrates the implementation and final results obtained by comparing SSA with other metaheuristic algorithms. Section 6 finally concludes the paper.
3 Methodology
The proposed methodology can be organized into the following segments. First, a description of problem statement is given and after that terrain construction is described. Following that, the cost function for the optimization is presented, and then finally the trajectory for autonomous UAVs is generated.
3.1 Problem Statement
The problem of route planning of multiple UAVs in 3D environment can be viewed as a mapping to a function in which start and goal location are presented as inputs and obtain an optimal trajectory in terms of output. The primary interest of route planning is to generate an optimal, collisionfree route with the least cost.
(1) 
where represents start location of the UAV ; represents the goal location of the UAV ; represents a collisionfree trajectory of UAV refx .
The initial position of UAVs can be represented with the help of the following matrix:
(2) 
Where represents position UAV in dimensional space. Since a 3D space is used, therefore . The aim is to decrease path length for each given UAV by following objective function:
(3) 
subject to constraint
(4) 
Where and represent the different UAVs; denotes the path of UAV which is computed by
(5) 
Where, denotes cost associated with path refx .
represents violation of the same path constraints between the trajectories of UAV and . So and are taken from nonintersection paths from source to destination. Figure 2 shows the paths followed by the UAVs to reach their destinations while not suffering any collisions in between.
3.2 Terrain construction
To understand and solve the problem of route planning, an environment is required to simulate the UAVs to generate a route. The environment will contain several areas where the movement is prohibited, and those areas can be termed as obstacles. To prevent a collision, UAVs shall stay away from these areas. Obstacles of cuboidal shape with distinct sizes are chosen however in the reallife situations, obstacles generally don’t possess a specific geometrical shape. To perform modeling in an environment where obstacles do not have a perfect geometrical shape is challenging and hampers the experimentation. Irregular obstacles are also included in modeling and testing of environment, and SSA will avert the uneven obstacles efficiently.
Two dimensional route planning is related to the planning of motion for vehicles on land and also in air or underwater while restricting one dimension. Simulation in 3D environment is complex and requires expensive computations to generate the routes. At the same time, a 3D environment better models the complex reallife scenarios.
The details of the boundary, starting positions of UAVs and goal locations, as well as positions of obstacles for four maps used are depicted in Tables 1, 2 and 3 respectivelyrefm . Using a different set of maps, as presented in Figure 3, performance of SSA is compared and analyzed with deterministic and other metaheuristic algorithms.
Map  Start Boundary  End Boundary 

Map 1  (0, 5, 0)  (10, 20, 6) 
Map 2  (0, 0, 0)  (20, 5, 6) 
Map 3  (0, 5, 0)  (10, 20, 6) 
Map 4  (0, 0, 0)  (26, 20, 10) 
Map  Start Position  Goal Position 

Map 1  (2, 10, 2) (1, 4, 1) (9.2, 17, 3) (9.2, 10, 3) (0.1, 10, 2)  (1, 4, 1) (0.1, 17, 3) (9, 4, 1) (0.9, 4, 5) (9, 10, 2) 
Map 2  (0, 1, 5) (0, 2, 5) (0, 3, 5) (19, 4, 5) (19, 5, 5)  (19, 0, 5) (19, 5, 5) (19, 4, 5) (0, 3, 5) (0, 1, 5) 
Map 3  (2, 10, 2) (1, 4, 1) (9.2, 17, 3) (9.2, 10, 3) (0.1, 10, 2)  (1, 4, 1) (0.1, 17, 3) (9, 4, 1) (0.9, 4, 5) (9, 10, 2) 
Map 4  (17, 2, 5) (3, 2, 5) (7, 2, 5) (7, 18, 7) (17, 18, 5)  (21.5, 12, 4) (6, 6, 5) (13, 1, 3) (12, 14, 6) (22, 14, 8) 
Obs  Map 1  Map 2  Map 3  Map 4 

1  (0, 2, 4.5)  (10, 2.5, 6)  (3.1, 0, 2.1)  (3.9, 5, 6)  (0, 2, 0)  (10, 1.5, 1.5)  (0, 12, 0)  (1.5, 20, 10) 
2  (0, 2, 1.5)  (3, 2.5, 4.5)  (9.1, 0, 2.1)  (9.9, 5, 6)  (0,2, 3)  (10, 1.5, 5.5)  (0, 0, 0)  (5, 6, 10) 
3  (7, 2, 1.5)  (10, 2.5, 4.5)  (15.1, 0, 2.1)  (15.9, 5, 6)  (0, 2, 0)  (10, 2.5, 1.5)  (4, 0, 0)  (5, 16, 10) 
4  (0, 2, 0)  (10, 2.5, 1.5)  (0.1, 0, 0)  (0.9, 5, 3.9)  (0, 2, 4.5)  (10, 2.5, 6)  (9, 10, 0)  (10.5, 20, 10) 
5  (0, 15, 0)  (10, 20, 1)  (6.1, 0, 0)  (6.9, 5, 3.9)  (0, 2, 1.5)  (3, 2.5, 4.5)  (9, 0, 0)  (10.5, 4, 10) 
6  (0, 15, 1)  (10, 16, 3.5)  (12.1, 0, 0)  (12.9, 5, 3.9)  (7, 2, 1.5)  (10, 2.5, 4.5)  (14.5, 0, 0)  (16, 10, 10) 
7  (0, 18, 4.5)  (10, 19, 6)  (18.1, 0, 0)  (18.9, 5, 3.9)  (3, 0, 2.4)  (7, 0.5, 4.5)  (14.5, 10, 8)  (16, 18, 10) 
8  (3, 0, 2.4)  (7, 0.5, 4.5)    (0, 15, 0)  (10, 20, 1)  (14.5, 10, 3.5)  (16, 18, 6) 
9      (0, 15, 1)  (10, 16, 3.5)  (14.5, 10, 0)  (16, 18, 1.5) 
10      (0, 18, 4.5)  (10, 19, 6)  (14.5, 18, 0)  (16, 20, 10) 
11      (0, 7, 0)  (10, 7.5, 0.5)  (19, 10, 0)  (20, 18, 10) 
12      (0, 7, 2)  (10, 7.5, 5.5)  (20, 4, 0)  (23, 7, 10) 
13      (0, 11, 0)  (10, 11.5, 2.5)  (20, 0, 0)  (26, 1, 10) 
14      (0, 11, 4)  (10, 11.5, 5.5)  (23, 6, 0)  (26, 20, 10) 
15        (25, 1, 0)  (26, 4, 10) 
3.3 Cost Function
Due to the random nature of generated routes, there exists a possibility that the UAVs might collide with the obstacles and cannot continue its motion, so the goal location cannot be reached. So, various costs are required to be introduced in the route planning problem like fuel cost, cost due to sharp turns and cost due to an incomplete route. The various costs involved can be illustrated asrefm :

: The cost of fuel which depends on length of the route followed. This cost is less when the route followed has a smaller length, which in turn leads to less consumption of fuel and lower time to reach the goal.

: This cost is governed by frequency of sharp turns present in route. Lower the sharp turns the smoother and stable the route is.

: This cost corresponds to the separation among the goal and the route’s end when the UAVs fail to reach the goal location. This situation could arise due to a significant obstacle which lies in between the route to goal. This cost corresponds to the highest interest amongst all the costs and assigned with the highest priority. This cost should have a zero value in the optimal solution.
The generated route to the goal location can be presented as a sequence of points from the source location as follows:
(6) 
where, represents the start location; represents the goal location; represent the points occurring in the route.
To determine the cost of the fuel, the speed of the UAV is assumed to be constant during route planning. Thus, the cost of the fuel can be obtained by using total distance traveled by the UAVs. The cost of fuel is presented using Equation 7.
(7) 
The cost due to sharp turns occurs when change in direction from to do not match the change in direction from to . It can be computed by searching the cases in obtained route with a considerable amount of turn in the angle between the two. This cost will increase with the increase of sharp turns in the planned route. This cost can be inferred from equation 8.
(8) 
Now the most significant cost, i.e., is computed using the Euclidean distance. The two required points are end point of route and the goal location. If the endpoint and goal location is the same than this cost is set to 0 else, it is determined with the help of equation 9.
(9) 
represent the endpoints of the generated route; represents the target location.
The total cost of a route can be computed using equation 10.
(10) 
The total cost function helps to achieve the optimal route from the route set.
Here are the experimental parameters and their values are actuated with the help of experiments and constraints of the problem description. In scenarios where a more substantial route length is taken as a preference, then is assigned a higher value. Similarly assigns inclination towards the route smoothness. From , it is ensured that the route planned reaches the goal. The UAVs posses a propensity to include information regarding their locality only, and for the subsequent increment, they might alter their location among one of the cells in the neighborhood. Thus, UAVs do not have any prior knowledge regarding at what time and location it will face an obstacle; that is why UAVs steadily continue to modify their paths whenever they encounter the obstacles.
3.4 Trajectory generation for multiple UAVs
The generated trajectory by the SSA may include some sharp turns which practically are not feasible for UAVs to follow. So, it becomes crucial to smoothen the generated route. The movement and speed of the UAVs can be presented using polynomial functions for vehicular mobility. The polynomial function involves the component of time. A continuous route is generated by the fifthdegree polynomial, which indicates that the first derivatives are consistent. The polynomial derivative can be determined efficiently to obtain the results of the campaign in this manner. A conventional fifth order time polynomial functionrefx is represented using equation 11.
(11) 
While generating the trajectory, the subpoints are obtained in the initial phase. Subpoint can be considered as a necessary point in the confined route, which assists the UAV to avert any obstacle or steep turn. To produce a smooth route, the speed and movement of UAV traveling through subpoints are utilized by the fifth order polynomial based trajectory fitting strategyrefx .
The main objective of using SSA for multiple UAV route planning in a 3D environment is:

to localize the UAVs and destination location.

to plan a route between multiple UAVs and their corresponding targets and simultaneously ensure that no UAV collides with each other or any obstacle.
4 Salp Swarm Algorithm
Salp is a sea creature having a transparent barrelshaped body. It is a part of the Salpidae family. It’s movement is governed by pumping of water through the body and as propulsion to move forward. SSA is inspired by the swarming behavior of salps while foraging and navigating in the water. The shape of a salp is shown in Figure 4(a). The swarm formed by the salps in deep oceans is referred to as a salp chain. This chain is illustrated in Figure 4(b). This algorithm was first developed by Mirjalili et. al. in 2017refs . The primary reason to choose SSA for route planning was its simplicity and since the inspiration for the algorithm is from the natural navigating and foraging behavior of the salps in the ocean in search of food. With respect to multiUAV route planning, the foraging phase of the salp chains can be considered as a search for different targets in the environment and the navigating phase can be regarded as connecting the points in the environment to obtain waypoints for the generated path length.
For understanding the salp chains, a mathematical model was developed. The population is broken down into 2 segments leader and followers. Leader salp is present at the front of the chain while remaining salps are recognized as followers. The salp at the front escorts the swarm while the remaining salps follow each other and leader (either directly or indirectly).
Similarly to other swarmbased techniques, the position of salps is defined in an dimensional search space where denotes number of variables for a given problem. Thus, the position of all salps is saved in a twodimensional matrix called . It is an assumption that there exists a food source called in the search space as the swarms’ target.
The complete working of SSA can be observed from the following equations.
Equation 12 updates the position of the leader:
(12) 
Where = position of the leader; = position of the food source; and are upper and lower bounds in dimension; , , are uniform random numbers.
In Equation 13, maintains a balance between exploration & exploitation phase:
(13) 
Where, : current iteration, : maximum number of iterations.
Exploration is defined as the phase in which the algorithm tries to explore the search space. The avoidance of local solutions takes place in this phase. After the exploration comes the exploitation phase in which the primary concern is to improvise the solutions explored in the exploration phase.
Equation 14 updates position of salps except for the leader:
(14) 
The pseudocode of SSA algorithms is given in Algorithm 1.
Some assumptions are made in the research to get more efficient and useful results. The assumptions made here are as follows:

The UAV is considered as a point object.

The speed of the UAV is kept constant during the entire simulation.

Upon reaching the target point, a UAV can stop immediately irrespective of the momentum.
SSA algorithm has computational complexity
where = number of iterations; = number of variables (dimension); = number of solutions; and = the cost of the objective function.
5 Implementation Procedure
To validate the effectiveness of SSA on multiple UAV route planning problem in a static 3D environment, a set of experiments have been performed in MATLAB. Matlab 2017a version and a PC with intel processor, 3.40 GHz of CPU and 8 GB of RAM were chosen for performing the experimentation. In this section, experimental simulation is described, which is divided into two experiments. Then convergence analysis of the SSA algorithm on different maps is presented.
5.1 Simulation
Before analyzing the performance of SSA in a 3D environment for multiUAV route planning, it is first analyzed in a 2D environment and its performance as compared to deterministic and other metaheuristic algorithms, is examined. To illustrate the above experiments, a different set of maps corresponding to a different environment have been taken.
5.1.1 Experiment 1
The performance of different algorithms is investigated in a 2D environment whose layout is given in Table 4.
Obs No  Center (unit)  Radius (units) 

1  (1.5, 4.5)  1.5 
2  (4.0, 3.0)  1.0 
3  (1.2, 1.5)  0.8 
Map size: 30 30 i.e. (–10 to +20) 
The initial parameters and constants for the algorithms used in experimentation are listed in Table 5.
Algorithm  Parameters  Values 

SSA  Random Number 1 ()  [0, 1] 
Random Number 2 ()  [0, 1]  
Random Number 3 ()  [0, 1] 
The circular shape in the environment can be modeled as obstacles which should be completely avoided by the vehicle to prevent a collision. The start location of the vehicle was taken as (0, 0) and the goal location as (4, 6) refm . The initial experiments of SSA for route planning in 2D environment are performed to test the effectiveness of the algorithm implementation and to have a conjecture on the quality of solution for the 3D path planning of UAV. The convergence curve and planned routes for SSA are illustrated in Figure 5.
The Figure 5 depicts convergence analysis of SSA in the 2D arena simulated above. From Figure 5(c) it is clear that SSA converges quickly and there is little change in the cost with further increase in the number of iterations. The results of different algorithms for with respect to the cost and time in the 2D arena for single bot route planning in static environment are presented in Table 6.
Algorithm  Population  Iteration  Best Cost (points)  Time (units) 

WOA  150  500  8.0131  194.9152 
SCA  150  500  8.0042  197.0136 
GSO  150  500  8.0236  196.3792 
PSO  150  500  8.0234  196.3822 
IBA  150  500  7.9321  192.8920 
BBO  150  500  7.9803  191.2722 
GWO  150  500  7.9560  189.4108 
SSA  150  500  7.9340  186.4025 
5.1.2 Experiment 2
After analyzing the performance of SSA in a 2D environment, simulations are performed in a 3D environment. A set of four different maps are taken whose layouts are depicted in Table 3.
The start and the end point concerning different obstacle number show the location of two diagonally opposite corners of the cuboid. Every map has different dimensions, different start, goal locations along with different lower and upper bound as given in Tables 1 and 2.
The initial parameters and constants for different algorithms are the same as in the case of a 2D environment and are given in Table 5. Figure 6 shows the trajectory generated by SSA on various maps.
For map 1, 2 and 3 all the algorithms listed above were able to find the paths without any collisions. Map 4 is relatively complex and not all the algorithms discovered collisionfree path in first run. SSA performed satisfactorily in map 4 and discovered a collisionfree path in all of the multiple runs. To compare performance of different algorithms wrt time and cost, Tables 7  10 are formulated.
Algorithm  Pop. Size  Iterations 







WOA  20  25  215  310  283  232  92  57.64  
SCA  20  25  199  306  293  232  92  59.90  
GSO  20  25  221  296  283  236  92  57.50  
PSO  20  25  221  296  283  232  92  57.15  
IBA  20  25  215  308  279  232  92  72.15  
BBO  20  25  201  322  299  232  92  65.70  
GWO  20  25  201  284  295  232  92  48.50  
SSA  20  25  202  284  290  230  92  45.30  
WOA  25  40  199  308  285  228  92  65.75  
SCA  25  40  213  296  285  232  94  67.35  
GSO  25  40  201  284  291  230  96  63.49  
PSO  25  40  207  298  285  232  94  91.27  
IBA  25  40  208  300  279  230  92  92.32  
BBO  25  40  201  300  289  232  92  70.40  
GWO  25  40  201  284  295  232  92  56.98  
SSA  25  40  200  280  285  230  92  50.03  
Algorithm  Pop. Size  Iterations 







WOA  20  25  345  333  323  417  341  145.67  
SCA  20  25  333  323  343  385  455  142.90  
GSO  20  25  355  325  327  387  391  136.27  
PSO  20  25  333  313  337  365  423  136.06  
IBA  20  25  313  381  365  393  401  138.54  
BBO  20  25  375  405  629  758  389  256.87  
GWO  20  25  321  381  317  353  375  132.90  
SSA  20  25  321  378  313  352  375  125.76  
WOA  30  40  313  311  371  367  403  152.20  
SCA  30  40  357  341  351  403  373  153.87  
GSO  30  40  339  321  317  333  319  146.29  
PSO  30  40  325  343  299  327  377  197.94  
IBA  30  40  331  343  397  341  355  146.01  
BBO  30  40  387  375  345  704  389  266.83  
GWO  30  40  319  313  315  333  345  142.90  
SSA  30  40  318  305  312  329  342  130.87  
Algorithm  Pop. Size  Iterations 







WOA  20  25  219  328  343  256  94  95.02  
SCA  20  25  235  302  393  278  92  99.75  
GSO  20  25  219  322  339  294  92  108.69  
PSO  20  25  231  324  371  244  94  95.76  
IBA  20  25  203  320  425  268  92  102.47  
BBO  20  25  215  346  716  266  94  108.74  
GWO  20  25  213  300  355  274  94  92.46  
SSA  20  25  210  300  345  274  94  90.30  
WOA  25  40  245  308  347  246  96  101.81  
SCA  25  40  225  280  369  246  92  105.79  
GSO  25  40  215  324  335  254  92  141.91  
PSO  25  40  215  318  333  254  92  146.95  
IBA  25  40  247  324  375  302  92  151.41  
BBO  25  40  215  346  716  266  94  108.74  
GWO  25  40  201  312  339  254  92  104.87  
SSA  25  40  202  305  340  250  91  102.55  
Algorithm  Pop. Size  Iterations 







WOA  20  25  256  388  459  318  122  229.66  
SCA  20  25  259  383  457  320  122  211.86  
GSO  20  25  249  352  369  324  122  141.91  
PSO  20  25  261  354  401  274  124  95.76  
IBA  20  25  233  350  455  298  122  102.47  
BBO  20  25  245  376  746  296  124  274.43  
GWO  20  25  243  330  385  304  124  92.46  
SSA  20  25  242  325  385  281  124  85.20  
WOA  25  40  256  365  359  309  122  247.13  
SCA  25  40  260  374  358  308  122  211.42  
GSO  25  40  245  354  365  284  122  108.69  
PSO  25  40  245  348  363  272  122  146.95  
IBA  25  40  277  354  405  332  122  151.41  
BBO  25  40  231  350  355  302  122  108.74  
GWO  25  40  255  342  369  284  122  104.87  
SSA  25  40  250  322  370  276  122  101.44  
The results from the tables can be visualized in Figure 7.
5.2 Convergence analysis of SSA algorithm
By analyzing the following Tables 1114, it becomes evident that the SSA algorithm generates nearoptimal results in significantly fewer iterations if there are no obstacles in the workspace. A number of iterations are required to converge towards the optima when obstacles are presented in the workspace; but after completing 1520 iterations, results do not alter even if more increments are introduced.
Iteration  GWO  GSO  PSO  BBO  IBA  WOA  SCA  SSA 

1  250.80  260.80  252.00  419.79  328.40  256.40  267.20  256.65 
5  238.40  245.20  238.80  264.80  249.60  239.20  238.80  235.55 
10  228.80  230.00  236.80  243.69  238.40  229.40  236.20  224.80 
15  222.80  228.40  228.80  242.40  237.20  224.40  226.80  219.60 
20  221.20  227.20  228.60  232.00  234.60  222.40  225.20  218.65 
25  220.80  226.80  220.80  226.40  234.00  221.60  222.80  218.05 
30  219.60  224.20  224.40  226.00  228.80  219.80  221.60  217.80 
35  219.20  222.40  224.00  224.40  226.40  219.20  219.20  217.40 
Iteration  GWO  GSO  PSO  BBO  IBA  WOA  SCA  SSA 

1  644.03  644.88  698.75  698.56  1038.79  690.40  696.60  621.92 
5  392.80  394.26  425.67  474.20  683.41  396.00  398.20  440.76 
10  385.40  391.40  415.60  422.60  512.52  386.60  388.80  382.50 
15  361.00  390.40  398.60  385.40  507.04  374.60  373.80  347.81 
20  355.00  390.20  394.40  379.80  452.02  360.00  372.60  338.69 
25  348.20  359.80  378.60  377.40  432.97  353.80  352.20  330.18 
30  346.20  356.20  362.20  375.80  431.46  349.80  351.40  325.74 
35  343.00  354.20  354.80  374.20  422.72  347.00  346.20  321.22 
Iteration  GWO  GSO  PSO  BBO  IBA  WOA  SCA  SSA 

1  312.35  315.60  316.40  616.88  745.22  359.20  401.20  409.25 
5  272.60  274.00  304.80  356.00  449.28  282.00  314.00  341.50 
10  262.80  269.20  265.20  342.45  367.28  265.60  296.80  273.46 
15  257.60  264.00  263.60  283.20  358.20  258.20  261.20  244.60 
20  251.60  256.40  258.20  276.40  319.23  252.40  254.00  241.86 
25  250.80  246.80  250.00  276.00  271.60  252.20  251.60  239.90 
30  245.40  246.00  248.80  274.80  268.00  251.20  247.20  239.05 
35  245.00  245.80  248.60  272.80  266.40  251.20  247.00  237.65 
Iteration  GWO  GSO  PSO  BBO  IBA  WOA  SCA  SSA 

1  476.80  461.20  496.05  525.80  518.60  530.0  481.60  471.60 
5  356.65  340.75  350.80  365.75  370.80  402.65  360.50  342.95 
10  295.40  310.90  308.50  310.95  340.95  338.70  334.85  289.45 
15  277.25  283.20  282.80  290.20  310.10  308.60  308.20  273.40 
20  276.85  280.45  276.40  279.50  296.40  299.65  293.80  271.25 
25  275.10  277.30  273.70  268.15  294.10  290.20  289.40  269.85 
30  274.85  275.65  271.65  258.90  292.45  285.60  286.00  269.10 
35  274.40  274.00  270.00  257.40  291.60  282.25  284.45  268.55 
As seen in Figure 8, the execution time of algorithms are comparable to recently reported data refp , when a simple environment like Map 1 and 2 is considered. For complex environment like Map 4, the SSA achieves low time complexity and more influencing results. Thus, SSA becomes suitable for reallife scenarios like route planning for multiple UAVs in a complex reallife environment.
The average percentage improvement in cost and time of SSA algorithm with respect to GWO algorithm on Maps 1 to 4 as given in Tables 7 to 10, are calculated by equations 15 and 16.
(15) 
where = 1 to 4 represents Map 1, 2, 3 or 4, corresponds to results with respect to two different number of iterations for each map. The innermost summation in equation 15 calculates the effect of costs of all the five UAVs.
For Map 1, the improvement of SSA as compared to GWO is 1.04%. Similarly for Maps 2, 3 and 4, the improvements are 0.81%, 0.94% and 2.21%. Therefore using formula 15 we get the percentage average improvement in cost of SSA as 1.25%.
(16) 
The percentage improvement in time of SSA is computed to be is 9.40%, 6.90%, 2.27% and 5.57% for Maps 1, 2, 3 and 4 respectively. The percentage average improvement in time of SSA when compared to performance of GWO is 6.035%.
5.3 Comparison with other metaheuristic algorithms
Since there is no prior information regarding the best metaheuristic, that is why various metaheuristic algorithms are utilized for solving multiple UAVs route planning problem. Different algorithms like IBA, BBO, GSO, PSO, WOA, SCA, GWO, and SSA were tried, and it was observed that SSA has the best performance among them. SSA exhibits simplicity since it requires significantly fewer parameters, which are , and . This algorithm is also highly flexible since it is applicable to various types of problems and even its architecture need not to be changed. It has a gradientfree mechanism; thus, the need to calculate derivatives of search spaces is avoided. It optimizes the problem in stochastic fashion and prevents local optima stagnation which makes it suitable for solving multimodal optimization problems.
As stated in No Free Lunch (NFL) refv , there is no particular metaheuristic which is best for handling all optimization tasks. So a situation can arise, where a particular metaheuristic might outperform all other algorithms significantly, but the same metaheuristic can severely give a bad performance for some other set of issues.
6 Conclusion and future scope
This paper proposes the use of SSA for solving multiple UAV route planning problem in a 3D environment. After investigating the performance of SSA in various experimental scenarios, it is concluded that SSA takes the least time in all the cases when compared with deterministic and other metaheuristic algorithms and finds an optimal route in both 2D and 3D environment. In some of the cases, the route obtained by SSA has slightly more cost than the recently reported data reft . However, after combining the overall effect of time and cost tradeoff, it is realized that the time required in SSA is significantly less compared to other algorithms and thus accounts for the slightly higher cost and outperforms all other algorithms. So it becomes evident that SSA has the most superior performance than all other algorithms for fast, realtime, and optimal route replanning. The simplicity, flexibility and gradientfree mechanism of the SSA make it immune to local optima stagnation and thereby improving the speed of convergence and making it suitable for the route planning and various other optimizations problems in reallife.
Future work may be focussed on extending this work by constructing an environment which better mimics a realworld scenario by introducing dynamic obstacles which, along with priority assignment associated with the goals and some hardware related constraints like minimum turning radius or maximum pitch angles should also be considered. A hybrid or a modified algorithm based on SSA for route planning and other realworld problem can be proposed to enhance the performance even further.
References
 [1] Mac T. T., et al.: ‘Heuristic approaches in robot path planning: A survey’, Robotics and Autonomous Systems, 2016, 86, pp. 13–28
 [2] Cai C., Silvia F.: ‘Informationdriven sensor path planning by approximate cell decomposition’, IEEE Transactions on Systems, Man, and Cybernetics, PartB (Cybernetics), 2009, 39(3), pp. 672–689

[3]
Barraquand J., Latombe J. C.: ‘Robot motion planning: A distributed representation approach’,
The International Journal of Robotics Research, 1991, 10(6), pp. 628–649  [4] LaValle S. M.: ‘Rapidlyexploring random trees: A new tool for path planning’, 1998
 [5] Asadi S., et al.: ‘A novel global optimal path planning and trajectory method based on adaptive dijkstraimmune approach for mobile robot.’ 2011 IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (AIM), 2011
 [6] Kala R., Shukla A., Tiwari R.: ‘Fusion of probabilistic A* algorithm and fuzzy inference system for robotic path planning.’ Artificial Intelligence Review, 2010, 33(4), pp. 307–327
 [7] Wu J.P., Peng Z. H., Chen J.: ‘3D multiconstraint route planning for UAV lowaltitude penetration based on multiagent genetic algorithm’, IFAC Proceedings Volumes, 2011, 44(1), pp. 11821–11826
 [8] Zhang B., Duan H.: ‘Predatorprey pigeoninspired optimization for UAV threedimensional path planning’, Int. Conf. in Swarm Intelligence. Springer, Cham, 2014.
 [9] Mirjalili S., Lewis A.: ‘The whale optimization algorithm’, Advances in engineering software, 2016, 95, pp. 51–67
 [10] Zhu W., Duan H.: ‘Chaotic predator–prey biogeographybased optimization approach for UCAV path planning’, Aerospace science and technology, 2014, 32(1), pp. 153–161
 [11] Li S., Sun X., Xu Y.: ‘Particle swarm optimization for route planning of unmanned aerial vehicles’, IEEE Int. Conf. on information acquisition. IEEE, 2006
 [12] Mohanty P. K., Parhi D. R.: ‘A new efficient optimal path planner for mobile robot based on Invasive Weed Optimization algorithm.’ Frontiers of Mechanical Engineering, 2014, 9(4), pp. 317–330
 [13] Pandey P., Shukla A.,Tiwari R.: ‘Threedimensional path planning for unmanned aerial vehicles using glowworm swarm optimization algorithm’, International Journal of System Assurance Engineering and Management, 2018, 9(4), pp. 836–852
 [14] Hossain M. A., Ferdous I.: ‘Autonomous robot path planning in dynamic environment using a new optimization technique inspired by bacterial foraging technique’, Robotics and Autonomous Systems, 2015, 64, pp. 137–141
 [15] Dolicanin E., et al.: ‘Unmanned combat aerial vehicle path planning by brain storm optimization algorithm’, Studies in Informatics and Control, 2018, 27(1), pp. 15–24
 [16] Zhang S., et al.: ‘Grey wolf optimizer for unmanned combat aerial vehicle path planning’, Advances in Engineering Software, 2016, 99, pp. 121–136
 [17] Phung M. D., et al.: ‘Enhanced discrete particle swarm optimization path planning for UAV visionbased surface inspection’, Automation in Construction, 2017, 81, pp. 25–33
 [18] Zhou Y., et al.: ‘A novel path planning algorithm based on plant growth mechanism’, Soft Computing, 2017, 21(2), pp. 435–445
 [19] Mirjalili S., et al.: ‘Salp Swarm Algorithm: A bioinspired optimizer for engineering design problems’, Advances in Engineering Software, 2017, 114 pp. 163–191
 [20] Dewangan R. K., Shukla A., Godfrey W. W.: ‘Three dimensional path planning using Grey wolf optimizer for UAVs’, Applied Intelligence, 2019, 49(6), pp. 2201–2217
 [21] Duan H., Ma G., Luo D. L.: ‘Optimal formation reconfiguration control of multiple UCAVs using improved particle swarm optimization’, Journal of Bionic Engineering, 2008, 5(4) pp. 340–347

[22]
Wolpert D. H., William G. M.: ‘No free lunch theorems for optimization’,
IEEE transactions on evolutionary computation
, 1997, 1(1), pp. 67–82  [23] Raja P., Pugazhenthi S.: ‘Optimal path planning of mobile robots: A review’, International journal of physical sciences, 2012, 7(9), pp. 1314–1320
 [24] Tiwari R., Jain G.,Shukla A.: ‘MVOBased Path Planning Scheme with Coordination of UAVs in 3D Environment’, Journal of Computational Science, 2019
Comments
There are no comments yet.