Genetic Algorithm Based Decentralized Task ...

Technical Paper Int’l J. of Aeronautical & Space Sci. 12(2), 163–174 (2011) DOI:10.5139/IJASS.2011.12.2.163

Genetic Algorithm Based Decentralized Task Assignment for Multiple Unmanned Aerial Vehicles in Dynamic Environments Hyunjin Choi*, Youdan Kim** and Hyounjin Kim*** School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea

Abstract Task assignments of multiple unmanned aerial vehicles (UAVs) are examined. The phrase “task assignment” comprises the decision making procedures of a UAV group. In this study, an on-line decentralized task assignment algorithm is proposed for an autonomous UAV group. The proposed method is divided into two stages: an order optimization stage and a communications and negotiation stage. A genetic algorithm and negotiation strategy based on one-to-one communication is adopted for each stage. Through the proposed algorithm, decentralized task assignments can be applied to dynamic environments in which sensing range and communication are limited. The performance of the proposed algorithm is verified by performing numerical simulations. Key words: Decentralized Task Assignment, Multiple unmanned aerial vehicles, Combinatorial Optimization, Genetic Algorithm, Negotiation

1. Introduction

et al., 2004). Mathematical programming approaches often provide solutions that are better in quality than solutions derived from meta-heuristic algorithms, but mathematical programming usually requires much more computation time than its counterpart. Conversely, the meta-heuristic approach obtains solutions quickly, however the quality of the solution may be poor. Communication among multiple UAVs within dynamic environments also presents difficulties. Off-line task assignment sufficiently allows UAVs to perform missions in stationary environments. However, on-line task assignment becomes highly necessary in changing environments. If all UAVs share information, task assignment can be regarded as centralized. The implementation of on-line task assignments to centralized systems is difficult because communication and computation loads. The centralized systems gather task information of each UAV and process the information to find an effective task assignment. Therefore, the amount of the information is enormous to the centralized systems. In actual

The operation of multiple UAVs requires decision making processes such as task planning (Murray, 2007). Task assignment has been regarded as a combinatorial optimization problem in which combinations between UAVs and various tasks must be deciphered (Papadimitriou and Steiglitz, 1982). Examples of combinatorial optimization problems include the traveling salesman problem (TSP) or the vehicle routing problem. Finding exact solutions are very difficult because combinatorial optimization problems possess non-deterministic polynomial time (NP), which results in computational complexity. Two approaches have been developed to overcome this complexity. One approach is a mathematical programming approach such as mixed integer linear programming (MILP) (Chandler et al., 2002; Richards et al., 2002; Schumacher et al., 2004). The second approach is a meta-heuristic algorithm such as the genetic algorithm (GA) (Eun and Bang, 2009; Potvin, 1996; Shima et al., 2006) and particle swarm optimization (Cruz Copyright © 2011. The Korean Society for Aeronautical and Space Science

Received 6 April, 2011, Accepted 1 June, 2011

* Graduate Student ** Professor, Corresponding author

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Copyright ⓒ The Korean Society for Aeronautical & Space Sciences

E-mail: [email protected] Tel: +82-2-880-7398 Fax: +82-2-887-2662

*** Associate Professor

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Int’l J. of Aeronautical & Space Sci. 12(2), 163–174 (2011)

2.2 Combinatorial Optimization Problem

missions, communication between UAVs is restrictive. To compensate for communication restrictions, decentralized and distributed task assignment approaches have been developed (Alighanbari and How, 2005). Decentralization schemes require specified communication structures, such as an auction scheme or negotiation scheme. Furthermore, each UAV within a dynamic environment must decide and communicate the task plan. This paper describes a decentralized task assignment algorithm for multiple UAVs within a dynamic environment. Each UAV is assumed to exchange environment information with other UAVs. The balance of the information between UAVs can be broken. Thus, a communication strategy based on negotiation (Sujit et al., 2007) is adopted to manage unbalanced situations. The strategy is divided into two stages. Stage I is the order optimization stage, and Stage II is the communications and negotiation stage. In Stage I, each UAV adjusts its task order, which in turn reduces costs by using GA. Task exchange occurs at Stage II. On-line decentralized task assignment can be performed through these stages. Each UAV is autonomously assigned proper tasks. This paper is organized as follows. In Section 2, the problem is formulated by considering the task assignment scenario, combinatorial optimization, and path planning with cost prediction. In Section 3, the decentralized task assignment algorithm is proposed, which consists of a genetic algorithm for the first stage and negotiation for the second stage. Section 4 explains the results from the numerical simulation. Finally, Section 5 concludes the study.

Multiple UAV task assignment is considered a combinatorial optimization problem. Combinatorial optimization possesses NP-hard computational complexity (Papadimitriou and Steiglitz, 1982); thus, a specified method for obtaining an optimal solution does not exist. The only known method is to search all possible cases. Typical search methods include the exact search method or the heuristic search method. A formal combinatorial optimization problem follows a certain formulation. For an Nv amount of UAVs, the UAVs set V can be defined as follows. (1) The tasks set T for Nt tasks are defined as follows. (2) Now, the performance index and constraints are formulated as

min

(3)

subject to (4)

(5)

2. Task Assignment Problem of Multiple UAVs

(6) and

2.1 Missions for multiple UAVs

(7)

UAVs are widely used for surveillance and reconnaissance missions. Wide area search and munitions (WASM) or intelligence, search and reconnaissance (ISR) are examples of such missions incorporating the multiple UAVs. This study documents the task assignment for a specified mission composed of multi-targets and multi-tasks. First, multiple UAVs and several known restricted regions were carefully evaluated. Then, task assignment was performed with respect to certain path constraints. The WASM mission was chosen that the UAVs would perform in this study. Thus, two sub-tasks for each target were designated as “Classification with Attack” and “Verification”. Thus, the total number of tasks was twice the number of targets. Accordingly, the UAV group was expected to sufficiently perform multiple tasks, as well as adjust the task order.

DOI:10.5139/IJASS.2011.12.2.163

where cv is the sequential task order of the v-th UAV with respect to the following binary decision vector xv (8) And Nt is the number of total tasks, and li is an additional function be satisfied by the target i, such as timing constraints. Complex subscripted problem formulation is used for multiple UAVs and multiple tasks. The performance index cv is a function of the sequential task order cv of the v-th UAV. In this study, a cumulative flight time of all the UAVs was taken as the performance index because the flight time is related to the endurance of the UAV and distances between the UAVs and the targets. Eq. (4) signifies that each task should

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the performance index because the flight time is related to the endurance of the UAV and distances between the UAVs and the targets. Eq. (4) signifies that each task should be assigned at once. Additional inequality conditions can be composed, as given in Eq. (6). These constraints can be adjusted according to the problem.

( xi , yi ) and ( x j , y j ) are the geometric positions of the

corresponding nodes, respectively. A visibility graph and A* algorithm are then adopted for path planning and cost prediction. The visibility graph comprises a general visibility graph algorithm (Choset, 2005) based on fixed obstacles with safety margins, as shown in Fig. 1. For computational 2.3 Path planning with cost prediction efficiency, cost look-up tables for (i) the target to target Kim.et.al Genetic Algorithm Based Decentralized Task Assignment for Multiple Unmanned Aerial Vehicles in Dynamic... The expenses incurred from each UAV must be and (ii) the UAV to target are constructed and utilized as predicted in order to assign multiple tasks to multiple shown in Fig. 2. The shortest path between nodes is A pathinequality planning algorithm is required when required in order to evaluate costs. In this study, we be assigned at once.UAVs. Additional conditions can obstacles and restricted regions exist. The cost is then adopted the A* algorithm, which provides the shortest ` be composed, as given in Eq.after (6).evaluating These constraints can beresult. Cost path that avoids the obstacle, as shown in Fig. 1. The A* predicted the path planning adjusted according tocan thechange problem. according to the task order, even if the algorithm is complete and will always find a solution if the given graph structure has the solution. The initial assigned tasks are same. and goal points in Fig. 1 denote the nodes of two targets. N N assignments In general, a UAV contains kinematic constraints on the is Therefore, the A* algorithm should be performed to all 2.3 Path∑∑ planning withradius costand prediction (5) xiv = N tturn difficult because velocity. Thus, the motion of a UAV is it v =1 i =1 combinations of two targets, and the look-up table as requires exhausting described the UAV following kinematic The expenses incurred frombyeach must 2-dimensional be predicted v shown in Fig. 2 should be pre-defined. These tables are li (χ ) ≤ bi , ∀Timodel: ∈T (6) computational Fig. 1. Visibility graph. whenever the costs are changed and expanded in order to assign multiple tasks to multiple UAVs. A path efforts. In order to updated and ⎛ x = V cosψ ⎞ or new graph. tasks are found. The heuristic term of the A* Fig. the 1. Visibility reduce planning algorithm is required when obstacles and restricted ⎜ ⎟ =T V× sin (7) xiv ∈ {0,1} , ∀ (Ti , V⎜vy) ∈ Uψ ⎟ algorithmisis separated set as the Euclidean complexity, (9) path planning from taskdistance from the node regions exist. vThe cost is predicted after evaluating the ⎜ψthen ⎟ to goal node, and convex obstacle regions are only u order ⎝ = ωmax ⎠ task of the v-th UAV assignment. The distance between node i and node j where χ is the sequential v

t

path planning result. Cost can change according tov the istaskapproximated through a Euclidean distance the control input isvector bounded with respect to thewhere following binary decision x by u ≤ 1 . Velocity ` the turn radius R . Therefore, the order, even if the assigned tasks are same. expression and min T v v v v is assumed to be a constant, and the minimum turn V ⎡ ⎤ (8) x  ⎢⎣ x1 a , x2UAV ,..., xN contains flight In general, kinematic constraints on time between node i and node j is approximated ⎥⎦ radius Rmin is: as follows. the turn velocity.of Thus, the motion a UAV is N t is and the number total tasks, and li isof an Andradius V additional function be satisfied by the target , such as i ( xi − x j ) 2 + ( yi − y j ) 2 described by the following kinematic model: (10) Rmin 2-dimensional = t

t (ni , n j ) ≈ considered when obstacles exist. (11) ωmax subscripted problem timing constraints. Complex V formulation is used for multiple UAVs and multiple Figure 3 shows the path planning function. If a new For this case, the distance between nodes depends2πonR min tasks. The performance index c v is a function of the target is added, table (i) will be updated. Table (ii) is ( , ) t n n ≈ (12) the heading angle of the UAV. It is also to i i (9)difficult V sequential task order UAV.described In this study, χ v of the updated whenever the UAV is moving. According to the applying the v-th model by Eq. (9) to task node,2. nLook-up j-th node, a cumulative flight time of all the UAVs was taken as where ni is the i -th Fig. of (i) and target to target and (ii) j is the tables task plan obtained byvehicle the to task assignment, the waypoint unmanned aerial target. the performance index because the flight time is related L  ook-up tables of (i) target to target unmanned aerial are the geometric positions of the and (ii)and ( xi , yi ) and Fig. (set x j , 2. y of ) j UAV can be obtained. Guidance control is to the endurance of the UAV and distances between the vehicle to target. where the control input is bounded by |u|≤1. Velocity V is nodes, respectively. UAVs and the targets. Eq. (4) signifies that each task correspondingperformed according to the waypoint set. A visibility graph and A* algorithm are then adopted should assigned atand once. Additional inequality assumed to bebea constant, the minimum turn radius Rmin conditions can be composed, as given in Eq. (6). These for path planning and cost prediction. The visibility is: graph comprisesProcedure a general visibility graph algorithm constraints can be adjusted according to the problem. PathPlanning( ) (Choset, 2005) Ifbased on fixed obstacles with safety (new target = 1) margins, as shown in Fig. 1. For computational (10) 2.3 Path planning with cost prediction [V, E] = Visibility(targets) efficiency, cost look-up tables for (i) the target to target = Update_table_i() toCost_table_i target are constructed and utilized as The expenses incurred from each UAV must be and (ii) the UAVCost_table_ii= Update_table_ii() shown in Fig. 2. The shortest path between nodes is For predicted this case,inthe distance between order to assign multiple nodes tasks todepends multiple on the [Way_set] = A_star(Task_plan) in order to evaluate costs. In this study, we UAVs. A of path is required when required heading angle theplanning UAV. It algorithm is also difficult to applying the the A* Fig. adopted algorithm, which provides the shortest 3. Path planning algorithm. obstacles and restricted regions exist. The cost is then path that avoids obstacle, as shown in Fig. 1. The A* Fig.the 3. Path planning algorithm. modelpredicted described Eq. (9) the to path taskplanning assignments is difficult afterby evaluating result. Cost is complete and will always find a solution if can itchange according to the task order, even if efforts. the algorithm because requires exhausting computational Ingiven graph structure has the solution. The initial the assigned tasks are same. order to reduce the complexity, path planning is separated and goal points in Fig.Decentralized 1 denote the nodes of two targets. Task Assignment In general, a UAV contains kinematic constraints on the Therefore, the3. A* algorithm should be performed to all from task assignment. The distance between node i and node turn radius and velocity. Thus, the motion of a UAV is GAand the look-up table as combinations Using of two targets, described by through the following 2-dimensional kinematic is required in order evaluate j is approximated a Euclidean distance expression shown in Fig.nodes 2 should be pre-defined. Thesetotables are costs. In this study, we model: updated and adopted expanded the whenever the costs are changed A* algorithm, which provides the shortest path and the turn radius Rmin. Therefore, the flight time between In general, multiple UAVs will perform its mission ⎛ x = V cosψ ⎞ or new tasksthat are found. The heuristic termThe of the A* avoids the obstacle. A* algorithm is complete and ⎜  node j is⎟approximated as follows. node i and given the prior task assignment. However, UAVs require (9) algorithm is set as the Euclidean distance from the node ⎜ y = V sinψ ⎟ will always find a solution if the given graph structure has ⎜ψ = ω u ⎟ online task assignment for changing environments to goal node, and convex obstacle regions are only max ⎝ ⎠

the solution. initialmust and goal points Fig. 1 denote the because theTheUAV adjust its inassigned tasks. Possible online task assignment schemes include the nodes of two targets. Therefore, the A* algorithm should be V is assumed to be a constant, and the minimum turn decentralized task assignment and the performed to all combinations of two scheme targets, and the lookradius Rmin is: 2πRmin distributed task assignment scheme. This study (12) t(ni, nj)≈ up table as shown in Fig. 2 should be pre-defined. These VV evaluated a fully decentralized task assignment (10) Rmin = tables are updated and expanded whenever the costs are ωmax algorithm. the i-th node, nbetween j-th node, where changed or new tasks are found. The heuristic term of the A* i is case, j is thenodes For nthis the distance dependsand on (xi, yi) For decentralized task assignments, communication and (xjthe , yj)heading are theangle geometric positions corresponding of the UAV. It is of alsothe difficult to algorithm is set as the Euclidean distance from the node to between UAVs should be dealt with. A UAV group the model described by Eq. (9) to task nodes,applying respectively. goal node,ofaand convex obstacle only considered Fig. 2. Look-up tables (i) specified target to target and (ii)regions are requires communication topology; thus, unmanned aerial vehicle to target. exist. A visibility graph and A* algorithm are then adopted when obstacles methods for solving the conventional combinatorial for path planning and cost prediction. The visibility graph Figure 3 shows the pathare planning If a new optimization problem not function. appropriate for target the comprises a general visibility graph algorithm (Choset, 2005) assignment. The Table decentralized task isdecentralized added, tabletask (i) will be updated. (ii) is updated assignment GA According in order to relieve based on fixed obstacles with safety margins, as shown in Fig. whenever theadopts UAV is the moving. to the task the plan computational loadassignment, and to adjust according to the 1. For computational efficiency, cost look-up tables for (i) obtained by the task thetasks waypoint set of UAV can communication between UAVs. GA is a meta-heuristic the target to target and (ii) the UAV to target are constructed be obtained. Guidance and control is performed according algorithm that solves the optimization problem. and utilized as shown in Fig. 2. The shortest path between to the waypoint set. where the control input is bounded by u ≤ 1 . Velocity

stage, each UAV adjus stage is similar to th regarded that each U optimization stage. Th Each UAV has its experiences improvem operators.

3.1.1 Modified sol The solution set candidates known as solution set is express candidate in the set, Figure 4 shows the composed of the seque is represented as T j , k ,

represents a target an represents the sub-task

(11)

Communication topology is a one-to-one communication based on negotiation for the fully decentralized task assignment. It is also assumed that http://ijass.org 165 there is no base station in this study. Strategy consists of two stages, the order optimization stage and the communications and negotiation stage. Through these two stages, the UAV is able to adjust its task order and exchange the assigned tasks with other UAVs.

Fig. 4. Solution candid

According to combination number given by Shima et al. ( ( NT N k )! NT Nk Nv ( N k !) NT

Each UAV should dea optimization stage. F

targets and N k tasks combinations will be g ( NT N k )! ( N k !) NT

Therefore, the numb reduced by decentrali could possibly viola assignment. Each solution set co the cost of each ca evolves its fitness th

solution set is expressed as C , and Cn is n-th solution candidate in the set, which is similar to χ in Eq. (3). Figure 4 shows the solution candidates, which are composed of the sequential order of the tasks. Each task is represented as T j , k , where the first subscript j ∈ ` NT

Cost_table_i = Update_table_i() Cost_table_ii= Update_table_ii() [Way_set] = A_star(Task_plan) Fig. 3. Path planning algorithm.

3. Decentralized Using GA

Task

Assignment

Int’l J. of Aeronautical & Space Sci. 12(2), 163–174 (2011)

represents a target and the second subscript k ∈ ` Nk represents the sub-task of the target.

In general, multiple UAVs will perform its mission 3. Decentralized Task Assignment Using GA given the prior task assignment. However, UAVs require online task assignment for changing environments

In general, multiple UAVs will giventasks. because the UAV mustperform adjustitsitsmission assigned the priorPossible task assignment. However, UAVs require on-line task the online task assignment schemes include decentralized assignment scheme and the assignment for changing task environments because the UAV must 4. Solution candidates of the problem. distributed task Possible assignment This study Fig. 4.Fig. Solution candidates of the problem. adjust its assigned tasks. on-linescheme. task assignment evaluated a fully decentralized task assignment schemes include the decentralized task assignment scheme According to the representations, feasible and thealgorithm. distributed task assignment scheme. This study For decentralized task assignments, communication combination number of the solution for all UAVs is evaluated a fully decentralized task assignment algorithm. (13) between UAVs should be dealt with. A UAV group given by Shima et al. (2006). For decentralized task assignments, communication requires a specified communication topology; thus, ( NT N k )! NT Nk betweenmethods UAVs should dealt with. A UAV group requires a (13) N v deal with its own task set at the order for be solving the conventional combinatorial NTshould Each( NUAV specified communication topology; for solving k !) optimization problem arethus, notmethods appropriate for the optimization stage. For example, if a UAV has NT targets and the conventional combinatorial optimization problem are task decentralized task assignment. The decentralized Each UAV should deal with its own task set at the order Nk tasks for each target, the number of combinations will be not appropriate for the decentralized assignment. The the assignment adopts the GA task in order to relieve optimization stage. For example, if a UAV has NT given by computational load and adopts to adjust according decentralized task assignment thetasks GA in order toto the targets and N k tasks for each target, the number of communication GAtasks is aaccording meta-heuristic relieve the computationalbetween load andUAVs. to adjust combinations will be given by (14) that between solves the problem. to the algorithm communication UAVs.optimization GA is a metaCommunication topology is a one-to-one N N ( )! T k heuristic algorithm that solves the optimization problem. (14) NT communication based on negotiation for the fully N ( !) Therefore, the number of feasible solutions can be k Communication topology is a one-to-one communication decentralized task assignment. It is also assumed that reduced by decentralization. decentralization based on for the fullystudy. decentralized task Therefore, the number of However, feasible solutions can be therenegotiation is no base station in this could possibly violate the optimality of the task assignment. reduced by decentralization. However, decentralization assignment. It is also assumed that there is no base station Strategy consists of two stages, the order optimization couldsolution possibly optimality of respect the task set violate containsthe a fitness set with to in this study. stage and the communications and negotiation stage. Each assignment. the cost of each candidate. The solution candidate evolves Strategy consists of two two stages, stages, the the UAV orderisoptimization Through these able to adjust its Eachthrough solutionthe setgenetic contains a fitness To setimplement with respect operators. theto task the ordercommunications and exchange the tasks stage. with other its fitness stage and andassigned negotiation the cost of each candidate. The solution candidate on-line process, a time extended cost function is defined as ThroughUAVs. these two stages, the UAV is able to adjust its task evolves its fitness through the genetic operators. To follows. order and exchange the assigned tasks with other UAVs.

3.1 Order optimization stage

3.1 Order optimization stage Each UAV follows a task order arrangement Each procedure UAV follows a task during theorder orderarrangement optimizationprocedure stage. In this during the order optimization stage. In this stage, each UAV adjusts the order of its own tasks. This stage is similar to the TSP, and therefore it can be regarded that each UAV solves the TSP at the order optimization stage. The GA is adopted during this stage. Each UAV has its own solution set, and each set experiences improvements due to the GA’s genetic operators.

where t is the elapsed time of the UAV, Cn is the solution of the set, and cp is the cost prediction function according to the Cn. Then, the fitness of each solution candidate is formulated as follows (16)

where cw is the cost of the worst case, cb is the cost of the best case, cn is the cost of n-th candidate in the set, and ks is selection pressure representing the ratio of the best case to the worst case. In this study, ks is set as 3.

3.1.1 Modified solution set The solution set is a set of feasible solution candidates known as a chromosome in the GA. The solution set is expressed as C, and Cn is n-th solution candidate in the set, which is similar to C in Eq. (3). Figure 4 shows the solution candidates, which are composed of the sequential order of the tasks. Each task is represented as Tj, k, where the first subscript j∈NN represents a target and the second subscript k∈NN represents the sub-task of the target. According to the representations, feasible combination number of the solution for all UAVs is given by Shima et al. (2006).

3.1.2 Genetic operators The genetic operators consist of selection, crossover, mutation, and substitution operators. To generate a new solution candidate, these four operators are executed. A proportionate selection with roulette wheel method is adopted as a selection operator. Two solutions are randomly chosen according to the fitness, as shown in Fig. 5. These selected solutions are pruned and attached to each other

T

k

DOI:10.5139/IJASS.2011.12.2.163

implement the on-line process, a time extended cost function is defined as follows. (15) (15) cn (t )  t + c p (Cn )

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The following assumptions were made for the process randomly chosen according the fitness, as shown in of communication between UAVs. to each other by the crossovertooperator as shown in Fig. Fig. 5. These solutionsisare prunedfor andthe attached 6. Thus, the selected order crossover adopted array The following assumptions were made for the process to each other by the crossover operator as shown in Fig. rearrangement of the solution candidate. Mutation is of Assumption communication 1. between There areUAVs. no base stations, and there 6. Thus, by the switching order crossover is randomly adopted for array solutions. InIn this executed the order as the shown in exists solutions. this stage, stage, the the terminated terminated tasks and and the the no centralized computers in the UAVtasks groups. rearrangement of the solution candidate. Mutation is newly added tasks are required for synchronization. And, Fig. 7. It is used for the local perturbation of the newly added tasks are required for synchronization. And, Assumption 1. are no base stations, and there 2. There Each communication is restricted to executed by switching the order randomly Through as shownthe in one-to-one the sending cost information are solution. Finally, substitution is performed. the tasks tasks sending reduced reduced cost information are only only exists no centralized computers inon the UAV groups. communication based the negotiation. Fig. 7. It is used for the local perturbation of the required. recursion of these procedures, theBased task Decentralized order would be required. Assumption 2. communication is restricted to Kim.et.al Genetic Algorithm Task Assignment for Multiple Unmanned Aerial Vehicles in Dynamic... 3. Each Tasks are only exchanged between solution. Finally, performed.ofThrough rearranged. Figuresubstitution 8 shows theisprocedures the GA.the one-to-one communication based on the negotiation. two UAVs based on the communication. recursion of these procedures, the task order would be Assumption 4. 3. Communication Tasks are only limit exchanged due to between a range rearranged. Figure 8 shows the procedures of the GA. twoProcedure UAVs based on the communication. Negotiation( ) limit is only considered. Procedure Negotiation( ) Assumption 4. CommunicationNewTasks) limit due to a range Synchronize(TerminatedTasks, Synchronize(TerminatedTasks, NewTasks) Select aatask for limit is communication only considered. The strategy is described as follows Select task forsending sending if if(send mode) (send mode) based on the assumptions above. Send aatask Send task The communication strategy is described as follows Receive the result Receive the result based on the assumptions above. tasks as well as the 1. Synchronize the terminated IfIf(UAV v v22receive the task) (UAV receive the task) additional tasks, and take into account the changes in Update the solution set Update the solution set 1. Synchronize the terminated tasks as well as the theiftask plan. mode) if(receive (receive mode) Fig. 5. Selection operator. additional tasks, and take into account changes in 2. Receive (UAV v1the ) Choose and send a task tothe UAV v 2 with Receive thetask task Fig. 5. Selection operator. the task plan. v1 evaluate the task the reduced cost cm of UAV v1 . evaluate the+ task Fig. 5. Selection operator. 2. if(UAV and send a task to UAV v 2 with v1v v 2v 2 v1 1+)+Choose ( + c c if ( +mcvm2+)+Evaluate 3. (UAV cp p ≤ ≤00) ) the received task and compute v1 the reduced cost task +cm v 2of UAV v1 . accept +cP of UAV v 2 the increased cost acceptthe the task 3. else (UAV ) Evaluate the received task and compute v 2 else 4. Ifreject the sum of thev 2 reduced cost of UAV v1 and the the task reject the +cP of UAV v 2 the increased costtask is less than zero, then UAV increased of UAV v 2algorithm. Fig. 9.9. cost Communication UAV: unmanned aerial Fig. 6. Crossover operator. Fig. Communication algorithm. UAV: unmanned aerial 4. If the sum of the reduced cost of UAV v 1 and the accepts the task. Otherwise, UAV rejects the vFig. 2vehicle. v 2 9. Communication algorithm. UAV: unmanned aerial vehicle. vehicle. increased cost of UAV v 2 is less than zero, then UAV task. Fig. 6. Crossover operator. Fig. 6. Crossover operator. task. Otherwise, UAV to rejects v 25.accepts v 2UAV UAV v 2the executes the same process v1 . the task. 5. UAV9vshows the same process to UAV v1 . 2 executes Figure the procedure of the communication f the UAV, Cn is the algorithm, and Fig. 10 shows the procedures for GA the prediction UAV, Cn function is the cost Figure 9 shows the procedure of the communication ost prediction function algorithm, and Fig. 10 shows the procedures for GA solution candidate is Fig. 7. Mutation operator. olution candidate is Fig. 7. Mutation operator. Fig. 7. Mutation operator. − cb (t )) , ks > 1 (16) Procedure GA( ) (t )) c−b 1) , ks > 1 (16) Select( ( C1 , C2 ) =GA( Procedure ) C) 1) t case, cb is the cost of Fig. Fig. 10. 10. Communication Communication procedures. procedures. UAV: UAV: unmanned unmanned , C ) = Select( ( CC CC1) , C2 ) = Crossover( 1c 2 aerial vehicle. Fig. 10. Communication procedures. UAV: unmanned aerial vehicle. case,candidate cb is theincost aerial vehicle. the of set, -th CcCm= Crossover( = Mutation(CC1 c, )C2 ) candidate theof set, hesenting the in ratio the Cmf m= = Mutation( Fitness(C Ccm) ) IfIfall allUAVs UAVsare areconnected, connected,tasks taskswill willbebedistributed distributed senting study,the ks ratio is setofasthe 3. without duplication. However, rules are communication between UAVs. f ifm ( =f mFitness( without duplication. However, rules arerequired requiredfor forthe the >tit,UB i ,UB 2 tasks per target 2 tasks per target 3 unknown targets unknown targets 100} 3 unknown targets m) function was 3tuned by adjusting the number of generations Forwardmutation() mutation() Forward (sensing range (sensing range (sensing range 6 known targets process GA, communication, ififττi i