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        Dynamic grouping of heterogeneous agents for exploration and strike missions?

        2022-02-18 13:48:20ChenCHENXiaochenWUJieCHENPanosPARDALOSShuxinDING

        Chen CHEN, Xiaochen WU?, Jie CHEN,2, Panos M. PARDALOS?, Shuxin DING

        1School of Automation, Beijing Institute of Technology, Beijing 100081, China

        2Department of Control Science and Engineering, Tongji University, Shanghai 200092, China

        3Center for Applied Optimization, Department of Industrial and Systems Engineering,University of Florida, Gainesville, FL 32611, USA

        4Signal and Communication Research Institute, China Academy of Railway Sciences Corporation Limited,Beijing 100081, China

        Abstract: The ever-changing environment and complex combat missions create new demands for the formation of mission groups of unmanned combat agents. This study aims to address the problem of dynamic construction of mission groups under new requirements. Agents are heterogeneous,and a group formation method must dynamically form new groups in circumstances where missions are constantly being explored. In our method, a group formation strategy that combines heuristic rules and response threshold models is proposed to dynamically adjust the members of the mission group and adapt to the needs of new missions. The degree of matching between the mission requirements and the group’s capabilities, and the communication cost of group formation are used as indicators to evaluate the quality of the group. The response threshold method and the ant colony algorithm are selected as the comparison algorithms in the simulations. The results show that the grouping scheme obtained by the proposed method is superior to those of the comparison methods.

        Key words: Multi-agent; Dynamic missions; Group formation; Heuristic rule; Networking overhead

        1 Introduction

        Multi-agent systems(MASs)are widely used to perform complex missions in different fields (Merabet et al., 2014), such as fire control and rescue missions or military detection and strike missions.The first problem to be solved in those missions is how to organize multiple agents to complete a mission, that is, how to assign the overall missions to each agent and ensure that the agents effectively cooperate. Group formation has a great influence on the ultimate performance of the whole MAS.

        When agents have different abilities or play different roles,it is particularly important to form their groups according to the needs of the mission. The problem of finding a reasonable partition of agents so that some utility functions are maximized is known to be NP-hard concerning different utility functions(Gerkey and Matari?, 2004; Vig and Adams, 2006).In the field of artificial intelligence and cooperative systems, especially in distributed collaboration, experts and scholars have done a lot of research on the organizational structure and synergy of MAS. They have focused on topics such as emergent rule theory(Murphey and Pardalos,2002),game theory(Pardalos et al., 2008), cooperative autonomous systems(Butenko et al., 2003; Kim Y et al., 2008; Khoshnoud et al., 2019), and the hierarchical cooperation model (Butenko et al.,2003;Hirsch et al., 2009).

        Many scholars have studied the self-organization or dynamic grouping of agents. Research results in the context of confrontation are rich(Ducatelle et al.,2010;Singh et al., 2010;Liu et al., 2013;Necsulescu and Schilling,2015;Orfanus et al.,2016;Skorobogatov et al.,2020).

        In terms of solutions, in addition to the classic models and the methods described above, some heuristic rules have been used in the formation of agent groups and their mission allocation. Ramchurn et al. (2010) and Padmanabhan and Suresh(2015) focused on solving the mission group formation problem by heuristic methods;Oh et al.(2018),Nejad and Kashan(2019),and Guo et al.(2020)designed heuristic methods to deal with the mission allocation problem.

        However,as the size of the agent community expands, the versatility of some heuristic methods becomes limited and they no longer apply to more complex mission environments. In this case,people turn to the individual behavior of the natural community and its emerging group behavior, and apply it to the agent system so that the individuals can spontaneously form groups to perform complex missions according to dynamic mission information. In this process, agents demonstrate greater self-organization,collaboration, and adaptability to the environment.For example, in Yang et al. (2014) and Khan et al.(2019), a special ant colony algorithm was used to solve the problem of constructing an intelligent dynamic alliance. In addition to the ant colony optimization(ACO),other bio-population-based heuristics have been used in group formation problems. In George et al. (2010) and Manathara et al. (2011),the particle swarm algorithm and some new heuristic strategies were used to solve the problem of group formation.

        As the scale of the task group formation problem continues to change, researchers have tried different methods to solve it. These existing methods have relatively good results when dealing with the dynamic grouping of a single type of agents. However, with the expanded number of agent types, the existing methods can no longer perform the task of group formation based on the mission requirement for heterogeneous agents. Therefore,in this study,different from the existing results, the matching of heterogeneous agents’capabilities with mission requirements and new evaluation criteria are specifically considered in the grouping process.

        This study aims to solve the mission group formation problem of heterogeneous agents in the battlefield environment. Each mission has different priority and capability requirements, and different agents must interact cooperatively. The ability requirement represents the minimum ability required to destroy the target. The purpose of the mission is to find the targets and eliminate them as soon as possible.

        Fig.1 briefly describes the process of collaborative mission execution by heterogeneous agents. In the left module, there are many different types of agents that need to form mission groups to perform missions 1 and 2. When new missions(missions 3 and 4) are discovered, agents must adjust the grouping pattern according to the new mission status, form a new topology structure, and adapt to the new mission requirements(as shown in the right-hand side of Fig.1). An algorithm needs to be designed to achieve dynamic grouping. In the algorithm, heuristic rules and the response threshold method are combined to form a hybrid grouping strategy, which ensures the realization of the above process.

        Fig. 1Formation and reconstruction of mission groups

        When agents perform missions in the group form, a mobile network (or some kind of connections) will be constructed to maintain information exchange among members in the group. However,excessive traffic will increase the network burden and the probability of the agent being detected by the enemy. To avoid the undesirable consequences caused by too much information transmission, unnecessary communication should be reduced when designing the heuristic rules for grouping.

        The main contributions of this study can be summarized as follows: first, a model is established to describe the attributes of the mission and the agent, and the grouping scheme evaluation method is given; second, a hybrid algorithm combining heuristic rules and the improved response threshold method is designed to solve the dynamic agent grouping problem proposed in this study.

        2 Problem formulation

        Our research focuses on the dynamic group formation problem, which involves heterogeneous agents with a mission to attack some enemy targets.In the actual grouping process, a unified model is needed to accurately describe the status of the mission and the behavior and capabilities of the agents.

        The model contains a mission areaG, which is a rectangular, two-dimensional plane. In areaG,there areqenemy targets (including stationary and moving targets) to be eliminated, and their initial positions are completely random. Each target is treated as a separate mission. Also, we deploypfreely movable agents in the area to detect and strike targets. Because each mission requires agents with various capabilities to collaborate, different types of agents must be grouped to accomplish the mission.When the mission situation changes based on the original grouping,the agents will reform their group according to the new mission list. The agents need to eliminate as many enemy targets as possible.

        2.1 Agents

        1. Definitions

        First, we give the following definitions of the agents used in this study:

        (1) Each agent is a carrier of resource capabilities and a mission platform with certain autonomous capabilities;

        (2) There are different types of agents with different capabilities;

        (3)The number of agents is limited and it is not possible to perform all missions at the same time;

        (4)Networking overhead will be generated when agents form new mission groups.

        2. Types and topology

        This study adopts two types of agents: detection agent and attack agent. The detection agents mainly conduct large-scale reconnaissance operations, discover new targets, and provide real-time updates of mission intelligence. The updated data serve as the basis for the current attack agent grouping. As the name implies,the attack agents mainly attack the enemy targets. The dynamic grouping method of these agents based on mission intelligence is our main research content. The attack agents can be divided into several types, because they have different capabilities to tackle various types of targets. Thus, we have to design a rational grouping method based on different types of agents to improve the efficiency of mission execution.

        In the process of forming a mission group,a mobile network topology is built among agents and used for information exchange between individuals. The hierarchical network concept is introduced into the system,and we achieve a three-dimensional topology through hierarchical modeling.

        All the agents involved in the mission form a hierarchical topology structure as shown in Fig. 2,which consists of two layers. The lower layer is the mission execution layer and contains mission groups composed of attack agents; the upper layer is the coordination layer, which contains only detection agents. In actual combat, a communication link is formed between the detection agent and the leader of the mission group. In addition to exploring the mission location and posting mission information,the detection agents need to coordinate among the mission groups when the mission is released. If each mission group is regarded as a small network,the detection agent can be understood as a mobile gateway node that is used for communication and coordination between networks.

        3. Capabilities

        The agents’ capabilities are described by a simple slot model, which has been used by researchers in the area of resource collection (Moritz and Middendorf, 2015). In this model, a slot is the smallest relevant unit of the agents’capabilities.

        Fig. 2 Hierarchical topology

        As Fig. 3 shows, slots of different colors represent the different agent capabilities. The number of slot types represents the number of capabilities the agent has. Agents have different slots, which means that their ability levels are different. There are three capability slots in Fig. 3. This indicates that the agent has three different capabilities. We usepijto represent the value of thejthcapability of agenti.Whenpij> 0, it means that agentihas thejthcapability. In the problem we study, the numbers of agent capability slots are different, and the value of each capability is also different.

        Fig. 3 Slot model

        4. Constraints

        Ignoring the impact of the environment, we assume that all agents can reach any location in the mission area. Thus, constraints on path feasibility are not considered in this study. In addition,regarding the characteristics of the agent itself,we consider two types of constraints in our research.

        Each agent has an energy storage device. When the energy in the device is exhausted,the agent cannot move or participate in any mission group, and it will take some time to replenish the energy. We choose to use the maximum distance,Lmax,that the agent could move to indicate the maximum capacity of the battery or fuel tank. LetEimax=Limax;Eimaxrepresents the maximum energy of agenti.Thus, the energy currently available on agentican be expressed as

        whereLimindicates the mileage of agentiandfchrepresents the number of charges.

        In the actual confrontation process,the amount of ammunition carried by the agent is limited, so in addition to energy constraints, ammunition constraints should be considered. We translate the ammunition constraints into the number of missions in which the agent could participate. Let amiindicate the remaining number of times that agentican participate in the mission. When

        2.2 Mission

        The characteristics of the agent and the mission scenario have been introduced above. Next, some attributes of the mission are introduced.

        In the combat environment of this study, there are multiple missions at the same time, and each mission is independent. Due to the limited capabilities of the agents, when attacking enemy targets,they need to form groups to complete the mission.Because our study focuses on the dynamic grouping mechanism of heterogeneous agents, we ignore the impact of the environment on their movement.

        To improve the model’s versatility, the mission settings need to be as close as possible to the actual situation. During the simulation, the positions of some targets are unknown and need to be obtained through exploration. The continuous updating of the mission list ensures the dynamic nature of the grouping process. In addition,some targets are removable,which improves the authenticity of the model. Moreover,the mission should be completed within a specified time, and when the time limit is exceeded, the mission is considered to have failed.

        1. Mission characteristics

        (1)Mission duration

        The time elapsed from the generation of the mission to the announcement of the failure of the mission is denoted bytd.

        (2)Mission requirements for capabilities

        Here, the capability requirement vector is used to represent a mission for each capability requirement. For a specific mission, the capability requirements match the types of capabilities that all intelligent agents have; that is, the dimension of the vector is the same as the number of the agent’s slot types. The vector of capability requirements can be expressed as

        wheredkm(m= 1,2,...,n) represents the demand for themthcapability of missionk, andnis the number of types of capability.

        (3)Mission time

        The mission timetckrepresents the time required to complete missionk. The sum of each ability requirement of the mission is positively correlated with the number of agents dispatched to perform this mission;thus,we fix the value oftck,which does not change with the needs of the mission.

        Fig. 4 shows the basic mission flow. When the missions are not completed,the mission group needs to be reconstructed according to the new mission requirements until all missions are completed.

        Fig. 4 Basic mission flow

        2. Constraints

        We assume that there is a missionkand a corresponding mission groupi. Then the relationship betweenkandimeets the following condition:

        wherejrepresents a certain ability and Cap(pij)represents the sum of abilityjin groupi. This condition ensures that the mission can be executed smoothly.

        2.3 The proposed model

        1. Objective 1: mission reward(R(M))

        In the process of forming a group,the sum of the capabilities of the members in the group is required to be greater than the mission’s demand for capabilities. According to the matching idea, certain principles should be satisfied for each mission group: the higher the degree of matching between the mission group’s capabilities and the needs of the mission,the greater the benefit of mission completion (Shehory and Kraus, 1998). This is because, in ensuring the completion of the mission,if a mission group is used whose ability far exceeds the mission demand, the agent’s capability resources will be wasted and the overall profit of the mission will be reduced. We measure mission rewardR(M)using the degree of ability matching. According to the above ideas,we give the numerical calculation method ofR(M)based on the matching degree:

        whereR(M) represents the overall mission reward,Pkrepresents the priority of missionk,rMkrepresents the reward of missionkbased on the matching degree, and the calculation method ofrMkis as follows:

        wherebkrepresents the ideal reward of missionk(that is, the benefits generated when the sum of the capabilities of the members of the group is exactly the same as the mission’s capability needs),and it is measured by the sum of the capability requirements of missionk. Parameterγis a weight coefficient.

        According to the relationship between the reward and the matching degree mentioned above,when the capabilities cannot be fully matched, the negative reward nekgenerated by the redundant part of the capabilities needs to be subtracted frombk.Eq. (8)is used to calculate the negative reward nek,

        whereOkrepresents the redundant part of the capability, and can be calculated by

        In addition to mission reward, we have to calculate the cost of the missions.F(M)represents the fuel cost generated during the movement of all agents and is described by the average moving distance of the agents. It can be calculated by

        whereLimindicates the mileage of agentiandpis the number of agents.

        3. Objective 3: networking overhead(E(M))

        In the process of mission execution, periodic data interaction between individuals must be guaranteed by each mission group. In the grouping algorithm,we can influence only the communication data that are generated and the energy consumed during the networking process. We use energy consumptionE(M) as a parameter to measure the communication overhead and its impact when networking. The larger the value ofE(M), the greater the communication volume and energy consumed during networking, and the greater the cost of the mission.

        To ensure stable data interaction during the mission, we choose a fixed distribution type, time division multiple access(TDMA), as the method for nodes to access the network. We do not study the access protocol or data structure; we only calculate the energy that is consumed in sending application data when the node uses the TDMA protocol to access the network. The following formula gives the calculation method:

        wherentis a parameter related to the transmission environment.

        Eq.(11)was given by Cui et al.(2004)and Jiang et al. (2010), and it is used to calculate the energy consumption of nodes’ transmitting data.Eipbitis the energy consumed by nodeito the leader per 1-bit of data transmission;Nsiis the hop number from nodeito the group leader;PctandPcrare the transmitting circuit power and receiving circuit power,respectively;ζrepresents modulation parameter;Rsis the bit rate;under the condition of point-to-point transmission,Tcan be regarded as a constant, and it depends on the modulation form, circuit compensation, antenna power gain, and other parameters;dtjrepresents the transmission distance from nodejto the next node in the transmission link.

        Under the conditions in this study,except fordtjandNsi, the remaining parameters can be regarded as constants,and the values have been given by Jiang et al.(2010).

        For all missions, the total energy consumption during the networking process is

        whereNeis the number of times that all nodes are connected to the network,andSirepresents the total amount of application data sent by nodei.

        Based on the above description, the model is formulated as follows:

        s.t. conditions (2)and(4)are satisfied.

        We give three objectives in terms of mission reward and mission costs. The decision variables include the sum of the capabilities of the mission group Cap(p), the transmission distancedt, the number of nodes applying to the networkNe, and the agent’s mileage{Lim}. The values of the above decision variables depend only on the grouping scheme.

        3 Dynamic group formation method based on the utility function and heuristic rules

        In the previous grouping method, the mission team was immediately disbanded after completing the mission, and then the decentralized agents formed a new group according to the mission requirements.

        Unlike previous research, we introduce a “dynamic adjustment” mechanism in the mission group reconstruction strategy. Once a mission is completed, team members will be adjusted to meet the new mission needs by combining available mission groups, absorbing new agents, group splitting, and other operations, instead of being disbanded immediately. Individuals in the group share member and mission information,and each group moves and performs the mission as a whole.

        3.1 Utility function

        wheretrepresents the current moment,andtfkis the moment when missionkwas discovered. The greater the value of confik, the higher the probability that the agent believes that missionkcan be completed.

        Based on the above three factors, the utility function of agentifor missionkcan be expressed as

        wherenjrepresents the number of agents in groupj.

        3.2 Heuristic rules for dynamic group formation

        Next,a networking-overhead-basedconstructive heuristic (NCH) self-organizing rule is introduced.When designing the heuristic rules, we consider the network overhead and try to maintain the original group staffing during the formation of the new mission group, to reduce the communication overhead when networking.

        We use mlist to save the missions that need to be executed currently,that is, a list of missions.|mlist|represents the number of missions in mlist.

        Step 1: Sort current missions in mlist based on urgency.

        Step 2(for 1

        Step 3 (for 1

        Step 4 (for 1

        Step 5: Sort the groups in oglist according to the value of ˉujkfrom high to low, and save the new group order in glist. The number of groups in glist is represented by|glist|,|glist|=|oglist|.

        Step 6: Let groupkbe the group used to perform missionk. Based on the needs of missionk,we will select the appropriate members in glist to join groupkto perform missionk. The purpose of this step is to select multiple individuals that are most suitable for performing missionkto form a group while maintaining the original mission group as much as possible.

        For 1

        (a)If the relationship between the capabilities of groupjand missionkdoes not satisfy condition(4),it means that groupjdoes not meet the current needsDk. Let all members of groupjjoin groupk.The difference between the capabilities of groupjand missionkis calculated as the newDk. Then return to step 6,j=j+1.

        (b) Conversely, if condition (4) is satisfied, it means that groupjmeets the current needs of missionk. At this time, if all the members of groupjjoin groupk, some individual capabilities may be wasted. Therefore,we need to combine the improved response threshold method to select suitable individuals from groupjto join groupkand avoid wasting agents. The improved threshold model comes from Kim MH et al. (2014):

        where Cap(puv)is thevthcapability of agentu,and its type is the same as the type of capability most needed by missionk. If max{Dk}=dkn,thenv=nand Cap(puv)=Cap(pun).

        We let the agent choose missionkwith probabilityP(Suk,θuk)every second. After each selection,let the individuals who choose missionkjoin groupk.There are also two cases at this time. When the relationship between groupkandDksatisfies condition (4), the grouping of missionkis completed.Otherwise,if the responding agent is insufficient this time, subtract the sum of the capabilities of the responding agent from the current mission demand to obtain the new mission demand, updateSuk, and continue to respond at the next simulation step. Repeat the above operation until groupkand missionkmeet condition (4). After obtaining groupk, the remaining agents in groupjform a new groupjand continue to participate in the grouping of subsequent missions.

        Through the above operations, we incorporate the response threshold method into the heuristic framework, and effectively solve the problem of screening agents.

        Step 7: repeat steps 4-6 and terminate the grouping process until one of the following two conditions occurs:

        (a) All missions in the current mission list are performed by a certain group.

        (b) When forming a group for missionkin the list,the remaining idle agents are not enough to perform that mission.

        When situation (b) occurs, to save time, the remaining idle agents go to the vicinity of missionkand stand by.

        In addition, all agents participating in the grouping must satisfy constraint(2).

        During the grouping process, some of the original connections will be disconnected, and new connections will be formed in the new mission. When choosing a leader for a new group, we try to choose the original leader included in the group,so that the connection between the leader and the surrounding nodes can be maintained.

        Through the above method, the dynamic agent grouping problem can be solved. After the formation of the mission group, when the agent moves to the vicinity of the mission, if its distance from the leader or the nodes around the leader is less than the communication radius,it can send an application to join the network. We stipulate that the information transmission link from the member to the group leader should not exceed two hops at most.

        4 Simulations

        After designing and describing the model and the dynamic agent self-organizing method, we conduct a series of simulations based on the selforganizing method designed in the study.We want to determine the algorithm’s performance using different scales and different scenarios through simulations.

        The response threshold method introduced from Kim MH et al. (2014)and the adjusted ACO which is based on the model in this study are selected as the comparison algorithms.

        Generally speaking, the ant colony algorithm is used to set up the population in the mission environment and spread the pheromone along the way through the ants. In the problem of this study, the pheromone needs to be set at the mission position to attract agents to perform this mission. The concentration of the pheromone of thekthmission is represented byτk, and the probability that agentichooses missionkcan be calculated as follows:

        whereτsrepresents the pheromone of thesthmission andαdis a heuristic factor. After a round of selection, if the needs of missionkare met, setτkto zero;otherwise,updateτkaccording to the following formula and continue to attract agents:

        where Δτis the concentration of increased pheromone.

        4.1 Settings

        Based on the problems studied in this study,we design four sets of simulations to compare the application of the algorithm with different mission numbers. Tables 1 and 2 show the different values used for the test runs for all model parameters. The parameter values in Table 1 can be adjusted in the simulation, and the parameter values in Table 2 are derived from Cui et al.(2004)and Jiang et al.(2010).From these tables,we can see the specific parameter settings when we perform the four sets of missions of different sizes in the same mission area.

        In the simulation, we use one type of detection agents and three types of attack agents. The parameters of the four agent types are given in Table 3.Some values in Table 3 refer to the relevant parameters of actual weapons and equipment. Table 4 sets the parameters of the algorithms for comparison. For the two comparison algorithms,we select parameters that can achieve better simulation results.

        Fig. 5 Simulation scenario

        Table 1 Variable parameters in simulations

        Table 2 Fixed parameters in simulations*

        Fig.5 shows the simulation scenario. The enemy deployment units (targets) are randomly generated in the mission area as the simulation advances. The large circle indicates the detection range of a detection agent positioned at the centroid. After the simulation starts,the detection agent loops through the mission area to update the mission information. The three types of attack agents perform strikes based on the grouping results from the edge of the mission area.

        4.2 Results

        By simulating the four mission scenarios,we can compare the running results of the dynamic group formation strategy under different mission numbers.We separately conduct 20 simulations on the four mission scenarios given in Table 1.

        Figs. 6-9 show the simulation results obtained under the four different mission scenarios. In these figures, the results of three objectives under different algorithms are shown. We perform simulations on missions of different sizes, and the results show that the NCH method is superior to the comparison algorithms in all three objectives. As the number of missions increases, the performance of NCH is improved. Figs. 8 and 9 clearly reflect the advantages of NCH compared to the two comparison algorithmswhen the number of missions is large.

        Table 3 Parameters of agents

        Fig. 6 Simulation results under the scenario with 10 missions (scenario 1): mission reward (a), average distance (b), and communication overhead (c) under the three algorithms; box plots showing the mean value and fluctuation range of the mission reward (d), average distance (e), and communication overhead (f) under the three algorithms

        Table 4 Parameters of the algorithms to be compared

        Fig. 7 Simulation results under the scenario with 25 missions (scenario 2): mission reward (a), average distance (b), and communication overhead (c) under the three algorithms; box plots showing the mean value and fluctuation range of the mission reward (d), average distance (e), and communication overhead (f) under the three algorithms

        Moreover,box plots of the three objectives,representing the mean value and fluctuation range of different objectives under different methods,are displayed in these figures. Through the box plot, simulation and comparison results can be more intuitively reflected. As the box plots show, compared with the comparison algorithms, when NCH is used to dynamically form the mission group, the average of the three objectives is better. However, the advantages of NCH are not obvious in terms of the volatility of the solution results, which means that in terms of stability, our method (NCH) has room for improvement.

        Table 5 shows specific grouping statistics of scenario 1. Through the grouping statistical results,it can be intuitively understood that because the heuristic rules of the NCH method consider the energy consumption factor, the original group member structure can be maintained as much as possible when the method is used for dynamic grouping. In contrast, the memberships of the mission groups of the two comparison algorithms are more random.The comparison results can prove the effectiveness of heuristic rules and the NCH algorithm.

        In terms of the algorithm characteristics, theuse of the NCH method is based on the layered distributed system designed in this study. The implementation of heuristic rules also depends on some simple decisions made by the detection agent (gateway node), such as sorting groups according to the utility value. Therefore, NCH is not completely a distributed algorithm,but combines some features of a centralized algorithm. The comparison algorithms(ACO and RTM) are distributed algorithms, which can completely realize the dynamic self-organization of agents without relying on superior nodes. In this respect, the performance of NCH is worse than that of the comparison algorithms. In other words, NCH has certain advantages in solving the problems in this paper, but under other conditions, the performance of NCH may not be as good.

        Table 5 Statistics of grouping results (scenario 1)

        Fig. 8 Simulation results under the scenario with 35 missions (scenario 3): mission reward (a), average distance (b), and communication overhead (c) under the three algorithms; box plots showing the mean value and fluctuation range of the mission reward (d), average distance (e), and communication overhead (f) under the three algorithms

        Fig. 9 Simulation results under the scenario with 50 missions (scenario 4): mission reward (a), average distance (b), and communication overhead (c) under the three algorithms; box plots showing the mean value and fluctuation range of the mission reward (d), average distance (e), and communication overhead (f) under the three algorithms

        5 Conclusions and future work

        The purpose of our research is to design a heuristic mission group formation approach with some selforganizing characteristics based on the dynamic mission requirements. In the actual battlefield,frequent transmission of data may cause nodes to be detected,or consume too much energy and lose communication ability for a period of time. We have designed a series of heuristic rules to preserve the original group’s organization as much as possible when forming a new group. This strategy effectively reduces the traffic generated by related steps by reducing the disconnection and reconstruction operations of links between nodes. In addition, based on the ability matching principle, we have made adjustments to the existing self-organizing algorithm and reduced the wasting of agent capabilities during the grouping process.The adjusted self-organizing algorithm and heuristic rules together form the mission group dynamic formation algorithm described in this study.

        In the simulations, we have designed a mission scenario where heterogeneous agents search and attack enemy targets. Three objectives have shown that the NCH method has advantages in solving this problem.

        In future work, more complex problems will be considered. In actual combat, when different types of ammunition are carried, the capabilities of each agent will need to be reconfigurable. Also,the actual mission environment may contain many obstacles or unknown factors, which will affect the movement of agents and their group formation. Therefore, in the next step, we will study the dynamic grouping of agents based on the above new requirements and constraints.

        In terms of applying the method, the dynamic self-organizing method studied in this study can be applied in the field of combat, and to the grouping problem of other kinds of missions. In future work,we will transform the model and consider the characteristics of other agents to expand the application area of the proposed method.

        Contributors

        Chen CHEN and Xiaochen WU conceived the idea of this research and studied the literature. Chen CHEN designed the simulations. Xiaochen WU processed the data.Chen CHEN and Xiaochen WU drafted the paper. Panos M. PARDALOS and Shuxin DING helped organize the paper. Chen CHEN, Xiaochen WU, and Jie CHEN revised and finalized the paper.

        Compliance with ethics guidelines

        Chen CHEN, Xiaochen WU, Jie CHEN, Panos M.PARDALOS, and Shuxin DING declare that they have no conflict of interest.

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