Coordination for Dynamic Weighted Task Allocation inDisaster Environments with Time, Space and

Communication Constraints

Xing Sua,∗, Minjie Zhanga, Quan Baib

aSchool of Computing and Information TechnologyUniversity of Wollongong

AustraliabSchool of Computer and Mathematical Sciences

Auckland University of TechnologyNew Zealand

Abstract

Coordination for dynamic task allocation based on available resources is a very chal-lenging research issue in disaster environments with time, space and communicationconstraints. In addition, the space and communication constraints and the dynamicfeatures of disaster environments make an extra difficulty to achieve efficient coordi-nation through centralised coordination approaches, which require the coordinators tohave global knowledge of the environments. To this end, a coordination approach fordynamic weighted task allocation is proposed in this paper. The proposed approachconsiders time, space and communication constraints in disaster environments and ur-gent degrees of workloads of tasks without requiring the global knowledge of the en-vironment. In particular, a dynamic group formation mechanism is developed to helpagents to form groups and share information for task allocation under space and com-munication constraints in a decentralised manner, which can reflect real-life situationsin disaster environments. The efficient coordination for task allocation is achievedthrough the utility calculation within each group. The experimental results show thatthe proposed approach outperforms most of other coordination approaches, such as thegroup formation approach proposed by Glinton et al. and the heuristics task allocationapproach proposed by Ramchurn et al. in terms of group formation and weighted taskallocation in disaster environments with time, space and communication constraints.

Keywords: intelligent agents, agent coordination, resource allocation, disasterenvironments

∗Corresponding authorEmail addresses: xs702@uowmail.edu.au (Xing Su ), minjie@uow.edu.au (Minjie Zhang),

quan.bai@aut.ac.nz (Quan Bai)

Preprint submitted to Elsevier December 27, 2015

1. Introduction

Nowadays, agent-based coordination for task allocation has been widely appliedin many environments such as disaster rescue, space exploration and distributed com-puting, etc [1, 2, 3, 4, 5]. The main objective of task allocation is to allocate limitedresources (agents) to suitable tasks in a rational way. Task allocation in disaster envi-ronments is a challenging issue in both research and applications.

In general, disaster environments have the following particular requirements whichneed to be considered for task allocation. 1) Time constraints. In disaster environ-ments, tasks include locating and saving survivors in debris, extinguishing fire of build-ings, etc. In such circumstances, each task should have a hard deadline and a task isworthy to be finished before its deadline [6, 7, 8] (i.e. the time point until which thesurvivor is still alive or the building is still standing). 2) Space constraints. In disasterenvironments, agents can move to different locations and tasks can also be discoveredat different locations. If an agent wants to work on a task, it first needs to move tothe location of the task, which will consume time [9, 10, 8]. Therefore, both loca-tions of tasks and agents are important issues to be considered during task allocation.3) Communication constraints. In disaster environments, communication constraints[11, 12, 13] include two aspects. The first aspect is the constraint of communicationcapacities. The second aspect is the constraint of communication ranges. Due to thedestruction of local infrastructures and other conditions in disaster environments, theamount of information transferred between agents is limited (i.e. the constraint ofcommunication capacities). In addition, agents can only directly communicate withother agents within a certain distance in many real-life situations (i.e. the constraintof communication ranges). 4) Dynamic features of the environments. In disasterenvironments, agents can be continuously entering and leaving the environments andtasks can be continuously being discovered and finished in the environments [6, 14]. 5)The urgent degrees of workloads of tasks. The workloads of different tasks shouldhave different urgent degrees [15, 16]. Tasks with higher urgent degrees of workloadsneed to be finished first, while tasks with lower urgent degrees of workloads shouldbe disregarded during task allocation if resources are not sufficient. An example isdemonstrated in Figure 1

Figure 1: Two tasks with different urgent degrees of workloads

In Figure 1, an agent discovers two tasks (i.e. Task A and Task B). Both of tasksneed the agent to provide 100 workload to finish. However, one task (i.e. Task A)is to rescue survivors in a collapsed building, while the other task (i.e. Task B) isto save good in debris. When the agent makes decision on task allocation, it is nodoubt that the task of rescuing survivors (i.e. Task A) should take precedence over

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the task of saving goods (i.e. Task B). From above example, it can be seen that theurgent degree of the workload of each task is obviously a key issue to be consideredduring task allocation, especially in disaster environments. In most existing relatedapproaches [17, 6, 18], the researchers only emphasise on finishing as many tasks aspossible before their deadlines, but ignore the difference between urgent degrees ofworkloads of tasks.

To handle task allocation in disaster environments, various models, mechanismsand approaches have been proposed to achieve efficient coordination for task allocationfrom different perspectives [19, 20, 21, 22, 23]. These approaches can be divided intothe centralised approaches and the decentralised approaches.

A number of centralised approaches [17, 6] have been developed to coordinatetask allocation in disaster environments. The centralised approaches can guaranteean optimal allocation solution, if the coordinator can have the global knowledge ofoverall tasks and agents in an environment. However, in most disaster environments,it is hard for a coordinator to have such kind of knowledge due to the time, spaceand communication constraints as well as the dynamic features of tasks and agents indisaster environments.

To overcome the limitations of centralised approaches, some decentralised ap-proaches [24, 19, 9] have been developed for disaster environments in the last twentyyears. One of the famous approaches is the fast-max-sum proposed by Ramchurn etal. [12], which employs the message passing mechanism (from the max-sum algorithm[24]) to enable agents to share information and make decision for task allocation in adecentralised manner. However, if the number of agents is large and the connectionsamong agents are complicated, agents need to spend a great deal of time and resourcesfor message passing so as to create a near-optimal solution for task allocation. There-fore, the fast-max-sum approach does not work well in disaster environments undermultiple constraints, especially under the dynamic features of the environments. Inaddition, the fast-max-sum approach does not consider the different urgent degreesof workloads of tasks. Actually, even if some task allocation approaches consider thecommunication constraints, most of them only consider either the constraint of commu-nication capacities or the constraint of communication ranges and few of them considerboth.

In order to meet the challenges of task allocation in disaster environments, a coor-dination approach for dynamic weighted task allocation is proposed in this paper. Theproposed approach first collects information for tasks allocation through forming tem-porary groups in a decentralised manner. Then, a token passing mechanism [25, 26]is employed to assist members of each group to share information for task allocationunder space and communication constraints. Finally, the coordinator of each groupemploys the proposed utility calculation mechanism to find the most suitable task allo-cation solution within its group. The proposed approach has the following merits. (1)The proposed approach considers time, space and communication constraints to reflectthe real-life situations in disaster environments. (2) The proposed approach considersthe workloads of tasks and their urgent degrees as well as dynamic features of disasterenvironments so as to meet the requirements of task allocation in disaster environments.(3) In the proposed approach, an innovative group formation mechanism is developedto help agents to form groups and share information for task allocation under space and

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communication constraints. (4) A comprehensive utility function for task allocation isdesigned to help the coordinator of each group to find the most suitable task alloca-tion solution in its group. The experimental results show that in disaster environmentswith time, space and communication constraints, the proposed approach outperformsthe group formation mechanism proposed by Glinton et al. [27] and the heuristics taskallocation approach proposed by Ramchurn et al. [6] in terms of group formation andweighted task allocation, respectively.

The rest of this paper is organized as follows. The problem is formulated anddefinitions are given in Section 2. The principle of the proposed approach is introducedin detail in Section 3. The experiments and analysis are given in Section 4. The relatedwork and discussions are given in Section 5. The paper is concluded and the futurework is outlined in Section 6.

2. Problem Description and Definition

In general, agent-based task allocation involves to model the coordinating problemof a set of agents during the task allocation process. The set of agents contains Mnumber of agents, which can be described as {A1, A2, A3, ..., AM}, where Ai repre-sents the ith agent and 1 ≤ i ≤M . Each agent can scan its surrounding area, discovertasks within its scanning range and give an ID to each task as Tij , where Tij representsthe jth task discovered by Ai. In the proposed approach, the following definitions aregiven to describe the coordinating problem in detail.

Definition 1: An Agent (Ai) can be defined as a six-tuple Ai=<ANo, Utii, Loci,MSpi, Commi, AStai>, where ANo is the ID of Ai; Utii is the work efficiencyof Ai, which represents how many units of workload that Ai can perform per timeunit; Loci is the current location of Ai; MSpi is the moving speed of Ai, whichrepresents how many units of distance that Ai can move per time unit; Comi is thecommunication range of Ai, which represents the maximum units of distance that Ai

can directly communicate with; and AStai is the status of Ai, which can be either‘available’ or ‘working’.

In order to distinguish different urgent degrees of workloads among tasks, the vari-able Emgij is proposed. By taking Emgij into account, the definition of a task isgiven as follows.

Definition 2: A Task (Tij) can be defined as a six-tuple Tij=<TNo, DLij , WLij ,Locij , Emgij , TStaij>, where TNo is the ID (generated by the agent which discov-ered the task) of Tij ; DLij is the deadline of Tij and DLij ∈ [0,∞]; WLij is theworkload of Tij , which represents how many units of workload must be done to com-plete Tij ; Locij is the location of Tij ; Emgij is the urgent degree of the workload ofTij and Emgij ∈ [1, 10], where 1 and 10 represent the lowest and the highest urgentdegrees of workloads of tasks, respectively; and TStaij is the status of Tij , which iseither ‘available’, ‘working’, ‘finished’ or ‘expired’.

The proposed approach in this paper deals with the task allocation problem by alsoconsidering the urgent degrees of workloads of tasks, which is called the weighted taskallocation problem. The main objective of a weighted task allocation problem is to find

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an allocation solution Alloc∗ to maximise the sum of weighted workloads of finishedtasks, which is described as follows.

Alloc∗ = argmax∑

Finish(Tij)=1

WLij · Emgij , (1)

where Finish(Tij) is a boolean function under the conditions that if Tij is finished,i.e. Finish(Tij) = 1, otherwise Finish(Tij) = 0; WLij is the workload of a fin-ished task; and Emgij is the corresponding urgent degree of the workload of Tij (see,Definition 2).

In the proposed approach, a token describing and passing mechanism is employedto describe information of tasks and agents and help agents to efficiently share suchinformation for task allocation. There are two types of tokens: agent tokens (e.g.ATokeni) and task tokens (e.g. TTokenij). The definitions of two types of tokensare presented in Definition 3 and Definition 4, respectively.

Definition 3: An Agent Token (ATokeni) is generated by Ai for itself, which canbe defined as a four-tuple ATokeni =< ANo, Utii, Loci, MSpi>, where ANois the ID of the agent represented by ATokeni; Utii is the work efficiency of theagent represented by ATokeni; Loci is the current location of the agent representedby ATokeni; and MSpi is the moving speed of the agent represented by ATokeni.

Definition 4: A Task Token (TTokenij) is generated by Ai for its jth discoveredtask, which can be defined as a five-tuple, TTokenij =< TNo, DLij , WLij , Locij ,Emgij>, where TNo is the ID of the task represented by TTokenij ; DLij is thedeadline of the task represented by TTokenij ; WLij is the workload of the task rep-resented by TTokenij ; Locij is the location of the task represented by TTokenij ; andEmgij is the urgent degree of the workload of the task represented by TTokenij .

Agents can have two different roles, i.e. coordinators and resource providers.

• A coordinator is an agent, which is in charge of allocating agents to tasks.

• A resource provider is an agent, which is in charge of finishing tasks.

In general disaster environments, the constraint of communication ranges is a com-mon problem. In this situation, an agent can only directly communicate with otheragents close to its location within its communication range (i.e. Comi, see, Definition1). The direct neighbours of an agent is defined as follows.

Definition 5: The direct neighbours of an agent Ai are the agents within Ai’s com-munication range. (i.e the Euclidean distances between Ai and its direct neighbourscannot be more than the communication range of Ai (represented by Comi, see, Defi-nition 1)).

3. The Principle of the Proposed Approach

The proposed coordination approach for dynamic weighted task allocation consistsof five looping steps: 1) token generation, 2) group formation, 3) token passing, 4)

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task allocation, and 5) solution return. The general process of the proposed approachis shown as follows.

Figure 2: The Process of the Proposed Approach

In Figure 2, the five steps of the proposed approach in one loop are demonstrated.After one loop of the five steps, the groups formed in group formation step will bedismissed and agents begin to work on their allocated tasks according to the allocationsolution. When some agents finish their allocated tasks and there are still availabletasks in the environment, the above five steps will be repeated again according to theinformation of available tasks and agents at that time, so the dynamic task allocationwill be achieved.

3.1. Token Generation

In this step, each available agent Ai (i.e. AStai = ‘available’ (see, Definition 1))scans its surrounding area and generates a task token, TTokenij=<Tij , DLij , WLij ,Locij , Emgij> (see, Definition 4) for each available task Tij (i.e. TStaij = ‘avail-able’, see, Definition 2) that Ai discovered. After task checking, Ai also generates anagent token, ATokeni=<Ai, Utii, Loci, MSpi> (see, Definition 3) for itself.

3.2. Group Formation

Due to space and communication constraints in disaster environments, each agentcan only directly communicate with its direct neighbours (see, Definition 5). In orderto get much information for task allocation in such disaster environments, agents couldform groups to share information with their surrounding neighbours for task alloca-tion. Under this consideration, the group formation mechanism should help agents toconnect as many other agents in the environment as possible. Many group formationmechanisms [28, 29, 27, 6] have been developed in multi-agent research under dif-ferent considerations and very few of them consider the communication constraints,especially the constraints of communication ranges. These group formation mecha-nisms form groups through connecting only direct neighbours, we call this kind ofmechanisms as Direct Neighbours Group Formation (DNGF) mechanisms in this pa-per. In order to collect as much information for task allocation as possible under spaceand communication constraints in disaster environments, we develop a group formationmechanism in the proposed approach to help agents to form groups through connectingas many agents as possible including direct and indirect neighbours within communi-cation ranges of agents in a decentralised manner. The formed group is a tree structure,

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in which the agent at the root node is chosen to be the coordinator of the group. To dis-tinguish with DNGF mechanisms, we call our group formation mechanism as IndirectNeighbours Group Formation (INGF) mechanism. The difference between DNGF andINGF can be described in Figure 3.

Figure 3: The Difference between INGF and DNGF Mechanisms

In Figure 3, the rectangles represent the agents and solid lines between agents indi-cate that the two agents are direct neighbours of each other (see, Definition 5). In theDNGF mechanism, an agent Ai can only form a group with its direct neighbours i.e.A1, A2, A3 and A4 (black stars), while in our group formation (INGF) mechanism, Ai

can add four indirect neighbours i.e. A5, A6, A7 and A8 (white triangles) to its group.The more agents in a group, the more information can be collected by the coordinatorof the group and the more efficient task allocation can be achieved.

In the proposed group formation mechanism, three ‘neighbour related’ variables aredefined for each agent, which are the parent agent (PA), the coordinator (C) and thenumber of direct neighbours of the coordinator (NNC). For example, for an agent Ai,the three ‘neighbour related’ variables can be denoted as Ai.PA, Ai.C and Ai.NNC,respectively. The proposed group formation mechanism is described by Algorithm 1.

At the beginning of Algorithm 1, the three ‘neighbour related’ variables of eachagent (e.g. Ai) are initialised as follows: Ai.PA is set to Ai, Ai.C is set to Ai andAi.NNC is set to the number of direct neighbours of Ai (since Ai is the coordinatorof itself) (Lines 1 to 2). Then, each agent (e.g. Ai) repeats the following three steps.Step 1: Ai finds an agent (e.g. Au), which has the highest value of the variable NNC(i.e. Au.NNC) from its direct neighbours (including Ai itself) (Line 5). Step 2: IfAu.NNC has a higher value than the value of Ai.NNC, the three ‘neighbour related’variables of Ai (i.e. Ai.PA, Ai.C and Ai.NNC) are updated as follows: Ai.PA isset to Au, Ai.C is set to Au.C and Ai.NNC is set to Au.NNC (Lines 6 to 7). Step3: If the three ‘neighbour related’ variables of Ai are updated in Step 2, each directneighbour of Ai (e.g. Al) compares its coordinator (i.e. Al.C) with the coordinatorof Ai (i.e. Ai.C). If a different coordinator has been found (i.e. Al.C 6= Ai.C), thethree ‘neighbour related’ variables ofAl (i.e. Al.PA,Al.C andAl.NNC) are updatedas follows: Al.PA is set to Ai, Al.C is set to Ai.C and Al.NNC is set to Ai.NNC(Lines 8 to 10). Through Step 3, the values of three ‘neighbour related’ variables

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Algorithm 1: Group Formation

1 for each Agent Ai do2 Ai.PA← Ai; Ai.C ← Ai; Ai.NNC ← the number of direct neighbours

of Ai

3 end4 for each Agent Ai do5 Get Au from Ai and Ai’s direct neighbours, where Au.NNC is the

maximum6 if Au.NNC > Ai.NNC then7 Ai.PA← Au; Ai.C ← Au.C; Ai.NNC ← Au.NNC8 for each direct neighbours of Ai:Al do9 if Al.C 6= Ai.C then

10 Al.PA← Ai; Al.C ← Ai.C; Al.NNC ← Ai.NNC11 end12 end13 end14 end

of Ai can be passed to its child agent Al and the agent with the highest number ofdirect neighbours in a group can be the root node of the tree structure and is chosen asthe coordinator of the group. The above three steps (Lines 4 to 10) will be repeatedby each agent until no further updating for three ‘neighbour related’ variables of anyagent, which means that each agent in the communication network has found its onlyway to pass message to the coordinator of the network.

A group formed by the proposed group formation mechanism can connect the max-imum number of direct and indirect neighbours of the coordinator. Therefore, if thereare two or more groups formed according to the proposed group formation mechanismin a disaster environment, these groups are completely isolated and cannot commu-nicate with each other according to current communication situations. The followingsub-sections describe the steps of task allocation in each isolated group.

3.3. Token PassingSince in a group, most of members (agents) are indirect neighbours of the coor-

dinator, which means that these neighbours cannot directly communicate with the co-ordinator, we employs a token passing mechanism to help the coordinator to collectinformation from its group members [25, 26]. The token passing mechanism beginsfrom the agents who do not have child agents and ends at the coordinator. By employ-ing the the token passing mechanism, each agent first receives agent and task tokens(generated in the token generation step) from its child agents. Different agents in thesame group can generate task tokens for the same task. For example, Al and Au arechild agents of Ai and they can generate task tokens, TTokenlj=<Tlj , DLlj , WLlj ,Loclj , Emglj> and TTokenuj=<Tuj , DLuj , WLuj , Locuj , Emguj>, respectively,for the same task. After Ai received the task tokens from Al and Au, Ai found that ex-cept the first element (i.e. ANo, see, Definition 4), the values of other variable of two

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task tokens (i.e. DLlj = DLuj , WLlj = WLuj , Loclj = Locuj , Emglj = Emguj ,see, Definition 4) are exactly same. In this situation, Ai only keeps one task token torepresent the task and abandons the other (i.e. TTokenlj created by Al is abandonedand only TTokenuj created by Au is kept). After that, Ai passes the agent tokens, theremaining task tokens, and the agent token of itself (i.e. ATokeni) to its parent agent.Finally, all of task and agent tokens generated by the group members are passed to thecoordinator of the group.

Figure 4: The Example of Token Passing

Figure 4 shows an example of token passing. There are four agents (i.e. A1 to A4

represented by rectangles), where A1 is the parent agent of A2 (A2.PA = A1), A2 isthe parent agent of A3 and A4 (A3.PA = A2 and A4.PA = A2 ) and three tasks (i.e.Task A, Task B and Task C represented by circles), where Task A and Task Bcan be discovered by A3 and Task B and Task C can be discovered by A4. Afterthe token generation step, A3 generates two task tokens ‘<T31, ...>’ and ‘<T32, ...>’,while A4 also generates two task tokens ‘<T41, ...>’ and ‘<T42, ...>’. Then, the tasktokens and the agent tokens of A3 and A4 are passed to their parent agent A2. Afterchecking the variables of received task tokens, A2 discovers that task tokens ‘<T32,...>’ and ‘<T41, ...>’ are generated for the same task by two different agents. Then,A2 abandons the task token ‘<T41, ...>’ and keeps the task token ‘<T32, ...>’. Afterthat, A2 passes the agent tokens received from A3 and A4 (AToken3, AToken4), tasktokens received from A3 and A4 (<T31, ...> and<T42, ...>), the remaining task token(<T32, ...>), and the agent tokens of itself (AToken2) to its parent agent A1.

3.4. Task allocationThis step is the core of the proposed approach. In this step, the coordinator tries to

calculate the most suitable allocation solution for its group according to the informationof tasks and agents collected in the token passing step. In the proposed approach, anallocation solution Aloca is a set of allocations (e.g. Aloca = {A1 → T12, A2 →T41, ..., Ai → Tij}). An allocation is a map from an agent to a task (i.e. Ai → Tij),which represents that the agent is allocated to the task. If an agent is not allocated toany task, Tij in the allocation equals to ∅. Since finding the most suitable allocationsolution is an NP-hard problem (the proof process can be found in [6]), the proposedapproach employs a utility calculation mechanism to help the coordinator to find the

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most suitable allocation solution. The process of finding the most suitable allocationsolution consists of two sub-steps: 1) the elimination of unuseful allocation solutionsand 2) the utilities calculation of allocation solutions.

1) The Elimination of Unuseful Allocation SolutionsBased on the combinatorics, the number of allocation solutions for a group includingM number of agents and N number of tasks is (N + 1)M (i.e. each agent can beallocated to one of N tasks or ∅). Among these allocation solutions, there are manyunuseful allocation solutions, in which some agents cannot finish their allocated taskson time (before the deadlines of tasks). In order to make the following utility calcula-tion more efficient, these unuseful allocation solutions should be eliminated first. Theprocess of the elimination of unuseful allocation solutions can be described as follows.First, the coordinator gets all (N + 1)M allocation solutions of its group. Second, foreach task Tij in each allocation solution Aloca, the coordinator calculates whether theagents allocated to Tij can finish it before the deadline of Tij according to current statusof the agents. UFin(Tij) is the unfinish indicator function of Tij , which is calculatedas follows.

UFin(Tij) =

1 WLij >

∑Aloca

(DLij − CT − Dis(Locij ,Loci)

MSpi)Utii

0 WLij ≤∑

Aloca

(DLij − CT − Dis(Locij ,Loci)

MSpi)Utii

, (2)

where WLij is the workload of Tij ; Ai is one of agents allocated to Tij in Aloca;DLij is the deadline of Tij ; CT is the current time; Dis(Locij , Loci) is the distancebetween the location of Tij and the current location of Ai; and MSpi is the movingspeed ofAi; Utii is the work efficiency ofAi. If Tij cannot be finished by the allocatedagents in Aloca, the function UFin(Tij) = 1, otherwise UFin((Tij) = 0.

Elim(Aloca) =⋃

Tij∈Aloca

UFin(Tij) =

{1 Aloca unuseful0 Aloca useful

, (3)

where Elim(Aloca) is the elimination indicator function of Aloca. If any allocatedtask, say Tij , cannot be finished in Aloca, the elimination indicator function of Alocaequals to 1 (i.e. UFin(Tij) = 1), which means that the Aloca is unuseful and shouldbe eliminated. For example, in a disaster environment, there are 2 agents (A1, A2) and2 tasks (T11, T21). Therefore, there are totally (2+1)2 = 9 different kinds of allocationsolutions, which are listed as follows.

Aloc1 = {A1 → ∅, A2 → ∅}Aloc2 = {A1 → ∅, A2 → T11}Aloc3 = {A1 → ∅, A2 → T21}Aloc4 = {A1 → T11, A2 → ∅}Aloc5 = {A1 → T11, A2 → T11}Aloc6 = {A1 → T11, A2 → T21}Aloc7 = {A1 → T21, A2 → ∅}Aloc8 = {A1 → T21, A2 → T11}

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Aloc9 = {A1 → T21, A2 → T21}

The information of T11 and T21 and status of A1 and A2 are shown as follows.

Figure 5: The Information of Tasks and Status of Agents

From Figure 5, it can be seen that both of workloads of T11 and T21 are 10 workloadunits and T11 will expire in 10 time units, while T21 will expire in 20 time units. Thework efficiency and moving speed of A1 and A2 are 1 workload unit and 1 distanceunit per time unit, respectively. In addition, the distances between tasks and agents areshown by the lines between them, where are 6 distance units (i.e. T11 to A1 and T21to A2) and 8 distance units (i.e. T21 to A1 and T11 to A2). After calculation, we canfind that UFin(T11) equals to 1 in any allocations (i.e. If only A1 is allocated to T11,A1 needs 8 time units to arrive the location of T11 and can only finish 2 workload unitsof T11 before the deadline of T11 (so T11 cannot be completely finished on time). Ifonly A2 is allocated to T11, A2 needs 6 time units to arrive the location of T11 andcan only finish 4 workload units of T11 before the deadline of T11 (so T11 also cannotbe completely finished on time). If both of A1 and A2 are allocated to T11, they canfinish 6 workload units of T11 before the deadline of T11, which still cannot finish T11on time.). Therefore, even if both of A1 and A2 work on T11, T11 cannot be finishedaccording to the information of T11 and status of A1 and A2. The allocation solutions(i.e. Aloc2, Aloc4, Aloc5, Aloc6 and Aloc8) involving allocations of A1 → T11 orA2 → T11 are unuseful and should be eliminated.

2) The Utilities Calculation of Allocation SolutionsIn this sub-step, the coordinator calculates the utilities of useful allocation solutions.The utility calculation depends on not only how many tasks that can be completed, butalso the benefits that agents can receive after completing their allocated tasks and thecosts that agents must spend on the completion of these tasks. Based on the benefitsand costs, the utility of an allocation solution Aloca can be calculated by the followingformula.

Utlity(Aloca) = Qbenefit −Qcost, (4)

where Qbenefit is the benefits that agents can receive after completing their allocatedtasks, which involves: 1) the sum of the weighted (urgent degree) workloads of allo-cated tasks and 2) the sum of saved time of completed tasks; and Qcost is the costs that

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agents must spend for completing tasks, which involves: 1) the sum of traveling timefor completing tasks and 2) the sum of working time for completing tasks.

Under above considerations, the Qbenefit of Aloca can be calculated as follows.

Qbenefit =∑

Tij∈ranAloca

Emgij · (WLij +(DLij − FTij)WLij

DLij), (5)

where WLij , Emgij and DLij are the workload, the urgent degree of the workloadand the deadline of Tij in Aloca, respectively, and FTij is the predicted completingtime of Tij in Aloca.

The Qcost of Aloca can be calculated as follows.

Qcost =∑

Ai∈domAloca

(FTij − CT )Utii, (6)

where FTij is the predicted completing time of Tij in Aloca, CT is the current timeand Utii is the work efficiency of Ai.

The FTij in Equation 5 and 6 can be calculated as follows:

FTij =

WLij +∑

Aloca

Dis(Locij ,Loci)

MSpi· Utii∑

Aloca

Utii+ CT, (7)

where WLij is the workload of Tij ; Dis(Locij , Loci) is the distance between thelocation of Tij and the current location of Ai; MSpi is the moving speed of Ai; Utiiis the work efficiency of Ai, which is allocated to Tij in Aloca and CT is the currenttime;

An example is employed to demonstrate the calculation process of Equation 7.

Figure 6: The Information of Tasks and Status of Agents

From Figure 6, it can be seen that the current time is 10 time units (i.e. CT=10),the workloads of T11 is 65 workload units (i.e. WL11 = 65) and T11 will expire in

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30 time units (i.e. DL=40). Three agents (i.e. A1, A2 and A3) are allocated to T11.The distance between A1 and T11 is 20 distance units (i.e. Dis(Loc11, Loc1) = 20).The work efficiency and moving speed of A1 are 1 workload unit and 2 distance unitsper time unit (i.e. Uti1 = 1 and MSp1 = 2), respectively. The distance betweenA2 and T11 is 10 distance units (i.e. Dis(Loc11, Loc2) = 10). The work efficiencyand moving speed of A2 are 2 workload units and 1 distance units per time unit (i.e.Uti2 = 2 andMSp2 = 1), respectively. The distance betweenA3 and T11 is 5 distanceunits (i.e. Dis(Loc11, Loc3) = 5). The work efficiency and moving speed of A3 are1 workload unit and 1 distance unit per time unit (i.e. Uti3 = 1 and MSp3 = 1),respectively. Based on Equation 7, the predicted completing time of T11 (i.e. FTij)can be calculated as follows.

FTij =WL11 +

Dis(Loc11,Loc1)MSp1

· Uti1 +Dis(Loc11,Loc2)

MSp2· Uti2 +

Dis(Loc11,Loc3)MSp3

· Uti3

Uti1 + Uti2 + Uti3+CT.

(8)After calculation, the predicted completing time of T11 is at 35 time units, which is lessthan the deadline of T11 (i.e. 40 time units).

Based on Equations 5, 6 and 7, the allocation solution (e.g. Aloca) with the highestvalue of the utility (i.e. Utility(Aloca)) is chosen by the coordinator to be the mostsuitable allocation solution of its group.

3.5. Solution Return

In this step, the coordinator sends the chosen allocation solution (e.g. Aloca) to itsgroup members. The process of solution return is the inverse process of token passing.Different from token passing, an agent (e.g. Ai) needs to perform following actions,when it receives the Aloca. First, Ai passes the Aloca to its direct neighbours andAi is dismissed from its group. After that, if Ai is allocated to a task in Aloca, Ai

changes its status (i.e. AStai, see, Definition 1) from ‘available’ to ‘working’ andstarts to move to the location of its allocated task. When Ai reaches the location ofits allocated task, it changes the status of the task (i.e. TStaij , see, Definition 2) from‘available’ to ‘working’. After finishing the allocated task, all agents working on thesame task change their status from ‘working’ to ‘available’ and the status of the task isalso changed from ‘working’ to ‘finished’.

4. Experiment and Analysis

Three experiments are conducted to evaluate the performance of the proposed ap-proach. Experiment 1 is to evaluate the performance of the proposed group formationmechanism. Experiment 2 is to evaluate the performance of the proposed approachon task allocation in disaster environments. Experiment 3 is to evaluate the impact ofurgent degrees of workloads of tasks on the proposed approach. Three experiments aredemonstrated and analysed in detail in the following three sub-sections, respectively.

4.1. Experiment 1: Test of Group Formation

The purpose of this experiment is to evaluate the performance of the proposedgroup formation (INGF) mechanism under different communication ranges of agents.

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4.1.1 Experiment settingsIn the proposed approach, before task allocation, the agents need to share informa-

tion for task allocation through forming groups under space and communication con-straints. Therefore, the performance of the proposed group formation mechanism has agreat impact on the results of task allocation. In this experiment, we compare the pro-posed group formation (INGF) mechanism with the group formation mechanism pro-posed by Glinton et al. [27] as the benchmark mechanism, (which we called DNGF) inthis experiment. The performance of the proposed group formation mechanism and thebenchmark mechanism is compared under different communication ranges of agents.The settings of Experiment 1 are described in Table 1.

Table 1: The Settings of Experiment 1Name ValueArea size 50× 50Number of agents 10Communication ranges of agents 5, 10, 15, 20, 25, 30, 35, 40

In Experiment 1, we employ the Euclidean space to describe the distance betweenlocations of two agents [30, 31]. Through the calculation, we can see that in a Euclideanspace, ifM agents with the same communication range D are randomly arranged in anN ×N area and the average number of direct neighbours of an agent can be calculatedas follow:

Poss = (M − 1) · π ·D2

N2. (9)

Based on Equation 9, when communication ranges of agents are 5, 10, 15, 20, 25,30, 35 and 40, the average numbers of direct neighbours of each agent are 0.28, 1.13,2.54, 4.52, 7.07, 10.18, 13.85 and 18.10, respectively. These settings can cover mostof communication situations of agents in disaster environments from ‘isolated’ to ‘full’communication. In this experiment, two indicators are employed to represent the per-formance of group formation mechanisms, which are 1) the average number of agentsof the formed groups and 2) the maximum number of agents of the formed groups.

4.1.2 Experimental results and discussionThe experimental results of Experiment 1 are shown in Figure 7. In Figure 7, the

X-axis is the communication ranges of agents, while the Y-axis is the number of agents.The two indicators (i.e. the average number and the maximum number of agents of theformed groups) in this experiment are represented by the bars and lines in Figure 7,respectively.

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Figure 7: Experimental Results of Experiment 1

From Figure 7, it can be seen that both DNGF and INGF mechanisms have the sameperformance on the two indicators, when the communication ranges (D) of agents areonly 5. Since the average number of direct neighbours of each agent is only 0.28,we call this communication situation ‘isolated’. In this communication situation, thebiggest agent groups formed by both of group formation mechanisms contain only 3agents and the average number of agents of the formed groups through both of groupformation mechanisms contain only about 1.5 agents, which means that most of agentsin this communication situation cannot form groups with other agents. With the in-crease of the communication ranges of agents, the two indicators of groups formedthrough both of group formation mechanisms increase. However, the two indicators ofgroups formed by INGF mechanism increase sharply. That is because groups formedthrough the proposed group formation mechanism contain not only the direct neigh-bours but also the indirect neighbours of group members, while groups formed byDNGF mechanism only contain direct neighbours. Therefore, the groups formed byINGF mechanism can reach the ideal status (one group contains all of 10 agents) whenthe communication ranges of agents are only 25. However, the groups formed byDNGF mechanism cannot reach the ideal status until communication ranges of agentsare 35. Therefore, we can conclude that when communication ranges of agents are lim-ited, the groups formed by INGF mechanism contain more agents than that of formedby DNGF mechanism.

4.2. Experiment 2: Test of Task AllocationThe purpose of this experiment is to evaluate the performance of the proposed

approach on task allocation under different communication ranges of agents.

4.2.1 Experiment settingsIn Experiment 2, we focus on evaluating the task allocation performance of the

proposed approach. Therefore, most of experimental parameters (i.e. the size of the

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area, the number of tasks and agents, the deadlines and workloads of tasks, the movingspeeds and work efficiencies of agents) are set to simulate real-life disaster environ-ments. In addition, the urgent degrees of workloads of tasks are set to 1 to remove theirimpact on this experiment. The settings of Experiment 2 are described in Table 2.

Table 2: The Settings of Experiment 2Name ValueArea size 50× 50Number of tasks 100Deadlines of tasks 5s ∼ 200sWorkloads of tasks 10 ∼ 50Urgent degrees of workloads of tasks 1Number of agents 10Work efficiencies of agents 1Moving speeds of agents 1Communication ranges of agents 5 ∼ 40 with 5 per step or 50

The benchmark approach of Experiment 2 is the heuristics task allocation approachproposed by Ramchurn et al. [6]. The reason for this choice is because that the exper-imental settings of this approach are similar to the proposed approach, both of whichconsider the time and space constraints in disaster environments. The difference be-tween the benchmark approach and the proposed approach is that the benchmark ap-proach uses a centralised method for task allocation without considering the communi-cation constraints, while our approach uses a decentralised manner for task allocation.Therefore, in the experiment, we assume that there is no communication constraintswhen conducting the benchmark approach in this experiment in order for the coor-dinator to get the global knowledge. For the proposed approach, we simulate eightdifferent kinds of communication ranges of agents (i.e. from 5 to 40 with 5 per step).As mentioned in Section 3.2, the proposed group formation mechanism can connectthe maximum number of direct and indirect neighbours of the coordinator based onthe communication ranges of agents so that if two or more groups are formed throughthe proposed group formation mechanism, these groups are completely isolated. Inorder to compare the performance of the proposed approach with the benchmark (cen-tralised) approach on task allocation, we use the sum of finished tasks in a disasterenvironment by all isolated groups of the proposed approach as its overall performancein the environment. Therefore, in this experiment, the number of finished tasks in adisaster environment is employed as the indicator to evaluate the performance of twotask allocation approaches.

4.2.2 Experimental results and discussionThe experimental results of Experiment 2 are shown in Figure 8. In Figure 8, the

X-axis is the communication ranges of agents of the proposed approach. The Y-axis isthe number of tasks that have been finished.

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Figure 8: Experimental Results of Experiment 2

From Figure 8, it can be seen that since the communication constraints are not con-sidered when conducting the benchmark approach, the performance of the benchmarkapproach is constant in this experiment. For the proposed approach, when the com-munication ranges of agents are very limited (i.e. the communication range is only 5),the performance of the proposed approach on task allocation is about 50% less thanthat of the benchmark approach. That is because when the communication range is 5,only many small scale isolated groups are formed in the environment. Although thecoordinator of each group trends to find the most suitable allocation solution for itsgroup, the performance of these isolated groups is far away from that of the centralisedapproach. However, with the increase of communication ranges of agents, the coor-dinator of each group can connect more and more agents and the performance of theproposed approach is becoming better and better. When the communication ranges ofagents are 25 (i.e. agents can communicate with each other in the environment), theperformance of the proposed approach is as good as the benchmark approach. Thatis because all 10 agents in a disaster environment form only one group, so the taskallocation result is similar to the benchmark (centralised) approach. Therefore, we canconclude that the benchmark (centralised) approach can achieve the optimal solutionthan the proposed (decentralised) approach, if the coordinator can have a global viewabout the environment. However, due to space and communication constraints, it ishard to have such a view in most of disaster environments. For that reason, the appli-cations of the benchmark (centralised) approach in disaster environments are limited.However, the coordinators in the proposed (decentralised) approach can create nearoptimal solutions under space and communication constraints without the global viewof the environment. Therefore, the proposed (decentralised) approach is more suitableto be applied in disaster environments with space and communication constraints thanthe benchmark (centralised) approach.

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4.3. Experiment 3: Test of the Impact of Urgent Degrees of Tasks

The purpose of this experiment is to evaluate the proposed approach on task allo-cation under different urgent degrees of workloads of tasks.

4.3.1 Experiment settingsIn Experiment 3, we focus on the evaluation of the impact of urgent degrees of

workloads of tasks on the proposed approach. Therefore, we still employ the settingsof general disaster environments as Experiment 2. In order to get rid of the impactof the proposed group formation mechanism on task allocation, the communicationranges of agents are fixed to 50 in this experiment. The settings of this experiment aredescribed in Table 3.

Table 3: The Settings of Experiment 3Name ValueArea size 50× 50Number of tasks 100Deadlines of tasks 5s ∼ 200sWorkloads of tasks 10 ∼ 50Urgent degrees of workloads of tasks 5 or 1 ∼ 9Number of agents 10Work efficiencies of agents 1Moving speeds of agents 1Communication ranges of agents 50

In Experiment 3, the performances of the proposed approach in two kinds of envi-ronments are compared to demonstrate the impact of the urgent degrees of workloadsof tasks. In the first environment, the urgent degrees of workloads of all tasks are sameand equal to 5, while in the second environment, the urgent degrees of workloads ofall tasks vary from 1 to 9 with normal distribution. The sitting of the first environmentis equivalent to the situation when the proposed approach does not consider the urgentdegrees of workloads of tasks.

4.3.2 Experimental results and discussionThe experimental results of Experiment 3 are shown in Figure 9 and 10. In Figure

9, the X-axis is the consumed time units, while Y-axis is the sum of the workloadsof tasks that have been finished. In Figure 10, the X-axis is the consumed time units,while Y-axis is the sum of the weighted workloads of tasks that have been finished.

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Figure 9: Sum Workload

Figure 10: Sum Weighted Workload

From Figures 9 and 10, it can be seen that the proposed approach can finish moreworkload, when the urgent degrees of workloads of all tasks are same. This is becausewhen the urgent degrees of workloads of tasks have no difference, the coordinator al-locates agents to tasks only based on the workload of each task, which equals to thesituation that the workloads of tasks do not have urgent degrees. However, when the ur-gent degrees of workloads of tasks are different, the proposed approach can finish moreweighted workloads than the situation when the urgent degrees of tasks are the same.The reason behind this is that the proposed approach considers the urgent degrees ofworkloads of tasks in its utility calculation function. Therefore, if we differentiate the

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urgent degrees of workloads of tasks in an environment, the proposed approach canallocate more urgent tasks before less urgent tasks. This result is encouragable whenallocating urgent tasks in disaster environments.

4.4. SummaryFrom Experiment 1, 2 and 3, we can make the following conclusions. (1) By

employing the proposed group formation (INGF) mechanism, each formed group canconnect more agents and share more information for task allocation in disaster envi-ronments than many DNGF based mechanisms under space and communication con-straints. (2) By employing the proposed approach, the coordinator can create the taskallocation solution as good as the task allocation solution created by the centralisedtask allocation approach under time, space and communication constraints. (3) By dis-tinguishing the different urgent degrees of workloads of tasks, the proposed approachcan finish more weighted workloads.

5. Related Work

Nowadays, disasters throughout the world have become important social and po-litical concerns. From the last century, multi-agent approaches have become very im-portant solutions to solve many challenging issues in disaster environments [32], [33],[34].

With the development of wireless technologies, wireless sensor networks (WSNs)established by agents have played an important role in disaster rescues in the last tenyears. Tziritas et al. have developed agent migration approaches to deploy agents indisaster environments [35] [36]. In their approaches, Tziritas et al. consider the limitedcapabilities of agents in disaster environments. Therefore, Tziritas et al. employeddistributed agent migration algorithms to adjust the deployment location of agents inWSNs. Based on their approaches, the robustness and effectiveness of the establishedWSNs can be greatly improved so as to extend their lifetime and performance in disas-ter environments.

Ramamritham et al. have developed a distributed coordination approach to handletask allocation with deadlines and resource requirements [15]. Their approach solvescommon task allocation problems based on the classification of tasks. However, theirapproach does not consider the space and communication constraints during task allo-cation. Furthermore, in disaster environments, most of tasks belong to the category ofcritical task in terms of time constraints and people’s life. Therefore, the approach pro-posed by Ramamritham et al. has the limitation to be applied to disaster environments.The proposed approach in this paper not only considers the time, space and commu-nication constraints, but can also deal with different urgent degrees of workloads oftasks.

Some researchers such as Ramchurn et al. and Koes et al. have employed MixedInteger Linear Programming (MILP) to deal with task allocation problem in disasterenvironments [6, 17]. The MILP based approaches can guarantee an optimal allocationsolution for task allocation if a coordinator has a global view of the environment. How-ever, the MILP based approaches have two weaknesses, which can limit their applica-tions in many disaster environments. First, in general disaster environments, it is hard

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for a coordinator to have a global view due to space and communication constraints.Second, the computation complexity of the MILP is high, as authors mentioned inpaper [6], ‘For small scenarios with not more than 4 agents and 7 tasks, the algorithmtakes more than 2 hours to find the optimal solution.”. Although the proposed approachin this paper can only get a near-optimal allocation solution for task allocation in disas-ter environments under time, space and communication constraints, its quickness andsimpleness make it more suitable for highly dynamic disaster environments.

In recent years, the DARPA coordinators program is a popular simulation environ-ment for testing task allocation approaches [37, 38, 9]. In the DARPA coordinatorsprogram, tasks have a complicated hierarchical structure. The difference between theenvironments of the DARPA coordinators program and the proposed approach can besummarized as follows. 1) The tasks in the DARPA coordinators program do not havehard deadlines, while our approach considers the deadlines of tasks; and 2) The envi-ronment of the DARPA coordinators program does not have either space or communi-cation constraints, while our approach deals with coordination for the task allocationproblem in disaster environments by considering time, space and communication con-straints.

6. Conclusion and Future Work

In this paper, an innovative coordination approach for dynamic weighted task al-location in disaster environments with time, space and communication constraints isproposed. A group formation mechanism is developed to help agents to form groupsunder space and communication constraints in disaster environments. The proposedapproach uses a comprehensive utility calculation function to enable each coordinatorto find the most suitable allocation solution for its group. In addition, the workloads oftasks and their urgent degrees, as well as dynamic features of disaster environments areconsidered by the proposed approach in order to reflect the real-life situations of disas-ter environments. The experimental results showed that the proposed approach couldprovide a more efficient way to handle multiple constraints in disaster environmentsfor task allocation than other existing approaches. In the future, we will work on taskallocation problems in more complex environments, e.g. agents can only have sparseinteractions.

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