Plan Recovery Process in Multi-agent Dynamic Environments

Leonardo Henrique Moreira

and C

elia Ghedini Ralha

Department of Computer Science, Institute of Exact Sciences, University of Bras

ılia, Brazil

Keywords:

Multi-agent Planning, Simulation, Dynamic Environments.

Abstract:

Planning is the process that focuses on the choice and organization of actions through their expected ef-

fects. Plans can be affected by unexpected, uncontrolled, non-deterministic events leading to failures. Such

challenging problem boosted works focusing agent distribution, communication mechanisms, privacy, among

other issues. Nevertheless, the plan recovery process does not have a deﬁned standard solution. Thus, in

this work, we present a three-phase plan recovery process to provide resilience to agent plans by supporting

a staggered solution. Whenever an action execution fails, agents try to solve individually through their own

capabilities. But when not possible, agents start an interaction protocol to ask for help. Finally, when previous

two phases were unsuccessful, a centralized planning process is trigged. Regardless the phase in which the

solution is found, agents’ plans are coordinated to guarantee cooperation maintaining information privacy.

An empirical analysis applying metrics such as planning time, ﬁnal plan length and message exchange was

conducted. Results give statistical signiﬁcant evidence that agents’ autonomy is better explored in agents’

loosely coupled environments. The contributions of this work include: a three-phase plan recovery process, a

simulation tool for benchmarks, and a statistical robust evaluation method to multi-agent planning.

1 INTRODUCTION

In multi-agent system (MAS), agents interact with the

environment and with other agents through the exe-

cution of actions towards the transformation of the

environment from a initial to a desirable state. The

sequence of these actions is a plan, being the result

of agents’ deliberation process performed before or

during acting (Ghallab et al., 2014). Furthermore,

planning and execution responsibilities are distributed

over multiple entities. Thus, agents must coordinate

continually their efforts towards the satisfaction of

individual or global goals to guarantee the coopera-

tion by deﬁning a multi-agent planning (MAP) model.

MAP applications are required in ordinary to com-

plex tasks, such as logistic and ﬁre rescue activities,

respectively. A common point in both scenarios is the

fact that agents depend on or affect other agents un-

der different levels, regarding the interaction that their

action executions induce.

In a classical MAP models, changes in the envi-

ronment are expected to happen only by agents’ ac-

tion executions. However, those models become inef-

fective in scenarios where events that are neither con-

https://orcid.org/0000-0003-0479-578X

https://orcid.org/0000-0002-2983-2180

trolled nor expected by agents can happen and update

the environment state. Those events, labeled as ex-

ogenous, are common in dynamic environments. In

this case, the planning process performed in an ear-

lier and single phase (disconnected from execution) is

not able to provide resilience to agents (Ghallab et al.,

2014; Komenda et al., 2014; Chrpa et al., 2020).

In the related work, the MAP models are com-

posed by two different and isolated recovery strate-

gies: replanning and repairing. Although each strat-

egy has its pros and cons, MAP models that apply

both of them regarding agents’ capabilities are miss-

ing in the literature.

Therefore, our goal is to propose a plan recovery

process that combines repairing and replanning strate-

gies, providing conditions to agents to perform a stag-

gered solution. As soon as agents detect an action

execution failure, they ﬁrst try a local repair by plan-

ning individually, considering only their own capabil-

ities. In this sense, agents keep the information pri-

vacy because they do not inform which actions they

are able to perform. When the local repair phase is

not possible, agents interact to ask for help. Finally, if

even so no solution is returned, a centralized planning

phase is triggered. Therefore, the proposed process

tries to avoid message exchange in conditions where

Moreira, L. and Ralha, C.

Plan Recovery Process in Multi-agent Dynamic Environments.

DOI: 10.5220/0010559301870194

In Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2021), pages 187-194

ISBN: 978-989-758-522-7

187

a local solution is possible. This ability is important

in environments where communication is complex or

agents must deliberate quickly towards the solution

of global goals, for instance, during rescue operations

after catastrophic events.

This work was motivated by the hypothesis that

agents’ autonomy in performing local repair is better

explored in environments with low levels of interac-

tion. Therefore, we followed a research methodology

that was guided by the literature review, process de-

sign, simulation of benchmarks and results analysis

with enough evidence to accept or reject the research

hypothesis.

Beyond the development of the plan recovery pro-

cess, our contributions to the MAP area also include a

simulation tool for benchmarks executions and a sta-

tistical evaluation method regarding ﬁnal plan length,

planning time and message exchange.

The rest of the document is structured as follows.

In Section 2, we present the MAP concepts. In Sec-

tion 3, we detail the proposed plan recovery process

along with the simulation tool, while in Section 4 we

describe the experiments and then, we discuss the re-

sults following statistical evaluation method. Finally,

we present conclusion and future work in Section 5.

2 BACKGROUND

In Section 2.1, we present MAS and MAP formal def-

initions. In Section 2.2, we detail plan recovery strate-

gies described in related work.

2.1 MAS and MAP Concepts

A MAS is a set of software entities able of sensing

(sensors) and modifying the environment state using

their actuators (Weiss, 2013). Thus, a MAS is com-

posed by autonomous agents that interact in a shared

environment through a communication protocol. To

interact agents need also a coordination model that

can put together competitive or cooperative agents.

A negotiation protocol is required when competitive

agents are deﬁned. But, when cooperative agents in-

teract in the same environment, a planning protocol

is necessary to deﬁne the individual and group goals,

avoiding conﬂicts in the shared resource usage.

Furthermore, MAP can be understood as the plan-

ning and executing process distributed over multiple

agents (Torre

no et al., 2017). The agent distribution

characteristic focuses on the number of agents and the

roles they adopt during the process of ﬁnding a so-

lution for the problem. The agents involved in the

reasoning stage of synthesizing the sequence of ac-

tions (plan) are the planning entities. Executors are

agents committed to execute actions, such as a robot

or a software entity in a simulator.

The MAP models can be specialized into many

different models and approaches regarding the as-

sumptions made about actions: deterministic, hier-

archical, temporal, non-deterministic and probabilis-

tic. In this work, we assume some premises to deal

with MAP similarly to related work (Borrajo and

Fern

andez, 2019): the environment is fully observ-

able, agents are collaborative, actions are unit cost and

instantaneous, communication process is free of fail-

ures.

An operator θ is a schema that deﬁnes actions us-

ing parameters and is represented by: name(θ), an

identiﬁcation to the operator; pre(θ), the set of pre-

condition that stands for literals required to apply the

operator; and e f f (θ) which is formed by a set of ef-

fects that stands for literals which are added (e f f

)

or deleted (e f f

−

) from the state of the world after ex-

ecuting the operator.

The set of operators, types and parameters deﬁnes

the planning domain. An action is a particular oper-

ator instantiation, where all parameters are replaced

by objects. So, the set of available actions, AG

, is

formed by the combination of the every parameter

value. A tuple that is formed by all available actions,

logical propositions, the environment initial state I

and the goal G is deﬁned as the planning problem.

In a multi-agent environment, agents’ plans coex-

ist. Thus, a MAS requires coordination when agents

execute their plans simultaneously, because they can

compete for some resources or even undo the effects

of each other’s actions. This coordination require-

ment derives from the fact that actions can be pub-

lic or private. According to Deﬁnitions 1 and 2 from

(Brafman and Domshlak, 2008).

Deﬁnition 1. An action is public whenever some

propositions of its preconditions or effect appears in

an action that belongs to other agents. The set of all

public actions is deﬁned by:

Pub

= {α|∃i, j : i 6= j, α ∈ A

, α

∈ A

and (pre(α)∪ e f f (α)) ∩ (pre(α

) ∪ e f f (α

)) 6=

0}.

Deﬁnition 2. An action is private whenever it does

not affect nor depends on actions that belongs to other

agents. The set of all private actions is deﬁned by:

Priv

= A \ A

Pub

When planning concerns only about private ac-

tions, it can be performed locally since actions do not

depend or are not dependent of other agent’s actions

(Komenda et al., 2014). Under this condition, a coor-

dination process is not necessary because there is no

ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics

188

competition or cooperation issues. Therefore, the co-

ordination complexity is formalized as a function of

the number of actions executed by an agent that af-

fect or depend on other agents. Complexity derives

from the agents’ coupling level or the interactions,

that are required to control the dependency among

agents (Brafman and Domshlak, 2008).

Regarding action classiﬁcation (Deﬁnitions 1 and

2) and coordination complexity, planning problems

can be deﬁned as follows. In loosely-coupled do-

mains, most of the available actions are private lead-

ing to low interaction level. In tightly-coupled, agents

need to interact to satisfy goals because of the public

behavior of actions.

In a multi-agent plan actions scheduled to be

started at the same instant must be independent of

each other to guarantee cooperation and avoid compe-

tition. A multi-plan ρ, with π[i, t] = α

, i ∈ AG, t ≥ 1 is

a sequence of actions that can be executed in parallel

by different agents at the same instant t. Thus, the set

of actions of a plan ρ to be executed at the instant t

is A

= {α

|∀i, j ∈ AG : i 6= j, α

∈ ρ, ϕ(α

, α

) =

0}.

Data representation of multi-agent plan ρ is:

ρ =





ε α





An agent updates the environment state by execut-

ing an action. The transition caused by the action α

applied in a state s is deﬁned by Equation 1.

γ(s, α) = (s \ e f f

−

(α)) ∪ e f f

(α) (1)

2.2 Plan Recovery Strategies

Problems may happen during the execution of a plan

because of different reasons. Actions may be not

executed because some of their requirements (pre-

conditions) are not held. For instance, a previous ac-

tion did not performed as planned. The set formed by

these uncontrolled, unexpected and non-deterministic

facts are labeled in literature as exogenous events.

Hence, there must recovery strategies that enable

agents with an adaptation ability insomuch they can

overcome a failure as soon (Ghallab et al., 2014).

Basically, there are two types of recovery strate-

gies and they differ from their results (ﬁnal plan). In

order to illustrate the difference between the replan-

ning results and repairing strategies, after the occur-

rence of a single failure, consider the conditions pre-

sented in Table 1.

Let the failure be the impossibility of executing

action α

because of some exogenous events. The re-

planning strategy provides a new plan replacing the

sufﬁx (α

, . . . , α

) of the initial plan, starting from

action α

, by a new sequence of actions α

, . . . , α

Here, nothing can be assumed about the ﬁnal plan

length, which can be bigger or smaller than the ini-

tial one. On the other hand, the repairing strategy

tries to return the environment state to the expected

conditions that support the execution of α

. Thus,

a new item β, that can be either a single action or a

sequence of actions, after α

and then preserves the

sufﬁx α

, . . . , α

. In this case, the ﬁnal plan is greater

than the initial one.

Table 1: Difference in results of recovery strategies.

Strategy

Initial Final

plan plan

Replanning [α

, . . . , α

] [α

, α

, . . . , α

]

Repairing [α

, . . . , α

] [α

, α

, β, α

, . . . , α

]

In (Komenda et al., 2014), authors propose a

multi-agent plan repair in dynamic environments

where a failure is caused by a state perturbation or

by an action removal from the plan. Three algorithms

are described: back on track (BoT), lazy repair (LR)

and repeated lazy repair (RLR).

The Hierarchical Iterative Plan Repair (HIPR) ap-

proach, proposed by (Mohalik et al., 2018), combines

an architecture and an algorithm to support hierarchi-

cal agent teams to replan after a hazard occurrence.

Agents try to repair its current plan locally or sent a

signal and try to recovery from failures related to pre-

conditions or actions.

The DRA

∗

is an extension of A

∗

algorithm suited

for the repairing of sequential plans. The goal-

set modiﬁcations and actions’ costs updates are ad-

dressed (Gouidis et al., 2018).

In (Cashmore et al., 2019), authors tackled the

problem of replanning for robots using temporal plan-

ning problem. Actions have well-deﬁned duration and

during their execution it is likely to replan in order to

recover a failure or to avoid wasting resources, such

as time and battery.

3 PLAN RECOVERY PROCESS

The plan recovery process proposed in this work com-

bines three MAP dimensions related to dynamic envi-

ronments: planning, coordination and execution. This

combination was motivated by the literature review

that highlighted an important conclusion: the need to

investigate planning and execution in dynamic envi-

ronments where exogenous events occur and render

plans useless (Torre

no et al., 2017).

In the proposed process, there are two types of en-

tities. The coordinator is responsible for handling a

Plan Recovery Process in Multi-agent Dynamic Environments

189

pair of ﬁles that represents planning domain and prob-

lem. Those ﬁles are described according to Multi-

Agent Planning Domain Deﬁnition Language (MA-

PDDL). Then, the coordinator searches for a plan-

ning problem solution. This initial (and centralized)

plan is transformed to a set of single-agent plans. In

such plans, actions are scheduled to a common step

whether they can be carried out simultaneously by

their executors. Then, these plans are sent to the co-

ordinator to start a monitoring loop.

The second type is deﬁned as agents that play

planning and executing roles. Therefore, each agent

has autonomy to run a deliberation process, whenever

it needs. Agents have the commitment of executing

the planned actions. Moreover, agents also performs

coordination activities to guarantee an environment

free of conﬂicts.

Regarding these premises, the dimensions are

handled in staggered solution when agents can try dif-

ferent strategies regarding their capabilities. The pro-

cess design can be summarized as a three-phase se-

quence that agents ﬁrst try to recover from a failure

using a local planning. If in this phase is impossible

to ﬁnd a solution, the agent that detected the problem

interact with other agents asking for help. Whether

some agents return positive answers, the caller will

compare the solutions and choose the best (plan with

the smallest number of actions) and coordinate with

all agents the new execution condition. Otherwise,

the caller agent triggers a centralized planning pro-

cess that is performed by a coordinator agent.

The plan recovery process is presented in Figure

1, where the pipeline of each entity type is described

in individual lanes. The process activities are detailed

in Sections 3.1-3.11 highlighted by section numbers.

3.1 Problem Instance

The planning domain and problem ﬁles are parsed to

identify the initial state, goals and operators. Then the

available actions are computed and the literals that are

updated in action’s effects are listed. Those literals are

special because they deﬁne the search space (relevant

facts). The other literals are rigid facts because they

are not affected by action results. Both classiﬁcation

are important since only relevant facts must remain

after an encoding phase with the purpose of reducing

the search space to be explored in the planning phase.

3.2 Centralized Planning

The ﬁrst planning activity is carried out centralized by

the coordinator. In this step, agents are considered as

resources. In addition, to compute the plan, this activ-

ity is also important to select agents to be committed

to execution.

In this sense, the centralized planning provides

a solution that minimizes the number of actions re-

quired to turn the environment initial state to the goal

state. Thus, only the executors of those actions are

granted to join the next activities. In case the planning

problem has no solution, no execution is triggered and

no further activities are performed.

3.3 Plan Coordination

After the deﬁnition of the initial plan, the coordina-

tor starts to build the multi-agent plan ρ. First, each

agent action is separated in individual lists. Then, a

loop is started where the ﬁrst action of each list is

checked about the possibility to be carried out simul-

taneously from the initial state I. The actions that sat-

isfy the conditions are popped from their agents’ list.

Otherwise, an empty action (idle state) is deﬁned to

the respective executor. Those actions are placed in

multi-agent plan and simulated to compute the next

expected environment state. The loop ﬁnishes when

every action of the initial plan is added to ρ.

3.4 Sending Problem and Plans

As soon as the multi-agent plan is deﬁned, coordi-

nator sends the single-agent plans (ρ matrix rows) to

their owners. Moreover, it sends a fragment of the

planning problem that is formed only by the initial

state, goals and available actions of each agent. Thus,

information privacy is kept because no agent knows

about other agents’ capabilities.

3.5 Environment Monitoring

At this point, coordinator starts to monitor the envi-

ronment with a double concern. First, it controls the

plan execution of every agent by receiving messages

when they ﬁnish their tasks. When there are no more

actions to be performed, the coordinator runs its sec-

ond veriﬁcation, namely, goal satisfaction. This is an

important activity because of the possibility of exoge-

nous events that impair the plan execution leading to

failures. If the coordinator detects a problem, it starts

a new centralized planning and follows with the next

pipeline activities.

3.6 Plan or Coordination Message

The ﬁrst activity in the agent’s pipeline is receiving

message about plan and problem. Now, each agent

knows its sequence of actions, that was checked and

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190

Figure 1: Plan recovery process.

scheduled by to coordinator to provide an execution

phase free of conﬂicts.

This activity can also be triggered when another

agent needed to updated its plan (recovery) and then

send a message to inform its efforts (number of ac-

tions) to overcome a failure. Hence, all the receivers

adjust their plans, adding waiting steps (empty ac-

tions), as a new coordination phase. We highlight that

the coordinator is not warned by the sender because it

only needs to control the end of agents’ plans.

3.7 Action Execution

The execution phase starts with agents’ evaluations

about the conditions to run their actions. Each agent

analyses the current environment state (s

) and veri-

ﬁes the possibility to execute the next action. When

the preconditions are held, the agent executes the ac-

tion α, turning s

to s

t+1

according to Equation 1, and

returns to the evaluation step.

After the execution of the last action, agents send

a message to the coordinator to inform that the tasks

are done. At the evaluation step, the agent may detect

a failure when its next action can not be carried out

because of error in the preconditions. Thus, it starts

the recovery process.

3.8 Local Repair

The ﬁrst step of the plan recovery process is per-

formed by the agent that has just detected the failure.

Then, it starts a local repair activity. The agent applies

the repairing strategy and tries to ﬁnd a solution that

leads the environment state to a condition where the

preconditions of the failed actions are satisﬁed.

If the agent ﬁnds a possible solution, it updates its

own plan by adding the actions in the beginning of its

list, keeping the sufﬁx of the plan from the failed ac-

tion. In the sequence, agent informs other executors

that it needs to run more actions to bring the environ-

ment to expected state. However, it is likely that the

agent does not ﬁnd a solution because of a lack of ca-

pabilities. Therefore, the next attempt is to ask other

agents for help.

3.9 Ask for Help

When an agent asks for help, it shares the conditions

the environment state needs to satisfy to guarantee the

execution of the failed action. As soon as other agents

receive the message, they try a local repair to send

back the results. In order to keep the information pri-

vacy, agents only share the number of actions they

need to recover, instead of sharing the actions them-

selves.

When just one agent returns a positive answer,

this is the solution. However, in the presence of two

or more answers, the agent evaluates the possibilities

and chooses the best solution considering the small-

est number of actions. Then, the selected executor

is warned to update its plan by adding the solution,

while other agents just receive a coordination message

Plan Recovery Process in Multi-agent Dynamic Environments

191

about the numbers of actions that the chosen agent

needs to perform.

3.10 Ask for a Centralized Planning

When the previous phases (Local Repair and Ask for

Help) fail in ﬁnding a solution, the next activity of

the agent that detected the failure is to send a mes-

sage asking the coordinator for a centralized planning.

While the earlier attempts applied the repairing strat-

egy, now the solution is tried through replanning.

As soon as the coordinator receives the message,

it runs a centralized planning. But different from

the ﬁrst round, the coordinator plans from the current

state rather than the initial one. If it ﬁnds a solution to

reach the goal from that state, it follows the pipeline

(Plan Coordination - Sending Problem and Plans - En-

vironment Monitoring), otherwise no further activity

is carried out.

3.11 New Coordination

Agents may receive messages about a new coordina-

tion phase. These messages are sent in two condi-

tions. First, when one agent runs a local repair activ-

ity and ﬁnds a solution. Then, the others agents needs

to adjust their plan regarding that new solution. Sec-

ond, a local repair fails, but after asking for help, the

agent receives one positive answer. In this case, all

agents, but the chosen one, updates their plans to wait

for the execution of that solution.

4 EXPERIMENTS

In this section, we detail the experiment setup (Sec-

tion 4.1) and discuss the results (Section 4.2).

4.1 Experiment Setup

In order to evaluate the proposed plan recovery pro-

cess, we used open source software to build a simula-

tion tool. As a solution for the parser and planning

issues (Sections 3.1, 3.2, 3.8 and 3.9), we decided

to use the PDDL4J

JAVA library (Pellier and Fior-

ino, 2018). Regarding to simulation engine, we chose

the Repast Symphony

platform for supporting agent-

based modeling and simulation (North et al., 2013).

The simulation tool is available in an repository

https://github.com/pellierd/pddl4j

https://repast.github.io/

https://gitlab.com/publicrepo/lcmap-de

The case studies applied in the experiments were

based on the domains and problems used in the

Competition of Distributed and Multi-agent Planners

(CoDMAP), which was carried out together with the

workshop on Distributed and Multi-agent Planning

(DMAP) at the ICAPS 2015 (cod, 2015). Regard-

ing the most used case studies described in the related

work, the domains chosen from CoDMAP were satel-

lite, logistics and taxi.

The experiments were carried out under multiple

conditions. The failure probabilities varied from 0.1

to 0.9 following a 0.1 step. Each case study had

three different conﬁgurations which were simulated

30 times. The conﬁgurations were selected according

to the ratio of public actions with the purpose of sim-

ulating problems with different levels of agent cou-

pling. Under those conditions, the experiments were

ran by 2430 simulations. The setup description re-

garding the number of agents, goals and actions in

each domain, is summarized in Table 2, where values

in cells stand for the minimum and maximum values.

Table 2: Setup description.

Domain Agents Goals Actions Public (%)

Satellite 3;5 6;10 497;1473 26.2;40.4

Logistics 3;5 6; 10 78; 308 61.5;62.3

Taxi 4;7 4;7 28; 126 100

We carried all experiments out in a single com-

puter with a Intel Core i7-10510U CPU and 16 GB

RAM. The operational system was Ubuntu 20.04.1

LTS 64-bit.

4.2 Discussion

The plan recovery process was evaluated regarding

three metrics: planning time, ﬁnal plan length and

message exchange. The case studies were classiﬁed

into three groups according to the agents’ coupling

level. The problems from the satellite, logistics and

taxi were labeled as loosely, intermediate and tightly

coupled domains, respectively. The results of each

group are discussed individually and a global evalua-

tion is presented.

The ﬁrst important step towards the evaluation of

the results is the deﬁnition of how many times each re-

covery activity (local repair, ask for help and central-

ized planning) was performed. The information about

recovery activities, planning time, ﬁnal plan length

and message is presented in Figures 2 to 3.

Regarding the loosely-coupled domain simula-

tions, the recovery activity was restricted to local re-

pair (Figure 2(a)). This behavior is justiﬁed by the

fact that agents carry out, at most, public actions. The

highest level of coupling is 40.2% (Table 2), hence,

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192

agents do not depend on or affect other agents. Thus,

agents do not need to interact to solve failures. There-

fore, the motivation hypothesis that agents’ autonomy

in performing local repair is better explored in envi-

ronments with low levels of interaction is accepted.

Regarding the intermediate-coupled domain sim-

ulations, agents could not solve the failures by using

the local repair activities. Indeed, they need to interact

asking for help (Section 3.9). Sometimes, they also

need to request for the centralized planning. Those

recovery strategies are shown in Figure 2. The reason

of that justiﬁes this different behavior in the logistic

domain simulations is inherited from the set of avail-

able actions. Thus, agents do not have all the capabil-

ities that are required to solve a problem. Hence, they

need to cooperate towards the search for a solution.

Regarding the tightly-coupled domain simula-

tions, agents needed to request more often for a cen-

tralized planning, as shown in Figure 3. The ratio of

public actions in the set of available actions was 100%

of public actions (Table 2). Thus, every action either

depends on or affects other actions. Therefore, it was

expected that the solution for the failure would only

be found by a centralized planning activity where all

actions were available in a common process.

The execution of higher recovery strategies in-

creases from loosely to tightly domains. The analy-

sis of the averages of the results from each strategy is

detailed in Table 3 by domains, which demonstrates

that: (i) the frequency of local repair calls in tightly-

coupled domains is 3.11× bigger that in loosely; (ii)

ask for help and centralized planning activities are

carried out 1.73× and 8.68× more often in tightly

than in intermediate domains. Therefore, the coupling

level among agents increases the complexity of the re-

covery process.

Table 3: Strategies calls (means) by domains.

Strategy Loosely Intermediate Tightly

Local Repair 2.73 7.76 8.5

Ask for Help 0 2.18 3.78

Centralized

0 0.28 2.43

Planning

Further conclusions can be drawn from the eval-

uation of the metrics shown in Figures 4. Regard-

ing the ﬁnal plan length (Figure 4(a)), although the

intermediate-coupled domain simulations have the

complexity levels (number of public actions) than

satellite domains, they presented ﬁnal plans with a

higher number of actions. The logistics domain sim-

ulation applied repairing (local repair and ask for

help) more than other simulations, and that is the

reason for bigger plans. The main drawback of this

strategy derives from the fact that repairing tends to

(a) Local repair (b) Local repair

Figure 2: Loosely and intermediate-coupled domains.

build bigger plans. The taxi domains highlighted

plans with fewer actions because of replanning strat-

egy (Komenda et al., 2014).

Regarding the planning time analysis (Figure

4(b)), loosely domains showed irrelevant and small

values when compared to the other groups where only

local repair was needed and repairing strategy tends

to be faster. The ﬁnal planning time in logistics was

higher than the values of taxi domains since plans

were bigger. Hence, more actions were likely to fail

and more recovery activities had to be performed.

(a) Local repair (b) Ask for help.

Figure 3: Recovery in tightly-coupled domains.

The message exchange (Figure 4(c)) highlights

the interaction of agents after facing a failure. Since

the loosely-coupled domains handle the problem with

local repair strategy, the agents only need to exchange

message to provide a new execution coordination.

However, in the intermediate and tightly-coupled do-

mains, the amount of messages to be exchanged tends

Plan Recovery Process in Multi-agent Dynamic Environments

193

to be higher than the ﬁrst one because agents needs to

ask for help and request a centralized planning with

more messages sent. Therefore, this is another ev-

idence that the hypothesis that agents’ autonomy is

better explored in environments with low levels of in-

teraction can be accepted.

(a) Final plan length. (b) Planning time.

Figure 4: Global evaluation.

5 CONCLUSION

In this work, a plan recovery process to dynamic envi-

ronments affected by exogenous events was proposed.

The process differs from related work because it com-

bines the replanning and repairing strategies provid-

ing an staggered solution that is formed by local re-

pair, ask for help and centralized planning.

In order to investigate the process performance,

a MAP simulation tool was developed to run differ-

ent problems. We evaluated case studies with differ-

ent levels of interaction among agents. We accepted

the motivation hypothesis that agents’ autonomy in

performing local repair is better explored in environ-

ments with low levels of interaction. Moreover, we

showed that the coupling level among agents, inher-

ited from the public actions ratio, increases the com-

plexity of the recovery and the metrics related to plan-

ning time, ﬁnal length and message exchange.

The contributions of this work are: a three-phase

plan recovery process, a simulation tool, and a sta-

tistical evaluation method to MAP in dynamic envi-

ronments. The study of other failures caused by the

agents removal and the use of distributed approach to

agents’ coordination are suggestions of future works.

ACKNOWLEDGEMENTS

Prof. C. G. Ralha thanks the support received from

the Brazilian National Council for Scientiﬁc and

Technological Development (CNPq) for the research

grant in Computer Science number 311301/2018-5.

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