Efﬁcient Selection of Consistent Plans Using Patterns and Constraint

Satisfaction for Beliefs-Desires-Intentions Agents

Veronika Kurchyna

∗

, Ye Eun Bae, Jan Ole Berndt and Ingo J. Timm

German Research Center for Artiﬁcial Intelligence (DFKI),

Cognitive Social Simulation, Behringstr. 21, 54296 Trier, Germany

Keywords:

BDI Agent, Agent-Based Simulation, Agent Deliberation, Complexity Optimization.

Abstract:

Agent-based models can portray complex systems that emerge from the actions of individual actors. The use

of many agents with complex decision-making processes in a large action space is computationally intensive

and leads to slow simulations. This work proposes an alternative approach to agent deliberation by pre-

computing valid action sequences and simplifying decision-making at runtime to a linear problem. The method

is demonstrated with pandemic self-protection as use case for an implementation of the concept. Additionally,

a step-by-step guideline for application of this approch is provided.

1 INTRODUCTION

Agent-based models (ABMs) and multiagent systems

(MAS) are widely used to study various complex

real-life systems, addressing diverse questions rang-

ing from industrial applications, such as agriculture

and land use (Bert et al., 2011), to social phenomena,

such as family planning (Rodermund et al., 2018) and

health behaviour (Cuevas, 2020). Agents are designed

to act autonomously while pursuing their goals, oper-

ating under constraints such as limited resources, in-

teractions with other agents, or incomplete knowledge

of their environment (Magessi and Antunes, 2015).

To formalize the decision-making processes of indi-

vidual agents, the Beliefs-Desires-Intentions (BDI)

architecture is commonly used (Caillou et al., 2017).

The typical deliberation process of an agent in-

volves taking into account its knowledge of the world

and current state—alongside its desires to formulate

intentions. These intentions represent the concrete ac-

tions the agent plans to take in order to achieve its ob-

jectives. A key challenge arises when conﬂicting be-

havioural options emerge. Various approaches have

been proposed to address this issue and enhance the

efﬁciency of agent deliberation. For instance, agents

can prioritize their desires and ﬁnd ways to recon-

cile the competing courses of action (Timm, 2004).

A goal deliberation method is proposed, aiming at re-

ducing computational resources and the burden of en-

suring the consistency of agents’ goal sets by mak-

∗

Corresponding author

ing agents select their own goals based on the sit-

uation (Pokahr et al., 2005). Moreover, the ad-hoc

computation of consistent and logical plans for agents

is commonly used in practice despite being resource-

intensive, particularly for models with large numbers

of agents, such as used in digital twins in smart cities

contexts (Caillou et al., 2017), as well as large action

spaces (Tkachuk et al., 2023). Another attempt was

made using a context-sensitive deliberation frame-

work, which prompts agents to employ alternative de-

liberation methods, instead of following default be-

haviour, only when there is a relevant change in con-

text. This approach helps reduce the computational

costs of decision-making (Jensen et al., 2022).

In light of such challenge, this paper proposes an

alternative approach that leverages best practices es-

tablished in software engineering, so-called design

patterns. By employing these techniques, we sug-

gest pre-simulation generation of consistent plans

for agents to follow. This approach eliminates the

need for at-runtime ﬁltering of options and consis-

tency checks, providing a more efﬁcient and effective

means of agents’ decision-making in ABMs.

We begin by introducing the fundamentals of

ABMs, outlining the relevant software desing patterns

applied in this work, and providing a brief overview of

key terminology, along with examples of our method.

We then delve into the procedure in detail, illustrating

it with a practical use case and offering a step-by-step

guide for applying the apporach to other contexts. Fi-

nally, the runtime efﬁciency of the proposed method

Kurchyna, V., Bae, Y. E., Berndt, J. O. and Timm, I. J.

Efﬁcient Selection of Consistent Plans Using Patterns and Constraint Satisfaction for Beliefs-Desires-Intentions Agents.

DOI: 10.5220/0013141700003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 1, pages 333-341

ISBN: 978-989-758-737-5; ISSN: 2184-433X

333

is demonstrated using a model for choosing protec-

tive behaviours in the context of the COVID-19 pan-

demic with comparisons made to hypothetical alter-

native implementations of decision-making.

2 FOUNDATIONS

The foundation section of this paper introduces the

basic principles of ABM and the BDI architecture

with a particular focus on the formalisation of de-

liberation. Additionally, design patterns, speciﬁcally

strategies, and their application within an ABM con-

text are discussed.

2.1 Beliefs, Desires and Intentions

ABMs simulate complex systems using autonomous

agents that interact with their environment and each

other in a reactive or goal-directed manner. In

such models, complex system-wide dynamics re-

sult from the individual-level behaviours of the

agents (Wooldridge and Jennings, 1995). Differ-

ent approaches for formulating agents exist, among

which BDI is a widely used architecture to describe

agents.

Agents operate on their Beliefs, which are com-

posed of subjective observations, knowledge and as-

sumptions, and Desires, which describe goal states

agents wish to achieve. Based on their beliefs, agents

identify possible courses of actions in an Option Gen-

eration function. These options are ﬁltered and pri-

oritized based on feasibility and compatibility with

desires. Finally, agents select one option as Inten-

tion to fulﬁll a certain desire and act upon it. The

resulting changes to the environment are fed back as

sensor input, which leads to a revision of beliefs and

checking if an agent remains committed to a chosen

option (Saadi et al., 2020).

2.2 Design Patterns: Strategies

Design patterns serve the purpose of reusable, mod-

ular and maintanable software engineering and pro-

pose best practices in several domains of software.

These design patterns are categorized by their pur-

pose, such as object creation, composite structures

and behaviour (Gamma et al., 1994). For this pa-

per, Behavioural Patterns are important, with dif-

ferent means of deﬁning program behaviour in a

modular way. Strategies are the pattern that will

be used to implement agent behaviour. The pur-

pose of strategies is to provide variations of code

which can be easily switched out programmatically

without large, hard-coded condition-action struc-

tures (Christopoulou et al., 2012).

A strategy is typically implemented as an inter-

face which deﬁnes methods, with each strategy imple-

menting the required functions. As a result, executing

objects require no knowledge of the inner workings

of a strategy and preserve the principle of encapsu-

lation (Wick and Phillips, 2002). The authors see a

major beneﬁt of using strategies for agent-behaviour

in the possibility to have agents execute a list of strate-

gies and move plausibility checks into the strategy in-

stead of a higher-level code block with more hard-

coded conditions.

2.3 Terminology and Deﬁnitions

To ensure a uniﬁed understanding and distinction of

terminology used in this paper, the deﬁnitions are

given as follows:

• Strategy. Using the term as used in the context of

design patterns in software development, a strat-

egy deﬁnes a behaviour or action which is exe-

cuted if certain conditions are met (Christopoulou

et al., 2012). Thus, a strategy is not a ﬁrm de-

cision of speciﬁc actions that will be performed,

but rather the willingness to perform them if the

preconditions are met.

• Behaviour. While the strategies in this model

determine when something should be done, be-

haviours deﬁne what needs to be done, such as in-

creased adherence to safety recommendations or

reduced contacts with others.

• Behaviour Package. A set of consistent strate-

gies which covers all possible preconditions, en-

suring that agent behaviour is well deﬁned at each

simulation step. Thus, a selected package resem-

bles Intentions of an agent. In this context, we use

the term plan synonymously.

• Package Class. Depending on the evaluation

mechanism, several packages can be evaluated

into the same (or a close) score which suggests

high similarity between packages. Assuming that

packages of the same class are equivalent means

of equal value, agents can be indifferent and do

not prefer a speciﬁc package, but rather a class

from which any package can be chosen randomly.

Programatically, these classes allow representing

equivalent packages as elements of an unordered

set.

• Constraints. A set of logical expressions which

must all be evaluated to True for a plan to be

valid (Brailsford et al., 1999).

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334

Three types of constraints are likely to be encoun-

tered when modelling behaviours, which are exampli-

ﬁed with A, B and C as boolean variables representing

three different strategies:

1. Mutual Exclusivity. A =⇒ ¬B, meaning that B

can never co-occur with A.

2. Co-Occurence. A =⇒ C, meaning that whenever

A holds true, C must necessarily also be true.

3. Deﬁnedness. B ⊕ C, meaning that, using the

XOR-Operator, either B or C must be true.

As shown in Table 1, the application of these

constraints eliminates 5/8 combinations, with each

remaining table row being an executable behaviour

package. Alternatively, the three sample constraints

can also be expressed in a matrix, as shown in Ta-

ble 2. 0 denotes mutual exclusivity and 1 forced

co-occurence. Empty cells indicate independence

between two variables. It is important to remem-

ber that this graphical representation cannot convey

the deﬁnedness-requirement. However, this format

can give an overview of necessary relationships and

the graphical representation facilitates deriving corre-

sponding logical constraints in a structured, commu-

nicable manner.

This approach is essentially a modiﬁed form of

the Boolean Satisﬁability (SAT) problem, which deals

with the question of whether a given logic expression

has at least one conﬁguration of boolean values that

evaluates to true. While the veriﬁcation of one con-

ﬁguration is fast, an exhaustive search is an exponen-

tial endeavour. Our approach includes the solving of

the #-SAT problem, which requires a full enumeration

and evaluation of all possible boolean conﬁgurations

that satisfy all constraints (Creignou and Hermann,

1996). As such, the complexity of the initial pack-

age generation and ﬁltering is exponential. However,

we also assume that the action space of agents is not

only ﬁnite, but also small enough for the exponen-

tial nature of the underlying theoretical problem to be

handleable. Further, we also assume that the action

Table 1: Truth Table summarising possible conﬁgurations

and ﬁltering out invalid rows.

A B C

((B ∧ ¬C) ∨ (¬B ∧ C))

∧(A =⇒ ¬B) ∧ (A =⇒ C)

1 F F F F

2 F F T T

3 F T F T

4 F T T F

5 T F F F

6 T F T T

7 T T F F

8 T T T F

Table 2: The matrix of the example with mutual exclusivity

between A and B, as well as necessary C in case of A.

A B C

A 0 1

B 0 0

C - 0

space is largerly static - no new actions or axioms are

added between model runs. Thus, we can save the re-

sults of an exhaustive search to a ﬁle and perform the

exponential enumeration only once.

3 USE CASE: PANDEMIC

MODELLING

The use of ABMs has gained signiﬁcant popularity in

studying pandemics, particularly due to the ongoing

COVID-19 pandemic (Lorig et al., 2021). It serves as

an illustrative example of how agents need to handle

intricate situations where a diverse range of actions

exists, some of which may be partially or fully mutu-

ally exclusive. To model agent behaviours in response

to the pandemic, researchers often rely on routines

and needs models. However, applying the BDI archi-

tecture to formalize agent behaviours leads to an in-

tricate decision process. Agents must possess the ca-

pability to identify and reject any combination of be-

haviours that are inconsistent or mutually exclusive.

Thus, this use case is well suited for the demonstra-

tion of this strategy-based constraint approach.

In this study, we focus on a model that en-

compasses a wide range of behaviours available to

agents. These behaviours include actions such as self-

quarantine in case of illness, compliance with exter-

nal quarantine orders, random rapid testing, testing in

case of symptoms, avoiding crowded locations, and

varying levels of contact frequency and preventive

measures like wearing masks correctly and maintain-

ing physical distancing during interactions.

We choose a total of 8 behaviours agents can

choose from. However, since two of these behaviours

have numeric levels (contact frequency and degree of

preventive measures), they were coded into multiple

binary choices to avoid fuzzy logic with increased

bases for the exponential number of possible combi-

nations. With a total of 14 strategies, there are over 16

thousand possible combinations of these behaviours

that an agent could potentially implement or refrain

from:

• Q

: Agents will quarantine voluntarily if they de-

velop disease symptoms

• Q

: Agents will comply with a quarantine order

due to an ofﬁcial positive test or contact tracing

Efﬁcient Selection of Consistent Plans Using Patterns and Constraint Satisfaction for Beliefs-Desires-Intentions Agents

335

• Cw

: Agents will avoid crowded locations (with

more than x visitors, assumed to be a limit at

which distancing becomes no longer possible)

• T

: Agents will occasionally randomly perform a

rapid test

• T

: Agents will perform a rapid test if they feel

disease symptoms

• Q

: Agents will quarantine voluntarily even if a

rapid test is negative

• C

: Agents cease all contacts entirely

• C

: Agents have a low level of contacts during

their daily routines

• C

: Agents have a medium level of contacts dur-

ing their daily routines

• C

: Agents have a high level of contacts during

their daily routine

• P

: Agents put high efforts into preventing an in-

fection or diseapse spread

• P

: Agents put medium effort into protecting

themselves and others

• P

: Agents put low effort into protecting them-

selves and others of infection

• P

: Agents refuse all types of protective behaviour

However, a substantial number of these combina-

tions lacks practicality or coherence. For instance, an

agent who restricts themselves to low contacts would

never have a large number of contacts simultaneously,

and an agent who willingly chooses to self-quarantine

upon experiencing illness symptoms would be un-

likely to refuse quarantine after receiving a positive

test result.

Such inconsistencies can arise from conﬂicting

goals. As such, the formalisation of forbidden or re-

quired combinations contributes to the resolution of

goal conﬂicts in agents, since they can only choose

from valid conﬁgurations without logical inconsisten-

cies. While this does not solve the question of goal

priorization, this step forbids attempts at satisfying

conﬂicting goals through incompatible and contradic-

tory actions.

3.1 Behavioural Packages

In classic BDI, agents construct a plan using a

bottom-up approach, evaluating different options re-

garding feasibility, compatibility with own goals and

possible outcomes. This is a process repeated by each

agent multiple times over the course of a simulation,

with agents typically operating on the same set of

rules and action spaces under different individual con-

ditions and desires.

Behavioural Packages advocate a top-down ap-

proach in which agents select from a list of be-

haviours, forming a consistent plan that can be ex-

ecuted. Using strategies, which are either enabled

or disabled, agents gain ﬂexibility in their decision-

making by providing a larger array of choices than

a manual selection. For that, one may also use aids

such as different levels represented as individual be-

haviours - while this increases the number of avail-

able actions artiﬁcially, handling of different levels of

the same behaviour type is easy with a set of binary,

mutually exclusive decisions. Assuming that each be-

haviour can be both a consistent, repeated course of

action (e.g. the number of contacts during work etc.)

as well as the general willingness to do something

(e.g. quarantining in case of illness symptoms), we

can consider the deliberation step as a periodic re-

evaluation of which behavioural combination to use.

As such, instead of deciding on individual be-

haviours, an agent would choose a package of be-

haviours, which corresponds to choosing a plan from

the set of possible intentions. These sets are referred

to as behavioural packages which must give unam-

biguous instructions to the agent. This means that,

besides consistency, behavioural packages also must

be complete: for behaviour types such as contacts

and preventive measures, a plan in which nothing was

chosen at all may be free from contradictions, but in-

complete, for an agent’s behaviour in all situations

that may arise during simulation must be deﬁned. As

a result, one also must consider behaviour types, of

which at least one level needs to be selected.

In the context of the BDI-architecture, as shown

in Figure 1, pre-generated plans replace the option

generation and ﬁltering. Using a scoring or selection

function, agents choose a plan from this existing set

of options as their intention.

Figure 1: Concept of how Behavioural Packages are inte-

grated in the BDI cycle using a selection function.

3.2 Building the Matrix

For the generation of the set of valid plans, we can

use a constraint satisfaction approach by ﬁrst con-

sidering which behaviours are mutually exclusive, or

logically co-occur. Table 3 summarises the differ-

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336

Table 3: Matrix of behavioural combinations that always (1)

or never (0) co-occur at the same time. Empty cells mean

no rules for co-occurence are deﬁned.

1 1 1 0 0

0 0

1 1 0 0

1 1 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0

0 0 0 0

0 0 0 0 0 0 0 0 0 0

ent behavioural combinations and is to be read row-

wise. Note that this matrix is not symmetrical, since

some behaviours can co-occur, while the inversion

may become a must co-occur, such as Q

and Q

As an important disclaimer, it should be stated that

this is merely a demonstration of how such a be-

havioural matrix can be set up, and further empirical

research might be necessary to include probabilities

of behavious co-occuring in real life. For the purpose

of demonstration, however, we make basic common-

sense assumptions.

The ranges [0,1] score the probability of co-

occurence, with 0 signifying mutual exclusivity and

1 meaning mandatory co-occurence.

3.3 Filtering Using Constraints

Once a matrix has been built, the generation of con-

straints may either be automated or, for small use

cases, simply determined manually. For our example

in Table 3, eight constraints are sufﬁcient to express

all conditions which a consistent plan must meet:

1. Q

=⇒ (Q

∧ T

∧ Q

)

2. T

=⇒ (Q

∧ T

)

3. T

=⇒ (Q

∧ Q

)

4. Q

=⇒ (Q

∧ Q

∧ T

)

5. C

⊕ C

6. C

⊕ P

7. C

=⇒ ¬(Q

∨ Q

∨ Qw

∨ T

∨ Q

∨ C

∨

∨ C

∨ P

)

8. P

=⇒ ¬(Q

∨ Q

∨ Qw

∨ T

∨ Q

∨ C

∨

∨ P

)

By generating a 2

binary table, with n being the

number of possible behaviours, these constraints are

used to ﬁlter out all rows with invalid combinations.

After ﬁltering, 58 behavioural packages remain.

3.4 From Plans to Intenions

The major beneﬁt of our strategy-and-constraint ap-

proach is the pre-computation of valid action combi-

nations into packages that deﬁne agent behaviour to

reduce computational burden at runtime. However,

agents still need to choose a plan which aligns with

their desires, such as by computing utilities or using

other means of selection. During the development of

this method, several approaches have been explored

by the authors, including decision trees, fuzzy sets

and utility scoring. After careful examination of the

advantages and disadvantages of each method, the

plan selection function was not included as part of this

approach, since the suitability of a given method de-

pends on model-speciﬁc questions such as distinction

between actions, data availability for comparison and

empirical knowledge regarding decision mechanisms.

To complete the demonstration of this concept,

this work will present a scoring-approach based

on a psychological theory, which will allow agents

to choose an appropriate behavioural package us-

ing constant-time operations as efﬁcient mechanism

which is unaffected by the size of the action space.

In other words, the number of strategies, packages or

agents will not affect on the calculation needed for

each agent to choose a behavioural package, having

the same number of computational steps.

4 CONCEPT SUMMARY

Before demonstrating the integration of behavioural

packages into the agent decision mechanisms, we pro-

vide a summary of the individual steps to apply the

proposed concept to an ABM:

1. Deﬁne Behaviours. Identify relevant behaviours

agents can perform and the conditions under

which it would make sense for them to execute

those behaviours.

2. Deﬁne Strategies and Levels. Since strategies

are binary, selected behaviours might have to be

split into different, mutually exclusive strategies

differing by the level/magnitutde of execution.

3. Deﬁne Relationships. For each combination of

two strategies, deﬁne whether there exists mutual

exclusivity or mandatory co-occurence.

4. Deﬁne Constraints. Deﬁne constraints to de-

scribe the relationships in the matrix using logic

expressions. Remember that more complex con-

ditions such as XOR might not be visualized.

5. Filter Packages. From a set of n

packages, ﬁl-

ter out all that violate any of the deﬁned con-

Efﬁcient Selection of Consistent Plans Using Patterns and Constraint Satisfaction for Beliefs-Desires-Intentions Agents

337

straints. Checking an individual combination for

constraint satisfaction has a runtime of O(n

6. Design Choice Mechanism. Depending on the

characteristics of the model, data availability and

the action space, the choice mechanism can be de-

signed accordingly, such as using decision trees,

approximation heuristics or utility functions.

7. Implementation. Implement the strategies using

design patterns as guideline. For higher efﬁciency,

save valid packages to a ﬁle which is processed

during model initialization. Implement the cho-

sen mechanism for agents to choose the class of

packages appropriate for their current state.

5 IMPLEMENTATION: CUSTOM

SCORING FOR PANDEMIC

SELF-PROTECTION

Using the same behavioural strategies as deﬁned in

Section 3, we build up a custom scoring of packages

based on a psychological theory to demonstrate how a

set of valid plans can be integrated into a model using

constant-time operations.

The chosen psychological theory is the Protec-

tion Motivation Theory (PMT) (Hedayati et al., 2023),

which delivers a framework for the explanation of

seemingly irrational behaviour. When individuals

confront a threat, they can either react adaptively to

protect themselves, or deny the threat with maladap-

tive reactions. Factors such as fear, self-efﬁcacy, per-

ceived response costs and rewards are weighed up

against each other to determine the reaction (Rogers,

1983). Previous works, such as Kurchyna et al. (2024)

have demonstrated the application of PMT in the con-

text of agents. Additionally, a variety of empirical

studies regarding PMT and the COVID-19 pandemic

is available to support modelling efforts (Hedayati

et al., 2023).

Deﬁning Protection Motivation as the difference

between Threat Appraisal (Perceived danger) and

Coping Appraisal (Ability to perform protective mea-

sures), the PMT offers a scale between adaptive (pos-

itive difference) and maladaptive (negative differ-

endce) responses and yields a single score which al-

lows identifying an individual’s stance on the spec-

trum of possible responses.

To use the PMT for a custom scoring system, we

take advantage of the adaptive-maladaptive axis and

assign each behavioural package a rating which cor-

responds to its package class as deﬁned in Section 2.3.

This is achieved by attributing a partial score to each

individual strategy, with the overall score of a package

being the sum of strategies which are true. The scor-

ing of individual actions is a debatable topic, since it

is a subjective assessment: do scores reﬂect the effec-

tiveness of an action, or the effort required? In this

exemplary implementation, the scoring primarily re-

ﬂects effort and attitude, rather than objective effec-

tiveness. Table 4 displays the scores assigned to each

strategy, which are not objective measures but evalu-

ations that are relative to each other.

Table 4: (Mal-) Adaptivity Scores of Individual Strategies.

Strategy Q

Score 2.5 1.0 1.5 0.5 3.0 3.0 3.0

Strategy C

Score 2.5 -3 -5 2 1 0 -10

High scores indicate a high motivation to per-

form protective behaviours, while low or negative

scores signify an inclination towards maladaptive be-

haviours. Packages of the same score will be consid-

ered as part of the same package class.

Assuming that the individual scores will only

change rarely, the overall score can be included in

the ﬁle saving valid strategy combinations. Addi-

tionally, by detaching the score computation from the

identiﬁcation of valid packages, new data regarding

scoring can be used to replace previously computed

scores without requiring a repeated identiﬁcation of

valid packages.

During runtime, each agent calculates their per-

sonal protection motivation score and chooses a be-

haviour package from the same package class that

corresponds to their score. As mentioned in Section 3,

the ﬁltering of packages resolves conﬂicting goals by

preventing invalid action combinations. Through the

scoring, agents can prioritize different goals - agents

who value their own safety will likely have high adap-

tivity scores. Social and conformist agents facing

negative reactions from their surroudings will, due to

high perceived costs of protective actions, likely veer

towards maladaptive behaviours. Thus, goals that are

based on needs and values are particularly suitable for

this priorization method through their direct inﬂuence

on the computation of the PMT score.

As a result, the complexity of decision-making

is reduced to the computation of a singular score to

choose which package class best matches the state of

the agent.

5.1 Implementation of Strategies

While Section 2.2 introduces the concept of strate-

gies in a general manner, a brief summary of how

strategies are implemented in our model is provided

to show an example of using this method. As shown

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

338

in Table 5, agents have routines for actions and strate-

gies which are applied to them. Strategies, gener-

ally, are tied to the executing agent (although a purely

functional implementation with the agent as argu-

ment is possible) and whether they are currently en-

abled/active or not.

In the Update Strategies Function, the agent calls

Update on each of its strategies, where additional

logic may happen, such as state changes, triggering

of immediate actions, or other logic which is state-

dependent. One example from this use case is, in

the case of Q

, agents checking whether they are still

feeling sick or if they may end their quarantine sta-

tus. Another example is T

, with check for disease

symptoms resulting in the triggering and execution

of a test-taking action. During the Perform Routine,

the agent executes Check Conditions for each strat-

egy and for each action until either one strategy yields

a negative result (violation of conditions for execu-

tion) or all strategies evaluated successfully. For some

strategies, such as T

, Check Conditions will always

yield True, since the strategy has no logical inﬂu-

ence on individual actions in the context of routine

behaviour.

5.2 Computational Complexity and

Runtime Evaluation

While a classic approach with ad-hoc plan generation

was not implemented, the pre-compilation of plans

was tested and, using code runtime proﬁling, found

to have no signiﬁcant impact on the runtime perfor-

mance of the simulation model due to the computa-

tion of agents’ scores only using constant-time opera-

tions. This was tested on a model with 20.000 agents

for 100 simulation steps.

Additionally, we also examined the runtime com-

plexity of a hypothetical alternative implementation

as visualised in Figure 2. The z-axis uses a loga-

rithmic scale, since linear-scaled values are skewed

beyond visibility by the range of z-values. In op-

tion a, each agent uses a greedy-search-strategy, iden-

tiﬁes feasible plans, evaluates those using constant-

time operations and selects the best option using lin-

ear algorithms. In comparison to that, b applies our

method of binary strategies and ﬁltering using con-

straints, followed by evaluation and selection. Fi-

nally, c depicts the proposed approach in which plans

Table 5: Overview of Agents and the Strategy Interface.

Agent StrategyInterface

Id Name

Routine List of Actions Agent Agent

Strategies List of Strategies Active boolean

update strategies() update()

perform routine() check conditions(Action)

have been generated and ﬁltered for feasibility ahead

of simulation, rather than being a repeated step per-

formed by each agent. Due to the exponential nature

of the SAT problem, this package-based approach sig-

niﬁcantly outperforms greedy computation if the gen-

eration and ﬁltering of plans are performed a single

time ahead of simulations. As such, a mixed strat-

egy still retains beneﬁts regarding communication and

modularity, but provides no better performance than

ad-hoc planning without polynomial heuristics.

These ﬁndings show that our method excels for

models with large agent populations and large palettes

of behaviours, since the computational effort primar-

ily depends on the number of agents, rather than the

size or complexity of the action space.

6 DISCUSSION

This contribution presents an efﬁcient approach to

agent-deliberation using pre-computation and strat-

egy patterns as used in software design. With its inte-

gration within the BDI-architecture widely accepted

by developers of ABMs, this method is compatible

with existing standards and practices.

With the examination of voluntary self-protective

behaviours during the COVID-19 pandemic, we

demonstrated a practical implementation of this ap-

proach and compared it to ad-hoc planning by agents.

The main advantage of this method is twofold:

as shown in Section 5.2, this method is efﬁcient and

scalable due to the one-time execution of the most

resource-intensive task, the initial plan generation and

ﬁltering. Additionally, there is a strong abstraction

between code, concept and meaning. Deﬁning be-

haviours and building a matrix can be achieved in

close interdisciplinary exchange with non-technical

experts in a communicable and structured way.

This method’s main downside is the requirement

for expert knowledge to deﬁne possible behaviours

and their relationships. With the current rise of Large

Language Models and attempts at including seman-

tic information in training data, reasoning on logical

and inconsistent action combinations might be par-

tially automated in the generation of constraints.

For actions with temporal dependencies, we can

consider planning as NP-complete problem which can

be translated into a satisﬁability problem. Therefore,

it is generally possible to include actions with tempo-

ral dependencies (Ullman, 1975). Due to the expo-

nential nature of the #-SAT problem, the scaling for

temporal sequences needs to be examined to verify

performance against heuristic planning algorithms.

In general, performance is a major venue for fur-

Efﬁcient Selection of Consistent Plans Using Patterns and Constraint Satisfaction for Beliefs-Desires-Intentions Agents

339

Figure 2: Comparison of Computation Steps depending on number of behaviours and agents using logarithmic scale for (a)

greedy, (b) mixed and (c) pre-computation.

ther research: while we only presented package selec-

tion using a custom scoring system based on the PMT,

there are also other methods for agents to select ap-

propriate behavioural packages. Exploring different

techniques, such as brieﬂy adressed in Section 3.4, is

an important contribution to understand the practical

usefulness of this approach for use cases in which no

appropriate pyschological theory with sufﬁcient sup-

porting data exists. Additionally, unoptimized plan-

ning was assumed in the comparison, without poly-

nomial search heuristics in lieu of exhaustive search.

Moreover, further models with more complex

agent behaviours, including interactions and temporal

dependencies between behaviours, need to be inves-

tigated to examine the range of use cases that can be

represented with our method.

Overall, the authors are optimistic that with more

examples of successful usage, the method of pre-

compiling plans using strategies provides opportuni-

ties to enhance the speed of large ABMs with complex

agents displaying heteregoenous behaviours from a

pre-evaluated selection of action combinations and

sequences.

ACKNOWLEDGEMENTS

This work is the result of research in the context of the

project SEMSAI, supported by the German Federal

Ministry for Education and Research (BMBF) under

the grant number 031L0295A.

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