Adaptive Market-Based Dynamic Task Allocation Under Environmental

Uncertainty

Hasan Berke Ozturk

, Nezih Bora Yavas

and Zafer Bingul

Department of Mechatronics Engineering, Kocaeli University, Turkey

Keywords:

Multi-Agent Systems, Uncertainty Theory, Swarm and Collective Intelligence, Decentralized Algorithms.

Abstract:

This paper presents a novel consensus-based adaptive genetic-optimized auction (CAGA) algorithm to solve

the dynamic t ask allocation (DTA) problem for a ﬂeet of autonomous vehicles. The algorithm employs an

auction routine for task assignment and a genetic algorithm (GA) to optimize task prices subject to the price

update rule. The proposed algorithm is devised to achieve superior solutions in real-world applications. Hence,

uncertainty theory was adopted to model uncertainties in task positions to create a realistic environment. In

addition, Monte Carlo (MC) simulations are performed to effectively determine the degree of uncertainty.

Several test scenarios have been carried out using other market-based methods, and the results illustrate the

effectiveness of the algorithm.

1 INTRODUCTION

Autonomous vehicles (AUVs) have been extensively

researched and used in numerous ﬁelds over the past

decade due to their adaptable nature. Potential appli-

cations include mapping, reconnaissance, distributed

sensor networks, hazardous metal handling, search

and rescue operations, etc. Although their individ-

ual effectiveness has been proven, the deployment of

multiple AUVs provides even more potent and appro-

priate so lutions. Hence, the term multi-a gent systems

(MAS) has become a major topic as the signiﬁcance

of the problem continues to grow.

The primary objective of MAS is to ensure that

agents in the ﬂeet exhibit cooperative behaviors to

effectively perform tasks. Also, from a task as-

signment perspective, it means multiple robots are

tasked with achieving optimal assignments under cer-

tain constraints and maximizing their overall score.

To establish a struc ture where a ﬂeet of autonomous

agents constantly perceives their surroundings and

takes actions with regard to their beneﬁt, coordination

and cooperatio n amo ng agents must be maintained.

Several research studies have been carried out in this

area, a nd th e key points have been elaborated.

The centralized planners (Chen et al., 2024),

(Hwang et al., 2022) assume a single computational

https://orcid.org/0009-0006-5730-4904

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https://orcid.org/0000-0002-9777-9203

unit that co ntrols and coordinates e ach agent in the

ﬂeet b y computing their cost and providing a com-

munication network throughout a ﬁxed location. Due

to this ce ntralized processing structur e , the computa-

tional burden on a gents is reduced, and they become

simpler to build. However, coordinating agents from

a stationary location restricts the workspace of the

entire ﬂeet, which further limits th e potential tasks

that the agents can handle and creates a single poin t

of failure in the system.

Decentralized methods (Peng et al., 202 4),

(Zhang et al., 2024), (Ozturk et al., 2024b) have

been proposed to solve the problems of centralized

task allocation . This approach distributes the to-

tal computational load among agents rather than

gathering it in a single unit. Thus, agents p erform

tasks based on their knowledge sets. Discarding

the central structure that forces the system to ﬁxate

on a limited workspace has led to more robust and

scalable agent cooperation. Conversely, to converge

on an exact solution, agents should be able to sh a re

their status and information set amon g themselves

through a particular network topology, which can

result in intensive communicatio n overhead and local

optimality.

Market-based strategies are another well-known

approa c h researched in the task allocation problem

context (Ozturk et al., 2024a), (Wang et al., 2024).

The auction algorithm mimics the auction environ-

ment, speciﬁcally by simulating bidders and auction-

Ozturk, H. B., Yavas, N. B. and Bingul, Z.

Adaptive Market-Based Dynamic Task Allocation Under Environmental Uncertainty.

DOI: 10.5220/0013522600003970

In Proceedings of the 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2025), pages 70-80

ISBN: 978-989-758-759-7; ISSN: 2184-2841

eers. First, bidders bid on the tasks they want to be

assigned and calculate their maximum payoff. Af te r-

ward, auctioneers collect these bids and announce the

highest bid as the contest winner.

Depending on how the problem is handled ,

market-based methods can be divided into single-

item and combinatorial auctioning. Single-item auc-

tions perform ta sk-wise operations at each iter a tion.

In contrast, combinatorial auctions p resent tasks as

bundles (task sets), and agents bid on these bun-

dles to minimize the path cost from their initial lo-

cation. Researchers have developed variants of these

approa c hes, includin g parallel single-item (PSI) and

sequential single-item (SSI) auctions. Un like single-

item auction procedures, PSI performs auctions in a

parallelized manner, in which agents are allocated to

tasks via simultaneously performed auctions. Thus, it

accelerates the assignment process but leads to subop-

timal solutions. The SSI method, on the other hand, is

a strategy that combines both combinatorial and PSI

auctions to leverage their advantages. The method is

based on a ser ies of single-item auctions, assuming

each agent is initially unallocated. To a llocate tasks,

agents place bids reﬂecting the increase in their small-

est path cost that arises from win ning the target they

bid on. The agent offering the overall smallest bid

is assigned to the corresponding target. Once agents

determine the winner by observing the bids from the

environment, the unassigned agents re-bid for the re-

maining tasks until all agents are assigned. Partic-

ularly in dynamic environments, SSI-based task up-

dates are highly motivated since environmental quan-

tities cha nge drastically. Nonetheless, these auction

methods neither provide a framework for resolving

conﬂicting assignments nor guarantee optimal solu -

tions in speciﬁc scenarios. Therefore, an agreement

among the ﬂeet should be consistently m aintained to

overcome th ese issues.

Consensus-based algorithms (Herty et al., 20 24),

(Bonandin and Herty, 2 024) have thus gained promi-

nence in addressing multi-agent co ordination chal-

lenges. However, the se approaches often face difﬁ-

culties in achieving a commo n situational awareness

(SA) among agents, that is, agreement that the per-

ceived environment is the same for all of them. Al-

though it is applicable across various network topolo-

gies, their impleme ntation demands signiﬁcant com-

putational resources, and the co nvergence process can

be notably time-intensive.

To resolve these problems, the consensus-based

auction algorithm (CBAA) and, for multitask as-

signments, the consensus-based bundle alg orithm

(CBBA) have been introduced by (Choi et al., 2009).

Both algorithms guarantee convergence on an agreed

SA while ensuring conﬂict-fr ee assignments. In con-

trast to traditional consensus approaches, these al-

gorithms leverage a decentralized auction scheme in

decision-making. Also, instead of agents’ SA, they

struggle to achieve an agreement on winning bid lists.

Unfortu nately, all of the methods discussed above

converge on a solution under the assumption of con-

stant states and neglect unce rtainty. This shortcoming

implies they are unsuitable for real-world applications

where the environment and its dynamics vary contin-

uously.

This paper proposes a novel consensus-based

adaptive gene tic-optimized auctio n (CAGA) algo-

rithm for dynamic task allocation of a multi-robot sys-

tem. Th e algorithm can also consider the uncertainty

in the environmen t and enable agents to make deci-

sions based on the scenario characteristics. Th erefore,

the utilization of genetic algorithms (GA) is motivated

by their ab ility to handle complex, multi-dimensional

optimization problems where analytical solutions are

infeasible to implement. In this context, the incre-

mental constant (ε) serves as a critica l parameter to

regulate the pace of optimization, ensuring both con-

vergence efﬁciency and computational feasib ility.

The remainder of this paper is organ iz e d as fol-

lows: Section 2 investigates the related works pro-

posed by other authors. Section 3 introduces the prob-

lem deﬁnition and preliminaries. Section 4 pre sents

the proposed algorithm and its partitions. Section 5

illustrates the conducted simulations and provides test

results, while Section 6 discusses the outcomes sub-

ject to th e scenarios. Finally, Section 7 concludes the

paper and gives valuable insights for futu re works.

2 RELATED WORKS

DTA has b een investigated in detail, and various ef-

forts have been made to solve this problem because

of its importance. The proposed meth ods can be clas-

siﬁed into two types: exact solutions and heuristics.

For heuristic methods, evolution a ry-based ap-

proach e s have mostly been utilized to solve the DTA.

(Yan and Di, 2023) investigated the multi-robot task

allocation prob le m and classiﬁed tasks as compul-

sory ( must be co mpleted) and functional (optional

but beneﬁcial). They aimed to op timize task as-

signments to minimize time c osts by focusing on a

novel hyper-heuristic algorithm. For this reason, re-

searchers introduced an d enlarged low-level heuris-

tic (LLH) and high-level strategy (HLS) algorithms.

LLH scores functional tasks based on an inﬂuence

diffusion model, while HLS optimize s LLH param-

eters using a particle swarm optimization (PSO) al-

Adaptive Market-Based Dynamic Task Allocation Under Environmental Uncertainty

gorithm. The proposed algorithm was compared

against classical greedy, metaheuristic, and SSI-based

approa c hes. It was shown that the proposed algorithm

is ﬂexible and scalab le . Nevertheless, it relies heav-

ily on parameter tuning and struggles with extremely

large or small rob ot groups, where simpler meth ods

may sufﬁce. Furthermore, adding one m ore layer in-

creases the complexity of the implementatio n.

(Li et al., 2024) investigates task allocation chal-

lenges for h e te rogeneous unmanned aerial vehicles

(UAVs), pa rticularly in re source con stra ints and dy-

namic task demands. The authors proposed a heuris-

tic allocation method grounded in the overlapping

coalition formation game framework (OCF) to en -

hance resource utilization and task u tility. This frame-

work allows UAVs to operate under multiple condi-

tions simultaneously, while the heuristic allocation

method avoids repetitive and inefﬁcient resourc e al-

locations. Moreover, the proposed task exit mecha-

nism allows UAVs to exit coalition s w hen their util-

ity contribution decreases. Although the algorithm

demonstra te s ﬂexibility and dyn a mically responds to

changes, the reliance o n heuristic strategies results

in high c omputational demands and a dependency on

overly simplistic models, limiting its applicability in

real-world scenar ios.

In (Bischoff et al., 2024), re-optimization meth-

ods a re introduced to tackle time-extended multi-

robot task allocation problems involving task dele-

tion and insertion in dynamic environments. The pro-

posed optimization framework offers mechanisms to

adapt to situations where new tasks are added or exist-

ing tasks are removed. As a heuristic approach, they

present the cheapest ma ximum insertion cost heuristic

(CMI) for task insertion by balancing comp lexity and

performance. The intr oduced optimization heuristics

are both scalable and efﬁcient. This method estab-

lishes upper bounds o n solution quality while ensur-

ing predictability and reliability in dynamic systems.

However, CMI heuristics can overestimate insertion

costs, rendering the resulting bounds limited applica-

bility and potentially inadequate in reﬂecting actua l

resource r e quirements.

Regarding exact solutions, these methods of DTA

tend to achieve better convergence. One of the most

commonly r e cognized strategies for solving DTA

problems is the market-based approach, which op-

erates main ly through auction routines. The study

presented b y (Hossain et al. , 2023) o ffers a parallel

task allocation framework using a multi-stage iter-

ative combina torial auction mechanism, introducing

uncertainties in multi-robot environments. The pa-

per aims to improve the task alloc ation process by ex-

ploiting different metrics, including task preferences,

path collision avoidance, task prioritization, and ex-

ecution deadlines. The prop osed method offers two

stages. In the initial stage, multiple round s of bidding

occur, and the temporary winner is determined. After

that, a single roun d in which robots submit their ﬁ-

nal bids based on updated task values is executed for

the ﬁnal stage. The proposed mechanism is scalable

and comprehensive, but it relies on a centr alized en-

tity, leading to a single po int of failure in the system.

Furthermore, the practical implementation of uncer-

tain environments requir es extensive ﬁne- tuning.

3 PROBLEM DEFINITION

3.1 Task Allocation

In multi-robot task allocation (MRTA), the re a re m

agents and n tasks, which can be deﬁned as

A , {a

,... ,a

}

T , {t

,. .. ,t

}

(1)

where A and T represent th e sets of agents and

tasks, respectively. The goal is for agents to ﬁnd

conﬂict-fre e assignments that maximize their payoff.

Conﬂict-free means each agent is assigned only one

task. The task assignment p rocedure continues until

all agents are allocated to the tasks.

The overall score function for a conventional auc-

tion procedu re is introduced. It can be expressed as

max

∑

i=1

∑

j=1

i j

− p

i j

subject to

∑

i=1

i j

= 1, ∀j ∈T

∑

j=1

i j

= 1, ∀i ∈ A

i j

∈ {0,1}, ∀(i, j) ∈ A ×T

(2)

where c

i j

is the beneﬁt of agent a

if it is assigned ta sk

and p

i j

is the price of ta sk t

for agent a

. The x

i j

a binary decision variable, ind ic a ting that agent a

assigned task t

if x

i j

= 1 and 0 otherwise.

3.2 Auction Routine

Auction-based strategies are widely employed to

solve task assignment problems. These routines pro-

mote competition among bidders, which signiﬁcantly

impacts the procedure’s completion time.

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Conventional auction sche mes assume that agent

receives the maximum proﬁt of c

i j

for task t

, where

i j

depicts the beneﬁt of agent a

if it bids for task t

It can be c oncluded that agent a

will not bid for a task

if it does not beneﬁt from it.

Suppose tha t agent a

pays the price p

for task t

;

then, the payoff can be calculated as c

i j

−p

. Thereby,

payoff functions of the agent and sy stem ca n be at-

tained in Eqs.(3) an d (4) as follows:

= ma x

∈T

i j

− p

), (3)

Θ =

∑

i=1

(4)

Here, T denotes the task set. In decentralized auc-

tion routines, if Eq.( 3) is ensured for each agent in the

ﬂeet, then the agents are satisﬁed with their decision,

and the global optimum is achieved. Th e system pay-

off Θ can be depicted as in Eq.(4).

If this is not the case, agents proceed to the next

round, whe re the price update rule is executed.

An agent can raise the price offered by another

agent to the extent that it becomes indifferent between

its op timal and suboptimal payoffs. In light of this

strategy, agents calculate their payoff for each task

and bid on the task to m a ximize their beneﬁt.

The optimal payoff is calculate d as in Eq.(5).

Where θ

is the o ptimal pa yoff for the agent a

and

∗

is the task number corresponding to the optimal

payoff.

= g

i j

∗

= ma x

∈T

i j

− p

) t

∗

∈ T , (5)

After that, calculate the suboptimal payoff g

i j

∗

for

agent a

i j

∗

= ma x

i j

− p

) t

∗

∈ T t

∗

6= t

∗

, (6)

where j

∗

is the task corresponding to the subop-

timal pa yoff. By exploiting these equ ations, the next

round offer of agent a

can be introduced as

i j

∗

= d

∗

+ g

i j

∗

−g

i j

∗

+ ε (7)

where d

∗

is the highest bid for task j

∗

offered

in the previous round, and ε denotes the incremen-

tal constant, which signiﬁcantly impa cts th e auction’s

course. I n fact, it allows the system to converge on op-

timal solutions and overcom e deadlocks (inﬁnite iter-

ations), whereas poor ε selection leads to higher com-

putational resource consumption. Thus, it ne eds to be

adjusted according to the speciﬁc scenario. Section 4

further elucidates how this value is optimized through

a genetic algorithm (GA).

3.3 Communication Topology

The graph G = (N ,V ) is adopted to estab lish

a network topology between decentralized agents.

Namely, N is the set of nodes, and V is the set of

vertices. If there is a d irect communication lin k be-

tween two agents, that is, (δ,η) ⊆ V , then these two

agents are adjacent. The number of a gents in the net-

work is N , and the adjacency matrix C of G can be

deﬁned as in Eq.(8).

δ,η

(

1, if (δ,η) ⊆ V

0, if (δ,η) * V

(8)

δ,η

is the eleme nt of the adjacency matrix C, a

binary decision variable tha t denotes w hether a link

exists between two nodes δ and η. When d ealing

with uncertainties and executing the algorithm, it is

assumed that the gr aph is undirected and fully con-

nected.

3.4 Uncertainty Theory

When allocating tasks to ag ents, the severity of the

uncertainty directly affects the dec isio n-makin g pro-

cess and, hence , how fast and effectively agents oper-

ate (ElGibreen and Youcef-Toumi, 2019).

Most conventional approaches do not c onsider

uncertainty and its possible effects on the assignment

proced ure. Conversely, in cases where the environ-

ment is highly dynamic, task positions are not deter-

ministic, and mea surements vary over time . In this

paper, uncertainty is introduced based on changes in

the environment and is used to determine the accuracy

of the agents’ sensor measurements.

Uncertainty can be introduced with an uncertainty

space (Liu and Liu, 2010), represented as (Γ,L,M )

where Γ is a n on-empty set, L is σ −algeb ra over a

non-empty set Γ, and M {∧} is an uncertainty mea-

sure which indicates the level of belief that an event

∧ will occur. This space has a measurable function

deﬁned as ξ that maps th e quantities from uncertainty

space to real n umbers.

The lognormal distribution is implemented to

model the uncertainty. Henc e, ξ ∼ LOGN (e,σ) and

the uncertainty distribution is measured by M {ξ ≤x }

for x ≥ 0 in Eq.(9).

Φ(x) =



1 + exp



π(e −ln(x))

√

3σ



−1

(9)

On the other hand, ﬁnding the uncertainty

distribution is not helpful since determining the un-

known value of x is not possible in a dynamic environ-

Adaptive Market-Based Dynamic Task Allocation Under Environmental Uncertainty

ment. Thus, the distribution must be reconstructe d us-

ing the un c ertainty theory’s ope rational prope rties. In

this case, the inverse uncertainty distribution Φ

−1

(α)

is obtained, and its uncertainty variable ξ has a regu -

lar distribution Φ(x), where α ∈[0,1] is a conﬁdence

constant. For ξ ∼ LOGN (e,σ), inverse uncertainty

distribution can be derived as

−1

(α) = exp(e)



1 −α



√

3σ/π

(10)

Utilizing the Eqs.(9) and (10), the overall score

function can be f ormulated as

max

∑

i=1

∑

j=1



1/Φ

−1

(α)

i j



− p

i j



i j

(11)

where Φ

−1

(α) is the inverse uncertainty distribution,

and it represents the uncertainty of ta sk position s.

Eq.(11) is used when calculating payoffs.

4 METHODOLOGY

In th is section, the proposed algorithm and its

modules are introduce d. Additionally, their working

principles are elaborated.

4.1 Algorithm Framework

The proposed algorithm comprises two phases: First,

a predeﬁned number of CBAA operations are exe-

cuted by agents in parallel, that is, each agent simul-

taneously performs a sp eciﬁc number of CBAA and

aims to maximize its own score. The properties of

locally executed CBAAs (level of possible task com-

binations, the a mount of CBAA opera tions) ar e de-

termined by GA’s evolutionary parameters, including

population size, crossover, and mutation. For each

CBAA execution, agents randomly initialize different

ε values ranging from



5.10

−6

,5.10

−4



and ﬁnd the

best possible ε value by determining the overall max-

imum payoff (d e rived in Eq.(11)) among calculated

CBAA procedures. Ultimately, the ﬁnal CBAA is car-

ried ou t with the best obtained ε values and allocates

tasks to agents.

As a toy example of the proposed algorithm, as-

sume that there are room s where potential bidders are

interested in the products being auctioned. The prod-

ucts are offered for sale to bidders in accordance with

speciﬁc auction ru le s. Bidders submit bids on the

most desirable item, thereby maintaining the momen-

tum of the auction. The auctions are conducted in par-

allel sessions, with the same products b eing offered

at varying levels o f aggressiveness in each session.

It is expected that the bidders maxim iz e their proﬁt,

and if this criterion is not met, the auction extends

for a predetermined number of days. At each au ction,

Bidders prioritize maximizing their own interests, and

if the auction does not yield the desired proﬁt, they

must re-bid on a subsequent day. Moreover, prior to

each auction, bidders conduct an internal assessment

of the upcoming session, analyzing past results to re-

ﬁne th e ir b idding strategies and optimize their offers

accordin gly. Subsequently, the most proﬁtable auc-

tion combinations are identiﬁed, and buyers are en-

courag e d to submit o ptimized bids for the correspond-

ing products. Thus, by conducting multiple auctions,

the proﬁts of the bidders will be optimized, and the

system will reach a state of equilibrium.

4.2 Monte Carlo Simulation

The Monte Carlo (MC) approach is adopted to deter-

mine the un certain positions of the tasks and increase

adaptability in a dynamic environme nt. Primarily,

random distances betwee n (0,150) were calculate d,

and by using Eq.( 9), severa l distance points were col-

lected to determine the LOGN (e,σ) uncertainty pat-

tern. Spec iﬁca lly, e and σ values are obtained over

1000 iterations, and the lognorma l uncertainty distri-

bution is acquired.

When locating task s to place bids, task positions

can be predicted by using the un c ertainty theory.

Uncertainty space can be reconstructed as {T , D,ξ},

where T is the tasks, D is the distances, and ξ is

the agent’s beneﬁt fun c tion. The goal is to ﬁnd the

uncertainty distribution of each task, in othe r word s,

∼ LOGN (e,σ).

Subject to the task position a mbiguity prob-

lem, suppose ξ

,ξ

,. .. ,ξ

are independent uncer-

tain variables with a regular uncertainty distribution.

(x),Φ

(x),... , Φ

(x) and the inverse uncertainty

distribution for ξ = f (ξ

,ξ

.. .ξ

), where f : ℜ

→

ℜ is strictly increasing function denoted in Eq.(12).

Thereby, agents have valuable insights and awareness

regarding their beneﬁts befo re assigning tasks in a dy-

namic environment.

−1

(α) = f (Φ

−1

(α),Φ

−1

(α),.. . ,Φ

−1

(α)) (12)

4.3 CAGA Algorithm

The CAGA algo rithm is proposed to solve the de-

centralized dynamic task allocation problem of the

MAS. The algorithm is divided into two phases: the

optimization phase and the assignment phase. Ini-

tially, with random ε combinations, agents conduct

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

parallel CBAA processes and compute their payoffs.

Further, GA optimizes the whole procedure by adjust-

ing the ε values.

input : ag ents A

, population size P

output: assignment matrix H

initialize y

, generations P

for each agent a

initialize populations

end

for each generation do

for each solution P do

calculate ﬁtn ess

share ﬁtne ss values

end

while new population < P do

select ﬁr st parent from P

select second parent from P

crossover ﬁr st and second parent

mutate c rossover-ed populations

add new solutions to the P

end

for each agent a

calculate global best solution

end

for each agent a

update p a rameters

end

Algorithm 1: Optimization Phase of CAGA Algorithm.

In the optimization phase, each agent initial-

izes parameters, including popu la tion size, crossover,

and mutation rate. Particularly, between the pop-

ulation members ( each CBAA performed by each

agent), combinations with the best payoffs are stored,

and the remainder sizes are ﬁlled with the arith-

metic crossover of former populations. In addition,

by leveraging Gaussian distribution, populations ex-

Table 1: Symbol description of CAGA algorithm.

Symbol Description

The task list of agent i

The winning bid list of agent i

The valid task list for agent i

i,J

The agent that currently assigned task J

P(·)

It i s the indicator function that is unity

if t he argument is true and zero otherwise

G The communication topology

k Agent k is the neighbor of agent i

posed to crossover are m utated, and new epsilon com-

binations are obtained. After these operations, each

combination is reserved, and agen ts proceed to the as-

signment phase.

In th e assignment phase, after determining the ε

that provides the highest system payoff, agents carry

out the original CBAA and assign themselves to tasks.

input : The agent set A the task set T , the

communication topology G and the

initial price p

i j

output: system payoff

while iteration < max iteration do

for each agent a

(t) = z

(t −1)

(t) = w

(t −1)

∑

i j

= 0 then

i j

= P(c

i j

> w

i j

(t)),∀j ∈ T

if v

6= 0 then

= argma x

i j

·c

i j

i,J

(t) = 1

i,J

(t) = c

i,J

update the price p

i j

end

send w

to k with g

(τ) = 1

receive w

from k with g

(τ) = 1

i j

(t) = m ax

(τ) ·w

k j

(t),∀j ∈ T

i,J

= argma x

(τ) ·w

k,J

(t)

if q

i,J

6= i then

i,J

(t) = 0

end

Algorithm 2: Assignment Phase of CAGA Algorithm.

In addition, the MC simulations help them effec-

tively detect the exposed uncertainty and make deci-

sions acco rdingly.

5 SIMULATION RESULTS

This section provides a detailed description of the cru-

cial aspects of the simulation process and presents

various test scenarios. In fact, small-, medium-, an d

large-scale applications are conducted, and the re-

sults are visualized to illustrate the adaptability of the

CAGA alg orithm.

Adaptive Market-Based Dynamic Task Allocation Under Environmental Uncertainty

5.1 Experimental Setup

The simulation setup introduces the preliminaries, in-

cluding initial conﬁgura tions, M C operations, and

the evaluation metrics used for analysis. Initially,

agents and task positions are set, and then agents ex-

ecute the CAGA algorithm to determine assignments.

Once targets are identiﬁed, the simulation begins to

demonstra te scenarios at predeﬁned scales. Due to

environmental uncertainty, agents must periodically

update their measurements fo r accurate task execu-

tion. Also, these updates should be synchron ized to

ensure feasible b id assessment and task re-allocation

when necessary.

During simulations, the uncertainty degree is as-

sumed to increase proportionally with distance and

follow a lognorma l distribution. The simulation en-

vironm ent adjusts the ﬂeet’s measurem e nt frequency

to improve assignment efﬁciency, co nsidering the dis-

tance of the farthest agent from the task, as this agent

experiences the highest level of uncertainty. In con-

trast, the time step is adjusted inversely to the de -

gree of unc ertainty, ensuring ad a ptive responsiveness.

This relationship can be expressed as

∆t =

max(γ) + κ

(13)

where ∆t represents time step, C signiﬁes constant

scale factor deﬁned as 1, γ denotes the set of uncer-

tainty degre e ( γ ∈ [0,1]) experienced by each agent

and κ depicts the increment to avoid d ivision by zero.

For the purposes of illu stra tion, consider a sce-

nario in which three agents (a

) ar e involved

in a given problem, with the agents positioned 10,

20, and 30 meters away from their de signated tasks,

respectively. Accor ding to the simulation, the agent

positioned 30 meters away exhibits the highe st de-

gree of uncertainty. To determine the furthest one,

agents share their degree of uncertainty with them-

selves. Late r, they deﬁne the highest bid and use it to

calculate Eq.(1 3) while updating their status. As the

agents appro ach their assigned tasks, the uncertainty

decreases, thereby enhancing the agents’ conﬁdence

in their me asurements and decreasing the me asure-

ment frequency. Conversely, in a scenario where the

agents are distant from the task s, the uncertainty is

elevated, and the measuremen ts are rec eived at more

frequent intervals.

The CAGA algo rithm introduces an MC simu-

lation to capture uncertainty characteristics at var-

ious levels of uncertainty. This way, agents will

have more informatio n about their workspace. Be-

fore performing assignments, agents are informed of

the p resented uncertainty (LOGN (3.6,0.6)) with the

historical data collected from MC operations in a

100 ×100 workspace.

0 50 100 150

Distance (m)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Level of Uncertainty (x)

Relationship Between Distance and Uncertainty Degree

Figure 1: Lognormal uncertainty distribution function.

Figure 1 visualize s the uncertainty distribution

adopted in this pa per. By using this knowledge,

agents have the capability to analyze the environment

and make decisions more accurately.

Carry out MC simulations

while system progress < t do

for current positions do

calculate E uclidean distance D

i j

if D

i j

< 10

−6

then

nullify the uncertainty

coeff = 0

end

else

calculate measured distan ce

calculate measur e d target

end

calculate new positions

calculate ∆

value

end

Algorithm 3: Simulation steps.

5.2 Results

Simulations for scales of 3 × 3, 5 × 5, and 10 × 10

were carried out, and the task assignments performed

by the CAGA algor ithm have been visualized. The

proposed algorithm’s performance metr ic s w e re col-

lected using the same mode l created in Py thon.

For the simulations, the initial agent and task po-

sitions for sma ll-, medium-, and large-scale appli-

cations were randomly deﬁned within a 1 00 × 100

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

Figure 2: Initial payoff matrices for conducted scenarios.

workspace. The initial payoff matrices, which are

shown in Figure 2, were derived by calculating the

Euclidean distance b e tween the a gent-task pairs and

100

Z (m)

Y (m)

CAGA Algorithm Task Assignment - 3 X 3 Scenario

X (m)

Agents

Tasks

Checkpoints

Assignments

Initial Assignments

Figure 3: The CAGA algorithm performance for 3 × 3.

Table 2: Positions on XYZ (in meters) for 3 × 3 Scenario.

Agent Positions Task Positions Sensor Outputs

[54 23 65] [47 54 54] [32.1 72.2 40.51]

[75 21 53] [52 55 37] [38.5 76.1 41.4]

[17 23 34] [2 85 57] [42.2 58.6 42.8]

adding a LOGN (3.6,0.6) uncertainty noise to these

values. After that, at e ach checkp oint of th e simu-

lation, sensor outputs wer e obta ined from the corre-

sponding positions of the agen ts (To improve read-

ability, only the ﬁrst senso r measurement output is

provided for each agent) . These values are presented

in Tables 2, 3, and 4, respectively.

The simulation mechan ism devised for the scenar-

ios is as follows: Agents and task locations are ini-

tialized for each procedure, and tasks are allocated by

leveraging the CAGA algorithm subject to the payoff

matrices in Figure 2. The simulation is divided into

CAGA Algorithm Task Assignment - 5 X 5 Scenario

X (m)

Z (m)

100

Y (m)

100

Agents

Tasks

Checkpoints

Assignments

Initial Assignments

Figure 4: The CAGA algorithm performance for 5 × 5.

Table 3: Positions on XYZ (in meters) for 5 × 5 Scenario.

Agent Positions Task Positions Sensor Outputs

[54 23 65] [71 41 74] [70.3 40.2 73.6]

[75 21 53] [52 55 37] [53.6 52.6 38.1]

[17 23 34] [2 85 57] [4.27 75.6 53.5]

[53 11 65] [76 23 96] [74.3 22.1 93.8]

[21 56 51] [47 54 54] [45.8 54.9 53.8]

ﬁve time intervals, each containing a checkpoint. This

structure allows agents to simultaneously up date their

measurements, reﬁne their positions, and potentially

reallocate tasks. At each checkpoint, they recalcu-

late their payoffs to each task and, if a high e r payoff

exists, reallocate to another task by re-executing the

CAGA algorithm. Since age nts synchrono usly reach

checkpoints and ad just their progression rates accord-

ing to the agent most affected by the uncertainty, task

conﬂicts will not arise.

Adaptive Market-Based Dynamic Task Allocation Under Environmental Uncertainty

100

Z (m)

A10

CAGA Algorithm Task Assignment - 10 X 10 Scenario

T10

Y (m)

100

X (m)

Agents

Tasks

Checkpoints

Assignments

Initial Assignments

Figure 5: The CAGA algorithm performance for 10 × 10.

Table 4: Positions on XYZ (in meters) for 10 × 10 Scenario.

Agent Positions Task Positions Sensor Outputs

[54 23 65] [71 41 74] [84.2 40.9 74.4]

[75 21 53] [52 55 37] [54.2 51.6 38.5]

[17 23 34] [25 30 56] [24.6 29.6 55]

[53 11 65] [76 23 96] [74.6 22.2 94.1]

[21 56 51] [2 85 57] [3.69 82.4 56.4]

[22 35 12] [15 0 24] [15.4 1.98 23.3]

[37 42 53] [47 54 54] [46.7 53.7 53.9]

[53 41 23] [64 32 12] [63.5 32.3 12.4]

[47 32 52] [48 32 58] [47.9 32 57.8]

[78 63 74] [86 42 75] [71.2 41.8 74]

A sm a ll-scale app lication was initially conducted,

with results visualized in Figure 3. Due to uncertainty

and sensor errors, agents deviated fr om their trajecto-

ries. A t each checkpoint, they reassessed their po-

sitions and, if necessary, reallocated tasks. Notably,

at the secon d and third checkpoints, agents 2 and 3

switched tasks, but by the ﬁnal checkpoint, updated

payoffs led them to reallocate to their initial tasks.

This behavior distinctly illustrates the proposed algo-

rithm’s resilience to uncertainty.

In med ium-scale applications, as depicted in Fig-

ure 4, agents effectively navigated environmental un-

certainty while mainta ining their initial alloca tion

paths, in contrast to the deviations o bserved in small-

scale scenarios.

Ultimately, the CAGA a lgorithm was tested in a

10 × 10 scenario , with results presented in Figure 5

and Table 4. The simulation outcomes demonstrate

that agents suc cessfully ma intained their initial task

assignments while effectively adapting to uncertain-

ties. Througho ut the execution, they remained within

their designated m easurement corridors, ensuring sta-

ble an d reliable task completion.

Interestingly, during the execution of the simula-

tion scenarios, the uncertainty inhe rent in the envi-

ronment does not signiﬁcantly divert the agents from

their trajectories. In contrast, results clearly show

that the MC approac h introduces adaptability to the

CAGA algorithm, allowing agents to manage unc e r-

tainty effectively within d ynamic environments.

6 DISCUSSION

The CAGA algorithm was comp ared with CBAA

and other market-based approaches across differ-

ent scenarios both in terms of computationa l time

and total payoff. Particularly, the proposed optimal

market-based (OMB) (Liu and Shell, 20 13) and im-

proved market-based (IDMB) (Trigui et al., 2014) ap-

proach e s were performed, and re sults are shown in

Ta ble 5 and 6. A ll simulatio ns were imple mented in

Python 3.12.7 and tested on a system with a 4-core

4.2 GHz i7-7700K CPU and 16 GB of memory.

Table 5: The payoff comparison of the algorithms. The

boldface values are the best average for each algorithm.

Scenarios Algorithms

CAGA CBAA OMB IDMB

3 × 3 6.71 6.71 6.71 6.71

5 × 5 13.82 13.82 13.2 13.80

7 × 7 29.13 28.37 25.5 22.61

10 × 10 50.59 49.82 49.6 43.22

15 × 15 75.689 74.74 71.87 72.81

20 × 20 125.86 111.4 106.5 109.72

25 × 25 182.32 143.8 126.4 127.4

30 × 30 209.09 169.1 157.8 148.07

35 × 35 248.06 247.7 227.7 209.8

40 × 40 279.42 281.6 265.8 244.5

In the proposed algorithm, the assignments are de-

rived from the last checkpoint of the simulations. On

the other hand, since other algorithms do not utilize

checkpoints, assignments are made dire ctly based on

the initial cost matrix. After that, cost matrices with

uncertainties have been used to perform all assign-

ments. Finally, cost m atrices without uncertainty h ave

been used to calculate payoffs to ensure a consistent

evaluation of p ayoffs.

The payoff and runtime perf ormances of the algo-

rithms, as presented in Tables 5 and 6, were tested in

25 trials, and the arithmetic mean of the results was

used f or comparison. The resu lts are calculated using

SIMULTECH 2025 - 15th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

100 λ

−1

, where λ denotes the cost matrix. The ma-

trix elemen ts are derived based on the Euclidean dis-

tance between the positions of the agents and tasks.

To prevent extremely small values and enhance the

accuracy o f the results, the inverse of the cost ma-

trix is scaled by a factor of 100. Acco rding to the re-

sults, the proposed algorithm demonstrates superior-

ity for small- and medium-scale applications regard-

ing system payoff in an uncertain environment. It ex-

pands the search space and identiﬁes possible solu-

tions available to agents.

Table 6: The computational time comparison of the algo-

rithms (in milliseconds). The boldface values are the best

average for each algorithm.

Scenarios Algorithms

CAGA CBAA OMB IDMB

3 × 3 8.89 0.97 0.09 0.03

5 × 5 9.76 0.99 0.17 0.24

7 × 7 11.95 1.89 0.42 0.30

10 × 10 13.16 1.99 0.4 4 0.38

15 × 15 18.02 4.98 0.7 9 0.71

20 × 20 22.92 8.97 0.86 0.92

25 × 25 30.78 17.9 7 1.15 1.65

30 × 30 40.84 35.9 0 2.06 2.80

35 × 35 66.41 55.8 2 3.36 3.69

40 × 40 83.79 73.8 0 3.84 4.32

However, as the operational scale increases, the

CAGA algorithm struggles with the growing num-

ber of uncertain conditions in the system, which ul-

timately leads to computational overhe a d. Table 6 il-

lustrates the computational times of e a ch algo rithm

across various applications. The resu lts highlight the

efﬁciency of the OMB algorithm, where a s th e CAGA

algorithm demonstrates relatively poor performanc e.

Nevertheless, the CAGA algorithm accounts for un-

certainty and c an be easily adjusted for ap plication

scenarios where optim ality pre cedes time sensitivity.

7 CONCLUSION

In this paper, the decentralized dynamic task

allocation problem o f MAS was introduced and

solved with the proposed CAGA algorithm. The pro-

posed alg orithm was compared with several market-

based methods and the well-known consensus-based

decentralized task assignm ent alg orithm CBAA, and

the results are discussed. Accordin g to the sim-

ulations conducted in different operational sizes, it

has been demon strated that the proposed algorithm

provides valuable outputs in terms of system pay-

off in an uncertain environment, although it sacri-

ﬁces computational time to ﬁnd more optimal solu-

tions. Unlike CBAA or other conventional task al-

location algorithms, the CAGA algorithm introduces

adaptability and fea sibility for real-world applica-

tions. In future works, plans ar e to use un certainty

synergistically while tackling the formation ﬂight and

task allocation problems and cre a ting realistic en-

vironm ents much more analogous to real-world ap-

plications. Beyond the current uncertainty handling

framework of the algorithm, incorporating additional

checkpoints could enable more precise task assign-

ments for agents. This enhancement can potentially

improve efﬁciency, particularly in environments with

high levels of uncertainty. Moreover, the failures

that may arise due to the high communication bur-

den of the system can be investigated, and the lim-

ited communication problem can be used jointly in

the task assignment scenario. Also, an algorithm with

higher efﬁciency and performance can be created by

adapting the genetic parameters used in the proposed

algorithm to the speciﬁc problem. Future research

could explo re trajectory planning problems for agents

under uncertainty in conjunction with task assign-

ments. Enhancing agents’ adaptability and sensitiv-

ity in rea c hing tasks may lead to more efﬁcient and

robust decision-making in dynamic environments.

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