TELKOMNIKA Telecommunication Computing Electronics and Control Vol.
No.
April 2026, pp.
ISSN: 1693-6930.
DOI: 10.
12928/TELKOMNIKA.
Hybrid PSO-WOA approach for an efficient task offloading in mobile edge computing Fatima Z.
Cherhabil.
Sonia-Sabrina Bendib.
Maamar Sedrati.
Chahrazed Adouane.
Sifeddine Benflis Department of Computer Science.
Mustafa Benboulaid University (Batna .
Batna.
Algeria
Article Info
ABSTRACT
Article history:
Offering a promising solution for latency-sensitive and resource-constrained internet of things (IoT) applications, mobile edge computing (MEC) extends cloud capabilities to the network edge.
However, the decentralized nature of edge resources, coupled with stringent latency requirements and IoT energy constraints, presents significant challenges for efficient task offloading.
Integrating IoT with MEC and software-defined networking (SDN) can meet the growing demands for low latency and energy-aware resource This paper proposes a hybrid evolutionary algorithm combining whale optimization algorithm (WOA) and particle swarm optimization (PSO) with crossover, mutation, and Lyvy flight operators (CML) to balance exploration and exploitation.
The algorithm minimizes a weighted sum function .
nergy 35%, delay 35%, and monetary cost 30%) for joint task offloading and resource allocation in SDN-enabled MEC The proposed approach is evaluated against six well-known metaheuristics, analyzing performance across various metrics including scalability with up to 100 users.
Experimental results, validated by nonparametric statistical tests, demonstrate that the proposed algorithm achieves statistically significant improvements in convergence speed, solution quality, and scalability, making it a robust and promising candidate for real-time MEC task scheduling.
Received Jun 16, 2025 Revised Dec 4, 2025 Accepted Jan 30, 2026 Keywords:
Cost Delay Energy consumption Mobile edge computing Multi-objective optimization Task offloading Weighted sum This is an open access article under the CC BY-SA license.
Corresponding Author:
Fatima Z.
Cherhabil Department of Computer Science.
Mustafa Benboulaid University (Batna .
Constantine Avenue.
Fysdis, 05000.
Batna.
Algeria Email: f.
cherhabil@univ-batna2.
INTRODUCTION
With the rapid growth of wearable devices and internet of things (IoT) applications, efficiently processing delay-sensitive and resource-intensive tasks has become a major challenge.
These applications impose stringent quality of service requirements due to factors such as mobility, interactive environments, and the need for real-time responsiveness.
Due to limited resources and energy.
IoT devices cannot meet these stringent performance demands.
Offloading the whole or part of a task to another processor or server in proximity can be used to accelerate resource-intensive or latency-sensitive applications and reduce energy consumption when compared to cloud computing .
, .
Mobile edge computing (MEC) has emerged as a promising approach that brings computation closer to IoT devices, typically within the radio access network.
It can achieve a better trade-off between delaysensitive and computation-intensive tasks .
When integrated with software-defined networking (SDN), a recently proposed technology that separates the control plane from the data plane.
MEC gains additional flexibility in resource management through centralized control and dynamic network configuration .
, .
Journal homepage: http://journal.
id/index.
php/TELKOMNIKA TELKOMNIKA Telecommun Comput El Control Despite these advantages, the dynamic and heterogeneous nature of IoT environments makes the joint task offloading and resource allocation problem highly complex and non-deterministic polynomial-time hard (NP-har.
, especially when the number of users increases.
As the number of users and tasks increases, finding optimal offloading decisions becomes increasingly challenging due to interdependencies between energy consumption, execution delay, and monetary cost.
Traditional deterministic methods struggle to adapt to such dynamic conditions.
Evolutionary and swarm-based algorithms, metaheuristics known for their global search capability and adaptability, have shown great potential in addressing such problems .
They are emerging as a dominant approach due to their ability to handle NP-hard problems.
For instance, genetic algorithms (GA) have been used to optimize transmission power and execution frequency .
and to minimize task overhead in internet of vehicles (IoV) systems .
Zhu and Wen .
, an improved version of GA (IGA) using knowledge-based crossover was introduced.
The paper focused on comparing the proposed algorithm with the most commonly used benchmarks, which are all local and all offloaded execution strategies.
However.
GAs often suffer from high computational complexity .
A binary version of the cuckoo search algorithm (CS) was proposed in .
for offloading decisionmaking, focusing on minimizing time, energy, and cost.
The study highlighted how multiple parameters, such as the number of mobile devices and tasks, influence the effectiveness of the offloading process.
Meanwhile.
Abbas et al.
compared grey wolves optimization (GWO), ant colony optimization (ACO) and whale optimization algorithm (WOA) to find an optimal selection of offloading tasks.
Simulation results showed that the performance of GWO is relatively much better than ACO and WOA.
However, both works focused their experimental tests only on an environment of a single edge node and a number of end-devices.
Artificial bee colony (ABC) algorithm .
have demonstrated effectiveness in balancing latency and energy in a proposed three-tier edge-cloud integration framework.
Particle swarm optimization (PSO) was used in .
to address task dependencies in job-divided computation offloading with multiple users and MEC servers and multi-population cooperative elite algorithm (MCE-PSO).
A binary version of PSO was also applied in .
for resource allocation and offloading strategy optimization in multi-tier multi-MEC-server architectures within 5G heterogeneous networks.
WOA, known for its exploitation capabilities, has been integrated with other evolutionary techniques to enhance performance.
Li et al.
WOA was integrated with differential evolution (DE) and immune system to improve the searching strategy of the whale and enhance the efficiency of dependent task offloading in MEC environments, while in .
authors decomposed the problem of computation offloading in non-orthogonal multiple access (NOMA) based MEC system into sub-problems.
They solved them using convex optimization and the use of a gradient-free swarm intelligence approach of WOA.
However, the simulations were conducted with a single server and a very small number of users .
Zhang and Tuo .
, authors had merged WOA with Lyvy flight and GWO to improve the population initialization and alpha-wolf selection steps of the GWO algorithm.
The system used a multi-server and multi-user vehicular task offloading with a selective offloading, which is, in their case, the ability to execute the task locally, on edge server, or an idle vehicle.
Other evolutionary and swarm intelligence algorithms have been explored.
Gorilla troops optimization (GTO) was proposed and improved in .
to solve the dependent task-offloading problem in a multi-server MEC environment with the same three objectives, namely, the completion time, energy consumption, and monetary cost.
Furthermore, biogeography-based optimization (BBO) was employed in .
to solve the task offloading issues for edge servers and considering the central cloud.
It is worth noting that the architectural setups differ, making direct numerical comparisons challenging even for experimental evaluation.
As summarized in Table 1, the majority of prior works optimized only energy and delay objectives and they did not consider the payment cost objective.
They used a binary offloading, which makes it harder to compare with the proposed algorithm that uses a partial This approach enables optimization of all the objectives by exploiting the benefits of both sides, edge servers and end-devices.
Moreover, while effective, the above studies often struggle with explorationexploitation balance or premature convergence, especially in multi-objective contexts.
Thus, there is still a need for an algorithm that effectively balances exploration and exploitation while simultaneously optimizing all three performance metrics.
The current work distinguishes itself by proposing a novel hybrid algorithm that combines the strengths of PSO and WOA, enhanced with crossover, mutation, and Lyvy flight (CML) operators to provide a better balance between global exploration and local exploitation.
The hybrid PSO-WOA (CML) algorithm jointly optimizes energy consumption, execution delay, and monetary cost in an SDN-enabled MEC framework, achieving superior convergence behavior and scalability across various system sizes.
Our contributions include:
Oe An SDN-enabled MEC framework that simplifies management and addresses IoT heterogeneity and mobility through centralized control.
Hybrid PSO-WOA approach for an efficient task offloading in mobile edge A (Fatima Z.
Cherhabi.
A ISSN: 1693-6930 Oe A novel hybrid PSO-WOA (CML) algorithm integrating WOAAos spiral update.
PSOAos velocity-based learning, and CML operators for enhanced exploration and convergence.
Oe Comprehensive benchmarking against six metaheuristics under identical conditions, supported by statistical validation (Friedman and Wilcoxon test.
Oe Scalability analysis showing the algorithmAos robust performance and stable execution time (ET) as the number of users increases from 20 to 100.
The rest of this paper is structured as follows: section 2 presents the method, detailing the system model, problem formulation, and the proposed hybrid algorithm.
Section 3 provides the results and discussion, where we present the experimental setup and conduct a comparative analysis of performance, scalability, and statistical significance.
Finally, section 4 offers the conclusion and outlines future research Table 1.
Comparison with related works Reference .
Proposed algorithm
Algorithm
CSA
GWO
ABC
PSO
PSO
WOA DE
WOA Convex optimization WOA GWO
GTO
BBO
PSO WOA
Energy ue
Delay
Cost
Offloading degree Selective Binary Binary Binary Binary Selective Binary Binary Binary Binary Selective Binary Selective Partial
Multi-server ue
Multi-user ue
METHOD
System model We consider a multi-user, multi-server SDN-enabled MEC environment, where a set of IoT devices ycA = .
cO1 .
A , ycOycA } randomly distributed within a 100y100 m2 simulation coverage area.
These devices communicate wirelessly with a macro base station (BS) equipped with an SDN controller, which orchestrates task offloading to a set of edge servers ycA = .
cI1 .
A , ycIycA }, connected via high-speed wired links.
The SDN controller, with its network programming capabilities, stands out as a natural candidate for orchestrating the network, services, and devices by hiding the complexities of the heterogeneous environment from end-devices .
IoT devices periodically send task metadata and network status to the controller, which determines the offloading strategy using a hybrid evolutionary optimization algorithm.
Each task is processed either locally, offloaded to an edge server, or partitioned between both.
The offloading strategy aims to minimize energy consumption, delay, and monetary costs, with decisions encoded in two vectors:
Oe yu = .
A , yuycA ): Continuous values representing the offloading ratio for each task.
Oe yu = .
A , yuycA ): Discrete values indicating the server assigned to each task.
If a task is offloaded .
uycn > .
, then yuycn = yco, ycn OO .
A , ycA} designates the chosen server.
For local execution, yuycn = 0 and yuycn = 0.
Communication model Wireless transmission from IoT devices to the BS occurs over a shared radio spectrum with total bandwidth B .
, .
The uplink data rate for device Ui is modeled as:
ycIycn = yaA ycoycuyci2 .
ycEycn yaycn yua 2 OcycA yc=1,ycOycn ycEyc yayc where Pi is the transmission power.
Hi is the channel gain.
E2 is the channel noise, and the term OcycA yc=1,ycOycn ycEyc yayc represents the effects from other IoT devices.
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 514-526 TELKOMNIKA Telecommun Comput El Control Computation model Each task is defined by the triplet Qi= (Di.
Ci, ycNycnycoycaycu ), where Di defines the input data size.
Ci is the required CPU cycles, and Tmax is deadline.
The delay and energy consumption in the local execution are typically .
given as:
ycNycnycoycuycaycayco = yaycn yaycnycoycuycaycayco = yuI ycycyceyc .
ceycn )2 yaycn where yuI ycycyceyc a constant based on device architecture and fi is the computing capability of device Ui.
For offloaded tasks, the transmission time and energy consumption between device Ui and the BS are defined as:
ycNycnycNycycaycuyc = yaycn yaycnycNycycaycuyc = ycEycn yaycn ycIycn ycIycn The ET and cost on an edge server ycIyuycn are given by:
yayccyciyce ycNycn yayccyciyce yaycn = yaycuycyc.
uycn ) O yaycn ycyceycyc yuycn here yce represents the MEC server .
cIyuycn ) computational load allocated to device Ui, and yaycuycyc.
uycn ) is the unit cost per cycle charged by the server yuycn .
The final stage involves downloading the results from the edge server to the device.
This time is ignored due to the small output size compared to input data, which is a common simplification in the literature .
The total response time, energy consumption, and monetary cost are given by:
yayccyciyce ycoycuycaycayco ycN ycycuycycayco = OcycA yuycn .
cNycnycNycycaycuyc ycNycn ycn=1[.
Oe yuycn )ycNycn ycoycuycaycayco ya ycycuycycayco = OcycA yuycn .
aycnycNycycaycuyc )] ycn=1[.
Oe yuycn )yaycn yayccyciyce ya ycycuycycayco = OcycA ycn=1[ yuycn .
Problem formulation The goal is to find the optimal vectors and that minimize the weighted sum of energy, delay, and monetary cost with yuN1 = 0.
35, yuN2 = 0.
35, and yuN3 = 0.
3 predefined weights based on the preferences of the decision-maker.
ycE: ycAyaycA ( yuN1 ya ycycuycycayco yuN2 ycN ycycuycycayco yuN3 ya ycycuycycayco ) .
u,y.
Subject to:
C1: yuycn OO .
, .
OAycn OO .
A , ycA) C2: yuycn OO .
, 1.
A , ycA}.
OAycn OO .
A , ycA) ycyceycycycoycaycu C3: yaycuycayccyc = OcycA .
OAyc OO .
A , ycA) ycn=1[ yuyc,yuycn yuycn yaycn ] O yce C4: yceycn > 0.
OAycn OO .
A , ycA) yayccyciyce C5: [.
Oe yuycn )ycNycnycoycuycaycayco yuycn .
cNycnycNycycaycuyc ycNycn )] O ycNycnycoycaycu .
OAycn OO .
A , ycA) where: yuyc,yuycn is the kronecker delta function, which is equal to 1 if yc = yuycn .
ndicating task Qi is assigned to server .
, and 0 otherwise The constraint C1 ensures partial or full offloading.
C2 enforces valid server selection.
C3 ensures that the cumulative workload assigned to each server does not exceed its maximum computational capacity .
ce ycyceycycycoycaycu ), preventing overloading.
In practice, if this condition is violated, a penalty proportional Hybrid PSO-WOA approach for an efficient task offloading in mobile edge A (Fatima Z.
Cherhabi.
A ISSN: 1693-6930 to the overload .
uIya Oo .
aycuycayccyc Oe yce ycyceycycycoycaycu )) is added to the remote execution energy of all tasks mapped to that server, discouraging infeasible allocations.
C4 ensures the constraint of device local capacity .
ceycn ).
Finally, for constraint C5, which ensures task deadlines, if the local or remote response time exceeds the task deadline .
cNycnycoycaycu ), the value is scaled by a penalty factor .
uI ycN > .
, degrading the overall fitness as follows:
ycNycn = ycNycn yuI ycN Oo .
cNycn Oe ycNycnycoycaycu ), ycNycn > ycNycnycoycaycu This approach differentiates between small and large violations, providing a smoother search landscape and improving convergence.
Given the NP-hard nature of the formulated problem .
, exact methods become impractical for large-scale systems.
Thus, metaheuristic and evolutionary algorithms are adopted to obtain near-optimal solutions within reasonable computation time.
Proposed task offloading and resource allocation algorithm Evolutionary approaches, in practice, converge faster to the neighborhood of an optimal solution and can be very effective if the domain knowledge is exploited .
Among them WOA, which is inspired by the bubble-net hunting strategy of humpback whales, alternates between encircling prey, spiral movement, and global search phases for robust solution exploration and fine-tuned exploitation .
On the other hand.
PSO emulates the collective and intelligent behavior of bird flocking or fish schooling, where particles .
adjust their positions based on personal and group bests, facilitating efficient searches .
The hybrid PSOWOA (CML) algorithm combines PSOAos social learning and WOAAos spiral/encircling to balance exploration and exploitation.
It maintains diversity via mutation/crossover and escapes local optima using CS Lyvy flight jamps, while dynamically adapts parameters for convergence speed.
Each particle is updated using both PSO and WOA operators, followed by CML evolutionary operators .
utation, crossover.
Lyvy fligh.
The algorithm workflow is summarized as follows.
Initialization and solution representation The process begins by initializing a population of ycuycEycuycy particles and velocities.
Each particle ycUycn represents a potential solution and is composed of two distinct components, reflecting the mixed-variable nature of the problem:
Oe Offloading decisions .
: a continuous vector ycUycn .
yu = .
A , yuycA ), where yuycn OO .
, .
represents the portion of task ycn to be offloaded.
Oe Server assignments .
: a discrete vector ycUycn .
yu = .
A , yuycA ), where yuycn OO .
, .
, ycA} is the integer identifier of the MEC server assigned to task ycn.
This explicit separation allows for the correct application of continuous and discrete optimization operators to the respective parts of the solution.
Hybridization strategy Each particleAos velocity is adjusted by considering PSO three components .
: the influence of its previous velocity .
cOycn ), its personal best position .
cyyaAyceycycycn ), and the global best position .
ciyaAyceycy.
This is expressed as:
ycOycn .
= yc.
ycOycn .
cyyaAyceycycycn Oe ycUycn .
) yca2 .
ciyaAyceycyc Oe ycUycn .
) .
where: yc is the inertia weight, c1 cognitive factor, c2 social factor, and both ( yc1 , yc2 ) are random numbers in .
, .
to introduce stochastic behavior.
The particleAos position is then updated using WOA-inspired mechanisms .
, selected based on a random value yc OO .
Oe Shrinking encircling mechanism .
f yc < 0.
: update the position using the formula:
ycUycn .
= yciyaAyceycyc Oe ya UI ya .
where ya = 2yca UI yc Oe yca is a control parameter, ya = .
a UI yciyaAyceycyc Oe ycUycn .
|, ya = 2yc and yca decreases from 2 to 0 over iterations.
Oe Spiral updating Mechanism .
f yc Ou 0.
: use the spiral equation to update the position:
ycUycn .
= yaA .
yce ycayco .
yuUyc.
yciyaAyceycyc where yaA = .
ciyaAyceycyc Oe ycUycn .
|, yca is a constant, and yco is a random number in [Oe1, .
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 514-526 TELKOMNIKA Telecommun Comput El Control Next, the updated velocity is applied to further refine the particleAos position:
ycUycn .
= ycUycn .
ycOycn .
CML enhancement operators To enhance the search space, the algorithm further improves solution space exploration by applying one of the three CML operators based on predefined probabilities .
cy_yaycycuycyc, ycy_ycAycyc, and ycy_yayceycy.
Oe Crossover: combines the positions of two particles to generate new candidate solutions using blend crossover for the continuous vectors and a uniform crossover for discrete yu vectors.
Oe Mutation: slightly modifies a particleAos position to explore local regions by using Gaussian mutation to yu vector and random-reset mutation for yu vector.
Oe Lyvy flight: enabling occasional long-distance jumps in the search space to help the algorithm escaping from local optima.
Thus, a Lyvy step is calculated and added to the yu vector.
Dynamic parameter tuning To avoid static behavior across generations, key PSO parameters are adapted dynamically over the Oe The inertia weight yc is linearly decreased using a damping value d to shift the search from exploration to exploitation.
Oe The cognitive yca1 is gradually decreased while the social coefficient yca2 is increased to shift the search focus from individual experiences to global learning.
Fitness evaluation and optimal solution update During every iteration, boundary constraints for yuycn are enforced by clipping values to the range .
, .
, while yuycn values are rounded to the nearest integer and clipped to the range .
M].
Then, the fitness of each new particle is evaluated based on the three objectives .
nergy, delay, and monetary cos.
with weights set respectively as 0.
35, 0.
35, and 0.
Then, the ycyyaAyceycyc and yciyaAyceycyc values are updated until a maximum number of iterations is reached.
Pseudocode of the proposed algorithm The complete structure of PSO-WOA (CML) algorithm is summarized in the pseudocode below:
ycyceycycyu ycn ), and network conditions .
Oe Inputs: task parameters .
aycn , yaycn , ycN ycoycaycu ), device/server capacities .
ceycn , yce ycn Eaycn .
E ).
Oe Outputs: optimal task offloading decision .
ector yu O) and server assignments .
ector yu O) minimizing energy, delay, and monetary cost.
Algorithm 1.
PSO-WOA (CML) for MEC task offloading // --- Initialization --2.
Initialize population (P) of nPop particles with random and vectors Initialize empty velocity vectors for each particle FOR each particle Xi in P DO Calculate fitness F(X.
= .
35*Total_Energy 0.
35*Total_Delay 0.
3* Total_Cos.
Initialize personal best pBest_i with Xi and F(X.
END FOR Find global best .
Bes.
particle from P // the minimum value of F(X.
// --- Main Loop --10.
FOR t = 1 TO MaxIter DO FOR each particle Xi in P DO // --- Core hybrid update --13.
// -- Calculate PSO velocity vector -14.
Vi.
= calculate_pso_velocity(Xi, pBest_i, gBest, w, c1, c.
with eq.
// -- WOA strategic repositioning -16.
r = rand() IF r < 0.
5 THEN
Xi_new = shrinking_encircling (Xi, gBest, .
using eq.
ELSE
Xi_new = spiral_updating mechanism(Xi, gBest, .
using eq.
Hybrid PSO-WOA approach for an efficient task offloading in mobile edge A (Fatima Z.
Cherhabi.
A ISSN: 1693-6930
ENDIF
// -- Final position update with PSO velocity (Refinemen.
Xi = Xi_new Vi.
// --- CML enhancement operators --25.
r = rand() IF r < p_Mut THEN Apply mutation to Xi (Gaussian for , random-reset for ) ELSE IF r < p_Mut p_Cross THEN Select two parents P1.
P2 from P Apply crossover to Xi.
P1.
P2 .
lend for , uniform for ) ELSE
Apply Lyvy flight to the vector of Xi
END IF
// --- Evaluation and updates --35.
Enforce boundary constraints on Xi.
and Xi.
Evaluate fitness F(X.
IF F(X.
< F.
Best_.
THEN pBest_i = Xi IF F(X.
< F.
Bes.
THEN gBest = Xi
END FOR
// --- Dynamic parameter tuning --41.
Decrease w, c1, and increase c2
END FOR
RETURN gBest // The optimal solution Complexity analysis Let ycA be number of users, ycA number of servers, ycuycEycuycy population size, and ya number of iterations.
Fitness evaluation .
er particl.
: a naive calculation of the fitness function in .
is dominated by two Oe Calculating all ycA transmission rates .
, which requires computing the interference sum OcycA ycn=1 ycEycn yaycn for each user, resulting in an ycC .
cA 2 ) complexity.
Oe Verifying the server load constraint (C.
, which, if implemented by checking each of the ycA servers, requires summing ycA user loads, resulting in an ycC.
cA y ycA) complexity.
In our implementation, we reduce this cost significantly with two optimizations.
First, the ycC .
cA 2 ) interference term is reduced to ycC.
cA) by pre-calculating the global interference sum OcycA ycn=1 ycEycn yaycn once and then finding each userAos specific interference via ycC.
Second, the ycC.
cA y ycA) load check is reduced by initializing an M-sized array for server loads .
cA)), then updating it in a single pass over all N users .
cA)).
Consequently, the optimized fitness evaluation cost .
ncluding all objectives and constraint check.
for a single particle is ycC.
cA .
cA ycA)) = ycC.
cA ycA).
Given that ycA O ycA in our scenarios, this cost simplifies to ycC.
cA).
PSO/WOA updates: updating velocities and positions of all particles takes ycC .
cuycEycuycy UI ycA).
CML operators: mutation, crossover, and Lyvy flight modify particle positions and they require ycC .
cuycEycuycy UI ycA).
Updating best positions: ycC.
cuycEycuyc.
Total complexity: considering all iterations, the practical computational complexity of the algorithm is ycC.
a UI ycuycEycuycy UI ycA).
Furthermore, scalability to very large-scale systems can be improved through parallelized evaluation, as fitness computations for particles are independent.
Parameter tuning also can reduce constants.
Memory complexity: the algorithm must store the position, velocity, and ycyyaAyceycyc for all ycuycEycuycy particles.
Since each particleAos representation .
u and yu vector.
is of size N, the total memory complexity is ycC .
cuycEycuycy UI ycA), which remains modest for typical MEC settings.
RESULTS AND DISCUSSION
The performance of six state-of-the-art metaheuristic algorithms (GAs .
, .
, .
CS .
ABC .
GWO .
PSO .
, and WOA .
) is evaluated and compared against the proposed hybrid The objective is to minimize a composite cost (C-Cos.
function that incorporates energy consumption, execution delay, and monetary cost.
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 514-526 TELKOMNIKA Telecommun Comput El Control Experimental setup Simulations were conducted in a network with 20 IoT users and 3 MEC servers managed by an SDN Each algorithm was executed over 200 iterations and 10 independent runs to ensure statistical Table 2 summarizes the system parameters, which are based on common values found in the All algorithms were implemented in MATLAB 2013a on an Intel Core i7, 2.
11 GHz processor with 20 GB RAM to ensure fair comparison.
Table 2.
System parameters Description Input data size of a task to be executed (M.
CPU cycles required to complete each task (Gcycle.
Maximum tolerable delay by each task .
Local computing capacity of each user (GH.
Effective capacitance constant for end-device architecture Bandwidth of the wireless channel (MH.
Uplink transmit power of each user to MEC server .
W) Channel gain between device Ui and BS .
Gaussian channel noise Portion of MEC server computational load per user (GH.
Maximum server computing capacity (GH.
Unit cost per cycle charged by server yuycn Initial inertia coefficient Inertia coefficient damping factor Personal acceleration coefficient Social acceleration coefficient Probability of applying crossover operator Probability of applying mutation operator Probability of applying Lyvy flight operator Population size Symbol yaycn yaycn ycNycnycoycaycu yceycn yuI ycycyceyc yaA ycEycn yaycn yua2 yce ycyceycycyuycn yce ycyceycycycoycaycu yaycuycyc.
uycn ) yc ycc yca1 yca2 ycy.
yaycycuycyc ycy.
ycAycyc ycy.
yayceycyc ycuycEycuycy Value .
1, 0.
2, 1.
, .
2, 1.
5 y10-27 , .
, .
, .
5, 1.
Performance evaluation To provide a comprehensive analysis, we evaluated the algorithms based on convergence behavior, final solution quality, and statistical significance.
Figure 1 illustrates the convergence trends and Table 3 summarizes the average results.
The evaluation considers the mean A standard deviation of the final C-Cost, the approximate number of iterations required to converge (Conv_Ite.
, the ET of a full run, and the effective execution time (EET), which reflects the actual runtime required to find the final best solution and reach The proposed algorithm is further compared with the baseline strategies.
namely AuAll local modeAy where all the tasks are performed in end-devices and the AuAll offloaded modeAy where all the tasks are performed in edge servers .
Figure 1.
Convergence behavior of proposed hybrid algorithm vs.
standard metaheuristics Hybrid PSO-WOA approach for an efficient task offloading in mobile edge A (Fatima Z.
Cherhabi.
A ISSN: 1693-6930 Table 3.
Performance overview
Algorithm
GWO
PSO
ABC
WOA
Pure PSO-WOA
PSO-WOA CML
All local All offloaded Mean A std .
inal C-cos.
517 A 0.
415 A 0.
600 A 0.
375 A 1.
615 A 1.
474 A 0.
871 A 0.
296 A 0.
670 A 1.
675 A 1.
ET .
Conv_Iter 186 EET .
In terms of solution quality, the proposed PSO-WOA CML algorithm achieved the lowest average final C-Cost .
, outperforming all competing algorithms, including GWO .
PSO .
, and WOA .
It also outperformed the pure PSO-WOA .
indicating that naive hybridization may not always yield benefits and can degrade balance between exploration and exploitation, whereas the integration of CML operators significantly improved optimization efficiency.
Relative to the baseline strategies.
PSOWOA CML reduced the final solution by 24.
6% compared to all local execution and by more than 46% compared to full offloading, confirming its strong multi-objective optimization capability.
Regarding convergence behavior.
WOA demonstrated the fastest convergence .
but suffered from premature stagnation, yielding suboptimal solutions.
CS converged extremely slowly .
with minimal gains.
In contrast, the PSO-WOA CML algorithm achieved a balanced behavior, converging within 54 iterations, which is faster than GA .
and PSO .
while still providing the best overall solution quality.
This reflects the hybrid algorithmAos ability to maintain exploration in early stages and shift towards exploitation during later iterations.
The ET analysis shows that CS and WOA were the fastest algorithms in raw runtime .
1 sec and 2.
6 sec, respectivel.
, while Pure PSO-WOA was the slowest .
4 se.
The proposed PSO-WOA CML required 3.
8 sec per run, which is moderate considering the significant quality improvements achieved.
When considering the EET, which better reflects practical convergence speed.
PSO-WOA CML reaches stable solutions in 1sec, faster than GA.
PSO, and ABC, highlighting its suitability for real-time edge Statistical validation Since metaheuristic results are typically non-normally distributed, we adopted non-parametric tests following the methodology outlined in .
The Friedman test was applied to rank the algorithms across runs, and the Wilcoxon signed-rank test was used for pairwise comparisons with the proposed PSO-WOA CML.
Table 4 summarizes the Friedman ranks and Wilcoxon outcomes.
The proposed PSO-WOA CML algorithm achieved the lowest average rank .
est performanc.
, followed by WOA and PSO, while GA and ABC consistently ranked worst.
The Friedman test rejected the null hypothesis of equal medians .
< 0.
confirming statistically significant differences among algorithms.
For Wilcoxon signed-rank test, pairwise comparisons between PSO-WOA CML and each competitor confirmed that the improvements are statistically significant in most cases.
For example.
PSO-WOA CML vs.
GA .
< 0.
, vs.
ABC .
< 0.
, and vs.
< 0.
showed strong significance.
Differences with PSO and WOA were less pronounced but still statistically meaningful .
< 0.
These findings statistically substantiate the effectiveness of the proposed hybridization and its diversity-enhancing operators in avoiding premature convergence.
Table 4.
Friedman ranks and Wilcoxon test results Algorithm
PSO-WOA (CML)
WOA
PSO
GWO
ABC
Mean final C-Cost Friedman rank Wilcoxon vs.
CML .
-valu.
Ae 043 (< 0.
038 (< 0.
018 (< 0.
007 (< 0.
<0.
<0.
TELKOMNIKA Telecommun Comput El Control.
Vol.
No.
April 2026: 514-526 TELKOMNIKA Telecommun Comput El Control Scalability analysis To assess scalability, the algorithms were tested under an increasing number of users .
Ae.
with three MEC servers.
Figure 2 illustrates the evolution of mean final C-Cost and EET averaged over 10 runs.
As the number of users increases from 20 to 100, all algorithms show a natural rise in the mean C-Cost due to the heavier computational demand.
However, the proposed PSO-WOA CML algorithm consistently delivers the lowest cost across all scales, starting at 7.
and rising smoothly to 54.
contrast, other methods like GA and ABC exhibit much steeper growth, exceeding 129 and 131, respectively, at 100 users.
This highlights the superior scalability of the hybrid design, which maintains cost efficiency under increasing system load.
Notably.
PSO-WOA CML also outperforms the pure hybrid PSO-WOA, demonstrating the significant benefits of incorporating crossover, mutation, and Lyvy flight operators.
Figure 2.
Scalability behavior of proposed hybrid algorithm vs.
standard metaheuristics In terms of EET, the proposed PSO-WOA CML algorithm shows nearly constant runtime (OO1 se.
as user numbers grow compared to other algorithms such as ABC .
074 sec at 80 user.
or CS .
811 sec at 80 user.
This suggests that while the problem size increases, the enhanced search mechanism of the CML operators allows the algorithm to find high-quality solutions even faster, which implies good scalability in time complexity.
Interestingly.
WOA and pure PSO-WOA report lower EET values at larger scales, but their performance is unstable and paired with higher costs, reflecting premature convergence.
Overall.
PSO-WOA CML maintains a near-linear scalability trend, achieving the best balance between computational efficiency and optimization quality, which is essential for large-scale MEC task offloading environments.
Discussion The PSO-WOA CML clearly demonstrates superior robustness, rapid convergence, and high-quality solutions across diverse scenarios.
Its hybrid structure integrates complementary and diverse search strategies and mechanisms.
PSOAos social learning mechanism drives the population toward promising regions, while WOAAos dynamic spiral update provides powerful local exploitation.
Crucially, the inclusion of Lyvy flights allows the algorithm to make occasional large jumps, a proven strategy for escaping local optima where simpler algorithms might stagnate.
Likewise, the genetic operators of crossover and mutation maintain population diversity, preventing premature convergence and ensuring a robust exploration of the solution Finally, the dynamic parameter tuning gradually moves the search from exploration to exploitation, accelerating convergence.
The superiority of the hybrid approach observed in our results aligns with findings reported in recent For instance, .
demonstrated that integrating WOA with DE significantly improves task offloading efficiency compared to standard algorithms.
Similarly, our results confirm that hybrid mechanisms, specifically the inclusion of CML operators, prevent the premature convergence often seen in standalone WOA implementations.
Furthermore, while .
utilized GTO to minimize energy, delay, and cost, our proposed PSO-WOA CML achieves comparable stability in convergence but offers improved scalability for larger user sets .
p to 100 user.
This suggests that hybrid evolutionary strategies are increasingly essential for handling the high-dimensional search spaces typical of dense SDN-MEC environments, a conclusion also supported by the multi-user multi-server analysis in .
, .
CONCLUSION
This paper addressed the joint task offloading and resource allocation problem in SDN-enabled MEC environments for latency-sensitive IoT applications.
A hybrid PSO-WOA algorithm enhanced with Hybrid PSO-WOA approach for an efficient task offloading in mobile edge A (Fatima Z.
Cherhabi.
A ISSN: 1693-6930 crossover, mutation, and Lyvy flight CML operators was proposed to minimize a weighted sum of energy consumption, execution delay, and monetary cost.
Comparative evaluation against six benchmark algorithms (ABC.
CS.
GA.
GWO.
PSO, and WOA) demonstrated that the proposed algorithm delivers statistically significant improvements in solution quality, convergence speed, and scalability.
Notably, the algorithm maintained its performance advantage as the number of users scaled from 20 to 100, exhibiting a stable and EET that is critical for real-time systems.
The success of the hybridization is attributed to its effective integration of PSOAos explorative social learning and WOAAos exploitation capabilities, further enhanced by CML evolutionary operators that promote diversity and escape from local optima.
Future work will focus on validating this approach on real-world testbeds or through large-scale simulations using platforms like EdgeCloudSim.
We also plan to extend the model to dynamic scenarios with random task arrivals and explore adaptive mechanisms for real-time parameter tuning and workload prediction to further enhance its applicability in production MEC environments.
FUNDING INFORMATION
Authors state no funding involved.
AUTHOR CONTRIBUTIONS STATEMENT
The first author prepared the manuscript.
the second and third authors provided supervision and critical guidance, while the rest helped in writing reviews and editing.
Name of Author Faatima Z.
Cherhabil Sonia-Sabrina Bendib Maamar Sedrati Chahrazed Adouane Sifeddine Benflis C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
DATA AVAILABILITY
Data availability is not applicable to this paper.
REFERENCES