







































AQ. Almousawi et al. /Future Technology                                                                        February 2026| Volume 05 | Issue 01 | Pages 
303-313 

303 

 

 

 

Article 

An efficient novel deep learning-based predicting 

model optimized by an improved DAOA algorithm 

for microgrid energy management 
Ali Q. Almousawi 1*, Nabil Jalil Aklo 2, Zaid Alhadrawi 3  

1Electrical Engineering Department, Faculty of Engineering, University of Kufa, Iraq 
2Department of Biomedical Engineering, College of Engineering, University of Thi-Qar, Thi-Qar,64001, Iraq 

A R T I C L E   I N F O 
 

Article history: 
Received 29 August 2025  
Received in revised form 
20 October 2025 
Accepted 04 December 2025 
 
Keywords:  
Energy management, LSTM, Improved Dynamic 
Arithmetic Optimization, Photovoltaic, Wind 
Turbine, Deep learning 
 
*Corresponding author 
Email address: 
ali.almousawi@uokufa.edu.iq 
 
DOI: 10.55670/fpll.futech.5.1.26 

A B S T R A C T 
 

This paper presents robust energy-demand and renewable power forecasts for 
the microgrid using deep learning-based forecasting and a metaheuristic-based 
optimization model. A Long Short-Term Memory (LSTM) is used to model the 
temporal nonlinear dynamics of the energy datasets. A new Improved Dynamic 
Arithmetic Optimization Algorithm (IDAOA) is developed to fine-tune LSTM 
parameters, incorporating inertial weights, a mutation factor, and the triangle 
mutation operator to balance exploration and exploitation. The model's 
performance is verified on various datasets, including wind turbines (WT), 
photovoltaic (PV) systems,  load demands, and day-ahead electricity pricing. 
This work shows that the IDAOA-LSTM model outperforms other strategies. 
Practically, the Root Mean Squared Error (RMSE) was 0.021 in the forecast of 
WT power and 0.031 in the case of PV power. The model performs well in 
predictions, with high coefficient of determination (R²) values (R² ≥ 0.98) 
throughout all tasks. These findings strengthen the applicability of the 
proposed method to enhance energy-saving measures while preserving the 
stable operation of those microgrid (MG) systems. 

1. Introduction 

Examples of renewable energy generation systems that 
have recently gained popularity are Wind turbines (WT) and 
photovoltaic (PV) systems [1]. This integration into microgrid 
(MG) systems has the potential to reduce dependence on 
fossil fuels and their associated greenhouse gas emissions, 
resulting in a more secure electricity supply and a cleaner 
environment. However, renewable energy sources exhibit 
irregular, non-continuous power generation, as well as load 
demand patterns, which must be addressed to schedule and 
maintain grid stability [2,3]. Forecasting renewable energy in 
addition to load demand is essential for MG operations, cost 
control, and energy storage scheduling [4]. Conventional 
approaches for predicting MG uncertainty may be ineffective 
at capturing the temporal characteristics and nonlinearities 
inherent in renewable energy supplies, as MGs become more 
complex when multiple energy sources are added [5]. 
Therefore, more complex models that adequately capture the 
stochastic nature of renewable energy generation are 
urgently needed [6,7]. Because of its ability to extract 
hierarchical features independently and model nonlinear 
relationships, deep learning approaches have emerged as a 
viable alternative for processing complex processes [8]. 
Despite their potential, many fundamental challenges remain 

unresolved in the literature, particularly in hyperparameter 
selection and tuning, which are critical to achieving optimal 
model performance. As a result, ongoing research 
investigates effective strategies for hyperparameter 
modification that enhance the robustness, precision, and 
generalization capabilities of deep learning models [9]. 
Although deep neural networks, particularly LSTMs, have 
demonstrated promising results in sequence prediction, their 
effectiveness depends heavily on the selection of key 
hyperparameters, such as the number of hidden layers [10]. 
Most optimization algorithms suffer from premature 
convergence or limited search capabilities in the global search 
space, which significantly affects the fine-tuning of complex 
models [11]. To do this, this study developed a technique that 
combines LSTM networks with an Improved Dynamic 
Arithmetic Optimization Algorithm (IDAOA) to select 
hyperparameters efficiently. The primary goal is to develop a 
reliable, accurate, and efficient forecasting model for 
photovoltaic power, wind energy, and load demand in 
microgrid systems. This means that the proposed 
methodology in this paper not only seeks to enhance the 
model accuracy but also to provide real-time energy 
management in dynamic systems. 

 

 

Future Technology 

Open Access Journal 

https://doi.org/10.55670/fpll.futech.5.1.26 

 

 

Journal homepage: https://fupubco.com/futech 

 

ISSN 2832-0379 

February 2026| Volume 05 | Issue 01 | Pages 303-313 

mailto:ali.almousawi@uokufa.edu.iq
https://doi.org/10.55670/fpll.futech.5.1.26
https://fupubco.com/futech


AQ. Almousawi et al. /Future Technology                                                                        February 2026| Volume 05 | Issue 01 | Pages 303-313 

304 

 

 

 

 

 

 

 

 

 
The rest of the paper is structured as follows: Section 2 

reviews related works on forecasting and optimization 
methods for renewable energy. Section 3 describes the 
proposed technique, data preprocessing, the LSTM model 
structure, and IDAOA optimization. Section 4 discusses the 
outcomes and performance evaluations, as well as the 
superiority of the proposed approach. The work is 
summarized in Section 5, which focuses on major results and 
suggests potential directions for future research. 

2. Related works 

Many researchers throughout the world have 
investigated various strategies and techniques linked to this 
work. Zarma et al. [12] proposed energy demand forecasting 
models for hybrid MG energy management, using five 
algorithms: linear regression, random forest, artificial neural 
network, extreme gradient boosting, and support vector 
regression. The study sought to investigate many parameters, 
including irradiance, temperature, time of day, humidity, and 
season. These elements specify the performance of 
generators, grid systems, and photovoltaics. Cavus et al. [13] 
presented a new energy management technique known as 
deep-fuzzy logic control, which integrates LSTM-based 
conceptual modelling with adaptive fuzzy logic to improve the 
outcome in a microgrid system connected to the grid. 
Mahmoudabadi et al. [14] introduced a detailed energy 
management strategy for scheduling distributed generation 
systems in both normal and abnormal modes within 
microgrids connected to a distribution network. This strategy 
utilized an extreme learning machine model to predict solar 
and wind power outputs. 

The authors in [15] analyzed a networked microgrid 
system that includes biomass, PV panels, a wind turbine, a 
battery system, and pumped-hydro storage. The paper 
presents a hierarchical deep learning energy management 
method that is implemented under normal conditions, high 
demand, variation in renewable generation, and the worst 
weather conditions. Authors in [16] developed microgrids 
that can operate in parallel with the grid-connected mode and 
the island mode, utilizing synchronizing controllers for 
voltage, phase, and frequency stability based on a deep 
learning control scheme. Mahjoub et al. [17] employ LSTM as 
a prediction strategy in the microgrid energy management, 
which comprises a PV system, a permanent magnet generator, 
a wind turbine, and a battery system, to track energy 
generation and power flow. The authors in [18] suggest short-
term load prediction in a hybrid system using two 
approaches: an Artificial Neural Network (ANN) and an 
Adaptive Barnacle-Mating Optimizer (ABMO) by selecting 
and adjusting the key features of parameters to increase the 
efficiency of prediction, while the job of [19] is to predict 
output energy from wind turbines and PV in a microgrid, 

where the authors apply Support Vector Regression (SVR) to 
increase the accuracy and efficiency of power prediction.  The 
proposed method is compared with a linear regression model 
to minimize error variance, using historical data on weather, 
energy use, and a dynamic grid environment. The authors in 
[20] proposed to predict three main factors in a microgrid: 
next-day energy prices, energy demand, and generation 
capacity, using intelligent forecasting based on deep learning. 
An LSTM network is proposed in conjunction with a global 
attention mechanism (GAM) and genetic algorithm–adaptive 
weight particle swarm optimization (GA-AWPSO) to 
maximize prediction accuracy. Alabi et al. [21] put forward a 
deep learning-based optimization approach for the day-ahead 
scheduling of ZCMES-VPPs. Unlike base model approaches, 
the proposed model incorporates CCS to address emissions 
and EV flexibility, and features a CEM to ensure system 
reliability. It should be clearly mentioned that the objectives 
of the paper are as follows: 
• An efficient deep learning and metaheuristic optimization-

based framework is introduced that leverages advanced 
exploratory capabilities to identify and configure the LSTM 
neural network parameters optimally to maximize the 
energy prediction performance and management systems 
in MGs. 

• An enhanced dynamic Arithmetic Optimization Algorithm 
(IDAOA) is proposed, which incorporates a dynamic inertia 
weight update mechanism along with an adaptive mutation 
coefficient. This strategy adeptly balances the exploration 
and exploitation stages, thus reducing the possibility of 
prematurely converging on local minima. 

• A dynamic exploration technique is presented, which 
combines a dynamic mutation coefficient with a triangle 
mutation approach.  This strategy encourages population 
variety and improves the capability to search globally by 
restricting the algorithm from updating candidate 
solutions only dependent on the proximity of the best local 
solution at the moment. 

3. Methodology 

This work aims to create an accurate energy forecast 
system for effective microgrid energy management. It uses a 
deep learning framework based on Long Short-Term Memory 
(LSTM) networks. LSTM is a suitable solution for time-series 
research since it effectively addresses the disadvantages of 
classic RNNs by preserving long-term temporal relationships 
[22, 23]. As a result, LSTMs have achieved excellent predictive 
accuracy across both sequential and nonlinear datasets. The 
performance of an LSTM network is highly influenced by its 
configuration parameters, which are usually selected at 
random. The size of the hidden layer is an important factor to 
consider when designing an LSTM.  This parameter is 
optimally set in this work to increase LSTM performance 
using the proposed Improved Dynamic Arithmetic 
Optimization Algorithm (IDAOA). Figure 1 shows the 
suggested methodology. 

Our proposed model comprises a sequential process into 
four principal stages to elicit maximum synergy between its 
components: 
A. Data Preprocessing: This phase gathers pure time-series 
information on microgrid energy supply and demand. The 
data is then normalized, allowing the model to learn without 
scale bias between variables. The last step is to transform the 
whole normalized data into the input-output sequences 
expected for training the LSTM network. 

 
 

Abbreviations 

LSTM   Long Short-Term Memory 

IDAOA   Improved Dynamic Arithmetic Optimization Algorithm 

PV   Photovoltaic  

WT   Wind Turbines 

RMSE   Root Mean Squared Error 

MG   Microgrid 

ANN   Artificial-Neural Network 

ABMO   Adaptive Barnacle-Mating Optimizer 

SVR   Support Vector Regression 
GAM             Global Attention Mechanism 

 

 

 

 

 

 

 



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305 

 

 
Figure 1. The suggested framework’s flowchart 

B. Building a Baseline LSTM Model: At this point we have 
defined and built the baseline architecture of the LSTM 
neural network. Such decisions entail the design of the 
underlying LSTM network topology and architecture, the 
output and input layer sizes via time-series data pre-
processing, baseline hyperparameter values prior to 
optimization, and the choice of activation function. The base 
topology of this network determines the search space in the 
IDAOA algorithm. 
C. Hyperparameter optimization with IDAOA: during this 
step, the IDAOA begins searching for the best 
hyperparameters of the LSTM model. For each cycle in 
IDAOA, the LSTM model is trained on the training data using 
a set of hyperparameters. The prediction error(e.g. This 
process is repeated until the parameters that would give the 
lowest possible error are obtained. 
D. Final modeling and forecasting: Once the optimal 
hyperparameters are identified and IDAOA converges, the 
final LSTM model with these optimal parameters is fitted on 
the entire training dataset. Finally, we run the test dataset 
through the trained model, which yields the final predictions. 
These estimated values later guide performance evaluation 
and integration into the microgrid energy management 
system. 

3.1 Data preprocessing 
In this work, data preprocessing is separated into three 

main steps: data cleaning, normalization, and partitioning. 

• Data cleaning 
Data cleaning is primarily done to remove irregularities 

from the dataset, such as duplicates, missing items, and 
invalid entries. Missing values are imputed using the average 

of the preceding and succeeding values, as expressed in 
Equation (1): 

𝑥𝑖 =
𝑥𝑖−1+𝑥𝑖+1

2
                                                                                           (1) 

Where xi, x(i-1),  and x(i+1) represent the missing value, the 
value one hour before, and the value one hour after, 
respectively. 
In our dataset, the missing data rate was very low, and most 
missing points occurred as single points or within very short 
time intervals (e.g., 1 or 2 time steps). Under such conditions, 
where the gap between observed points is minimal, the 
difference between the output of simple linear interpolation 
and more complex techniques such as spline interpolation or 
KNN imputation is negligible in terms of their impact on the 
final model accuracy. In other words, nonlinear effects over 
such short time intervals are of lesser importance. In this case, 
linear interpolation gives a sufficient and consistent local 
estimate while improving the code's simplicity and efficiency. 

• Data normalization 
Variables with lower values may have a 

disproportionately low impact on the prediction model 
because the numerical ranges of distinct attributes differ. This 
is solved by translating all feature values to the [0, 1] range, a 
common technique to improve training convergence and 
model performance. To ensure reproducibility and 
consistency, min-max normalization was applied to each 
feature separately (per-feature scaling). The normalized 
value was determined for each characteristic 𝑥𝑗 , as follows: 

𝑥𝑗
𝑛𝑜𝑟𝑚 =

𝑥𝑗−𝑚𝑖𝑛⁡(𝑥𝑗)

𝑚𝑎𝑥(𝑥𝑗)−𝑚𝑖𝑛⁡(𝑥𝑗)
                                                                                    (2) 

The max⁡(𝑥𝑗) and min(𝑥𝑗) represent the maximum and 

minimum values of the j-th feature calculated across the 
training set. This per-feature min-max scaling avoids features 
with higher numerical ranges from dominating the learning 
process, while simultaneously ensuring that all input 
variables contribute appropriately to model optimization. 

• Data segmentation 
The dataset is divided into two sets:  training and testing. 

The current methodology employs 70% of the data for 
training and 30% for testing. The testing subset is used to 
evaluate the performance of the proposed model, while the 
training subset is used to optimize the suggested LSTM's 
learning process and identify the appropriate size of its 
hidden layer. To prevent information leakage and ensure 
methodological accuracy in time-series prediction, the data's 
chronological sequence was strictly maintained during 
segmentation. There was no random shuffling used. The 
dataset was divided into time intervals, with the first 70% of 
observations (earliest timestamps) assigned to the training 
set and the remaining 30% reserved for testing. 

3.2 LSTM network 
This study uses an LSTM network to estimate energy use 

because it can efficiently handle temporal dependencies and 
sudden variations in the data.  Due to its ability to preserve 
long-term dependencies and alleviate the vanishing gradient 
problem, the LSTM network demonstrates excellent 
performance across a range of sequence-based tasks.  



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306 

 

Figure 2 illustrates the scheme of the LSTM recurrent 
neural network [24]. The cell is the most important part of the 
structure of the LSTM. Every cell is equipped with a recurrent 
unit preserving the input and output side information 
sequences. An LSTM cell consists of four main parts: the input 
gate, the output gate, the forget gate, and the cell state. The 
gates use the sigmoid function to generate activation values 
ranging from zero to one, indicating how much information is 
lost, updated, or transmitted to the next state. However, the 
underlying trainable weights associated with these gates are 
real-valued parameters that lack such limitations. These 
weights are learned during training to optimize the network’s 
performance. The input gate is responsible for incorporating 
new information into the cell state; it selectively admits 
relevant sections of the new input. The output gate 
determines the output of the LSTM cell based on the updated 
cell state, controlling which portions of the state are revealed 
as output. Additionally, the cell state serves to maintain long-
term dependencies and is not modified directly; rather, it is 
regulated by the operations of the forget, input, and output 
gates. 

 
Figure 2. Structure of the LSTM recurrent neural network 

3.3 LSTM neural network optimization using IDAOA 
The size of its hidden layer heavily affects an LSTM 

network's learnability, and larger hidden layers can capture 
overly complex patterns, leading to overfitting. To improve 
the model’s accuracy, IDAOA is recommended to solve this 
problem. It is particularly well adapted to this task, as its 
unique structure enables highly efficient sampling of the high-
dimensional space and increases the likelihood of finding a 
near-optimal solution. The key IDAOA steps for optimizing 
the hidden layer size are summarized here:  

• Step 1: Parameter initialization 
This step comprises initializing the IDAOA's control 

parameters (α and μ). The parameter α, set to 5, determines 
the level of exploitation precision in each iteration.  With an 
initial value of 0.5, the parameter μ balances exploration and 
exploitation equally. 

• Step 2: Generation of initial candidate solutions 
Every IDAOA possible solution X indicates a potential 

LSTM network configuration. These solutions are iteratively 
improved after being randomly initialized within the 
problem's search space. Each solution X encodes a possible 

hidden layer size, and the algorithm progressively updates 
them to move toward the optimal configuration. The initial 
candidate solutions are produced using Eq. (3) with a size of 
N*n (where N represents the population size and n is the 
dimension), and during the iterative process, the optimum 
solution set in each iteration is retained as the current optimal 
or near-optimal value: 

X =

[
 
 
 
 
 

𝑥1,1 ⋯ …
𝑥2,1 ⋯ ⋯
⋯
⋮

𝑥𝑁−1,1

𝑥𝑁,1

⋯
⋮
⋯
⋯

⋯
⋮
⋯
⋯

⁡⁡⁡

𝑥1,𝑗 𝑥1,𝑛−1 𝑥1,𝑛−1

𝑥2,𝑗 ⋯ 𝑥2,𝑛
⋯
⋮

𝑥𝑁−1,𝑗

𝑥𝑁,𝑗

⋯
⋮
⋯

𝑥𝑁,𝑛−1

⋯
⋮

𝑥𝑁−1,𝑛

𝑥𝑁,𝑛 ]
 
 
 
 
 

               (3) 

• Step 3: Fitness function evaluation 
A core aspect of any optimization algorithm is the 

formulation of an appropriate fitness function (or objective 
function). In this study, the RMSE is used to evaluate the 
quality of each candidate solution. For each candidate hidden 
layer size proposed by the IDAOA, an LSTM model is trained 
and evaluated on the energy prediction task. The fitness score 
is then determined using the corresponding RMSE: 

𝑅𝑀𝑆𝐸 = √
1

𝑁
∑ (𝑋𝑎𝑏𝑠.𝑖 − 𝑋𝑚𝑜𝑑𝑒𝑙.𝑖)

2𝑁
𝑖=1                                          (4) 

Where N denotes the total count of observations, Xmodel.i is 
the forecasted value from the LSTM model, and Xobs.i is the 
actual value. 

• Step 4: Determining the best solution 
Based on the fitness values (calculated in the previous 

step), the best solution is selected at each iteration. This 
solution represents the most promising configuration of the 
hidden layer size at the current stage of the optimization 
process. 

• Step 5: Updating the math optimizer accelerated 
function (MOA) 
Before the Arithmetic Optimization Algorithm (AOA) 

begins its main process, it must decide whether to enter the 
exploration or exploitation phase. The MOA function is 
computed using the following equation: 

𝑀𝑂𝐴(𝐶𝐼𝑡𝑒𝑟) = 𝑀𝑖𝑛 + 𝐶𝐼𝑡𝑒𝑟 (
𝑀𝑎𝑥−𝑀𝑖𝑛

𝑀𝐼𝑡𝑒𝑟
)⁡⁡⁡⁡⁡                         (5)                                                                       

Definition: MOA(CIter) is the MOA function value at iteration 
t computed by (4). CIter represents the current iteration. Min 
and Max are the smallest and largest values of the 
acceleration function. 

• Step 6: Updating the math optimizer probability 
(MOP) 
The MOP function determines the probability of entering 

either the exploration or exploitation phase and is defined as: 

𝑀𝑂𝑃(𝐶𝐼𝑡𝑒𝑟 + 1) = 1 −
𝐶𝐼𝑡𝑒𝑟

1
∝

𝑀𝐼𝑡𝑒𝑟

1
∝

           (6) 

                                                                                       
Where MOP(CIter ) is the current iteration, α is a control 

parameter (set in Step 1), and MIter is the maximum count 

of iterations. 

 



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• Step 7: Updating the positions of the candidate 
solutions 
For each candidate solution in the population X, three 

random values r1,r2,r3∈[0,1] are initialized. If r1>MOA, the 
exploration phase is triggered; otherwise, the exploitation 
phase is executed. 

• Step 8: Exploration phase 
If r2<0.5, the division operator (D) is applied to update 

the position; otherwise, the multiplication operator (M) is 
used. The position update equations in this phase are defined 
as: 

𝑥𝑖.𝑗(𝐶𝐼𝑡𝑒𝑟 + 1) =

{

𝑏𝑒𝑠𝑡(𝑥𝑖) ÷ (𝑀𝑂𝑃 + 𝜀) × ((𝑈𝐵𝑗) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖), 𝑟2 < 0.5

𝑏𝑒𝑠𝑡(𝑥𝑗) ÷ (𝑀𝑂𝑃) × ((𝑈𝐵𝑗) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖),⁡⁡⁡⁡𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
⁡

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(7)

            

Where xi.j (CIter+1) is the new position of the j-th dimension 
of solution I, best (xi) is the best-known solution so far, UBj 
and LBj are the upper and lower bounds of dimension j, ԑ is a 
small positive number to prevent division by zero. 

• Step 9: Exploitation phase 
If r3 is less than 0.5, the subtraction operation (S) is 

applied to update the position; otherwise, the addition 
operation (A) is used. The update rules for this phase are: 

𝑥𝑖.𝑗(𝐶𝐼𝑡𝑒𝑟 + 1) =

{
𝑏𝑒𝑠𝑡(𝑥𝑗) ÷ (𝑀𝑂𝑃) × ((𝑈𝐵𝑗) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖), 𝑟3 < 0.5

𝑏𝑒𝑠𝑡(𝑥𝑗) ÷ (𝑀𝑂𝑃) × ((𝑈𝐵𝑗) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖),⁡⁡⁡⁡𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
⁡⁡⁡     

                                                                                                           (8) 

• Step 10: Updating the dynamic inertia weights 
The Arithmetic Optimization Algorithm (AOA) often 

suffers from local optima and slow convergence, mainly 
because it relies on the global best solution to update 
candidate positions. To address this limitation, IDAOA is 
employed to incorporate dynamic inertia weights, thereby 
accelerating AOA convergence. The rate at which the 
solutions are updated throughout each optimization step is 
directly controlled by the inertia weight. Greater exploration 
is enabled in the early stages of the optimization process by 
using larger inertia weights, which cause high-potential 
solutions within the search space to evolve more slowly. On 
the other hand, solutions might move more finely within a 
smaller area as the inertia weights are decreased later. To put 
it another way, exploration is facilitated by bigger inertia 
weights, whereas exploitation is supported by smaller 
weights. To enhance IDAOA's search effectiveness and 
accelerate convergence, this work proposes a dynamic inertia 
weight mechanism that reduces nonlinearity with increasing 
iterations. The dynamic inertia weight computation is shown 
in Eq. (9): 

𝑤(𝑡) = 𝑐 × 𝑤𝑏𝑒𝑔𝑖𝑛 (
𝑤𝑏𝑒𝑔𝑖𝑛

𝑤𝑒𝑛𝑑
)

1

(
1+𝑡
𝑇 )                             (9)                                                                              

In this equation, wbegin and wend are the maximum and 
minimum weights, and c is a randomly generated coefficient 
that dynamically varies around 1. Here, t refers to the current 
iteration, and T denotes the maximum number of iterations. 
By integrating the dynamic inertia weights into the position 
updating equations of the AOA, Equations (7) and (8) are 
respectively reformulated as Equations (10) and (11): 

 

𝑥𝑖.𝑗(𝐶𝐼𝑡𝑒𝑟 + 1) =

{
𝑤(𝑡) × 𝑏𝑒𝑠𝑡⁡(𝑥𝑖) ÷ (𝑀𝑂𝑃+⁡∈) × ((𝑈𝐵𝑗⁡) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖), 𝑟2 < 0.5

𝑤(𝑡) × 𝑏𝑒𝑠𝑡⁡(𝑥𝑗) × 𝑀𝑂𝑃 × ((𝑈𝐵𝑗⁡) − 𝐿𝐵𝑖) × 𝜇 × 𝐿𝐵𝑖), 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
     

                                                                               (10) 

𝑥𝑖.𝑗(𝐶𝐼𝑡𝑒𝑟 + 1) =

{
𝑤(𝑡) × 𝑏𝑒𝑠𝑡⁡(𝑥𝑗) − 𝑀𝑂𝑃 × ((𝑈𝐵𝑗⁡) − 𝐿𝐵𝑗) × 𝜇 + 𝐿𝐵𝑗),⁡⁡⁡⁡⁡𝑟3 < 0.5

𝑤(𝑡) × 𝑏𝑒𝑠𝑡⁡(𝑥𝑗) + 𝑀𝑂𝑃 × ((𝑈𝐵𝑗⁡) − 𝐿𝐵𝑗) × 𝜇 × 𝐿𝐵𝑗),⁡⁡⁡⁡⁡𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
     

                                                                            (11) 

• Step 11: Dynamic mutation 
In this study, a dynamic coefficient mutation is 

introduced, which grows as the number of iterations 
progresses. Through this strategy, the algorithm's ability to 
avoid local optima is enhanced by increasing the probability 
that parts of the population will explore alternative search 
areas.  The following equation computes the mutation 
coefficient: 

𝑝 = 0.2 + 0.5 ×
𝑡

𝑇
                                                                            (12)                

where p is the mutation probability coefficient, which is 
gradually increased as t repetitions are carried out. Three 
solutions are chosen at random and merged in this strategy 
by the following function:                                                                      

𝑋(𝑡) =
𝑋𝑟1+𝑋𝑟2+𝑋𝑟3

3
+ (𝑝2 − 𝑝1) × (𝑋𝑟1 − 𝑋𝑟2) + (𝑝3 −

𝑝2) × (𝑋𝑟2 − 𝑋𝑟3) + (𝑝1 − 𝑝3) × (𝑋𝑟3 − 𝑋𝑟1)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(13)                                                                                                                

where Xr1, Xr2 and Xr3 are three solutions selected randomly 
by (p2-p1), (p1-p3) and (p1-p3) respectively, and computed 
as follows: 

𝑝1 =
|𝑓(𝑋𝑟1)|

�́�
⁡                                                              (14)                                                                                                               

𝑝2 =
|𝑓(𝑋𝑟2)|

�́�
⁡                                                               (15)                                                         

Here, f() is the fitness function, and  p ́ is defined as follows: 

�́� = |𝑓(𝑋𝑟1)| + |𝑓(𝑋𝑟2)| + |𝑓(𝑋𝑟3)|⁡                               (16)                                                                            

The triangular mutation technique facilitates the 
generation of datasets from a randomly chosen pattern while 
maintaining updated solutions at the local optimum. 
Therefore, triangular mutation increases the capability of the 
algorithm to escape local optimal points. 

• Step 12: Stopping criterion 
Steps 3 to 11 are repeated until the stopping condition is 

met or the maximum number of iterations is reached. 

4. Results and discussion 

The outcomes presented in this section aim to evaluate 
the effectiveness and efficiency of the proposed algorithm in 
predicting the four main factors: PV, WT, day-ahead price, and 
load, respectively. The ultimate aim of this strategy is to 
balance demand with supply, so that grid stress is minimized, 
energy prices drop, and end-use consumer satisfaction 
improves. Additionally, forecasting the above four aspects can 
provide clear prospects for the system in the medium and 
long term and be beneficial for constructing a sound 
management system that uses renewables on the supply-
demand side to moderate the system's uncertainty or 



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308 

 

randomness. To evaluate the proposed model, the 
computational cost challenge posed by repeated training of 
the LSTM network within the GA-AWPSO algorithm's fitness 
function was carefully managed. To achieve an optimal 
balance between result accuracy and operational runtime, the 
main parameters of the GA-AWPSO algorithm were set as 
follows: the population size was set to 15 particles and the 
iteration number to 20, resulting in 300 fitness evaluations 
throughout the entire optimization process. It should be 
noted that the hyperparameter optimization process is 
performed only once, and after convergence, the optimal 
parameters are fixed in the model; this approach ensures that 
during the evaluation (testing) phase, the model is applied 
only once with the optimized parameters on new data, 
thereby significantly reducing the testing time. 

Simulations were performed using MATLAB on 
hardware comprising a 10th-generation Intel Core i7 CPU and 
an NVIDIA GeForce GTX 1660 Ti GPU. Under these conditions, 
the time required to train the LSTM model with optimized 
parameters was 25 minutes on average, while the time 
required for prediction on the entire test dataset was only 3 
seconds. Given the limited number of evaluations (300) and 
the very low runtime during testing, this model is 
operationally assessed as highly suitable for forecasting 
applications. To verify the validity and stability of the 
proposed method, the predicted results will be compared 
based on three statistical parameters (MSE, RMSE, and R²). 
These statistics are critical for comparing real and predicted 
performance using a model error calculation and for 
assessing generalization across families of materials.  The 
model's performance is measured at several key points, 
where R2 indicates the degree of convergence between actual 
and estimated values, and MSE and RMSE assess the 
predictive precision. The three parameters are shown in 
Equations (17) - (19). 

𝑅𝑀𝑆𝐸 = √
1

𝑁
∑  𝑛

𝑖=1 (𝑋𝑜𝑏𝑠.𝑖 − 𝑋model .𝑖)
2                                      (17)            

𝑀𝑆𝐸 =
1

𝑁
∑  𝑛

𝑖=1 (𝑋𝑜𝑏𝑠.𝑖 − 𝑋model .𝑖)
2                                            (18)            

𝑅2 = 1 −
∑  𝑛

𝑖=1 (𝑋𝑜𝑏𝑠.𝑖−𝑋model .𝑖)
2

∑  𝑛
𝑖=1 (𝑋𝑜𝑏𝑠.𝑖−�̅�𝑜𝑏𝑠.𝑖)

2                                                         (19)              

Where N is the number of observations, 𝑋model .𝑖  is the 
predicted value, 𝑋𝑜𝑏𝑠.𝑖  is the actual value, �̅�𝑜𝑏𝑠.𝑖  is the mean of 
the observed values. 

4.1 Dataset 
To assess the efficiency of the suggested prediction 

model, a real dataset on microgrid energy management was 
employed. This dataset covers wind turbines, photovoltaic 
(PV), and load demand. Data quality was ensured through 
preprocessing, enabling the model to achieve high accuracy 
during training. The dataset used for forecasting model 
evaluation was obtained from the PJM Interconnection 
database. The data refer to the PJM West Zone [25]. This zone, 
which includes Western Pennsylvania, the states of Ohio, and 
West Virginia, is regarded as one of the most important areas 
for power generation and load management. In total, 800 
hours of data (800 samples) were selected for the 
experiments, corresponding to a 34-day span in 2020. This 
period lasts from January 1, 2020, to February 3, 2020. The 
data were split into training and test subgroups. 30% of the 
total data was allocated to the test set to assess the model's 
validity during the trials [20]. Before applying our algorithms, 
the dataset underwent initial data cleaning. This stage 

identified missing values, which were recovered using a 
simple linear interpolation method (Eq. 1). Figure 3 provides 
an overview of the data used in this work. All parameters for 
the LSTM structure and training requirements are listed in 
Table 1. 

Figure 3. Dataset used in the work 

Table 1. The essential parameters for the LSTM Structure 

Parameters Values 

Number of hidden units in LSTM layers 100 

Dropout rate 0.2 

Max Epochs  100 

Mini Batch Size 32 

Learning Rate 0.001 

Activation function  sigmoid 

Optimizer type  adam 

Gradient Threshold  10 

Number of time steps in each input sequence 10 

 

4.2 Evaluation of proposed method performance in the 
training phase 
Figure 4 shows the convergence curve of the proposed 

method during training. The red curve shows the network 
loss over iterations, while the blue curve shows the RMSE at 
each iteration. As shown, the network loss decreases steadily 
with the number of iterations. The network loss converges 
after 3000 iterations, at which point the loss variations 
become minimal. This indicates that the model has 
successfully captured the patterns. 

4.3 Performance evaluation in PV power forecasting 
The effectiveness of the suggested approach in 

predicting the output power of photovoltaic (PV) systems is 
analyzed in Figure 5. The actual PV power curve (solid blue 
line) and the prediction curve from the suggested model 
(dashed red line) are shown in the upper part of the figure. 
The nearly perfect match between the actual and expected 
curves demonstrates the model's high accuracy and ability to 



AQ. Almousawi et al. /Future Technology                                                                        February 2026| Volume 05 | Issue 01 | Pages 303-313 

309 

 

track dynamic trends and changes in solar power generation 
over time. Furthermore, the error is limited to the range [-0.1, 
0.1], suggesting that the approach is stable and generalizable 
across a wide range of cases. 

 
Figure 4. The LSTM convergence curve tuned with IDAOA 

 

 
Figure 5. Performance evaluation in PV prediction 

The regression indicator between forecast and actual 
PV power, shown in Figure 6, is used to assess the accuracy 
of the suggested method. A: This graph shows the x, y 
coordinates of real value (x) against the output value of the 
model (y). The black circles show the data points, and the blue 
line shows the regression line between the two variables. 
The dashed diagonal line shows the optimal fit line (Y=T). 
Most of the points lie around the perfect line, and the 
regression line overlaps this line clearly. This illustrates that 
the predicted values fit very well with the actual values for 
our proposed model. Real vs model output form a linear 
relationship with R = 0.99852, confirming strong linearity. 
This value, which is close to one, indicates that the learning 
model did well in producing a linear function that accurately 
relates the inputs to the target output. Thus, the curves in 
Figure 6 prove that the prediction of PV production using the 
proposed method behaves very closely to the actual curve, 

and it can confidently be used in renewable energy-based 
energy management systems. 

 

Figure 6. Regression plot comparing the actual and forecasted PV 
power values 

4.4 Performance evaluation in wind turbine (WT) power 
prediction 
The results of wind turbine (WT) output power 

forecasting using the model described are shown in Figure 7. 
The top half of the plot shows the expected values (dashed red 
line) and the actual power (solid blue line). As shown, the 
proposed model captures the complex temporal-spatial 
structures and seasonal variations in wind power generation 
across different timescales. The model's hallmark is its ability 
to detect rapid, nonlinear variations in delivered power. 
Energy systems based on wind, which can be quite variable, 
depend heavily on this. The bottom half of the figure shows 
the normalized prediction error over time. Global error 
distribution is narrow. Most of the data is between ±0.2. This 
shows the model's consistency and reliability during 
evaluation. The lack of clear systematic errors indicates 
proper generalization and no overfitting on the training 
dataset.  

 

Figure 7. Evaluation of the WTs' power prediction using the 
proposed model 



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310 

 

Expected and real  wind turbine output power values 
are presented in Figure 8. The data points (black circles) are 
close to the Y = T line, showing that the model output 
represents well real values. The slope of the regression line 
(blue) is near one, and the intercept is small (around -0.21). 
We can tell that the recommended model performs uniformly 
through the spectrum of target values due to the high density 
of points around the ideal line and the lack of significant 
point scattering on high and low value ranges. This is 
particularly useful in applications such as wind power 
planning, where it is important to have an accurate estimate 
of performance across the full range of operation. The fact 
that the model accurately reproduces wind production on 
this dimension, as shown by the close match between actual 
values and projections, indicates its structural accuracy and 
its ability to effectively portray variability among wind 
production. 

 

Figure 8. Regression analysis of the WT output power 

4.5 Performance evaluation in load power prediction 
The performance of the proposed method for load 

demand forecasting is shown in Figure 9. The dashed red line 
corresponds to estimated quantities, whereas the solid blue 
line displays real data; their correlation is obviously 
significant, as shown by the curves shown earlier. It has 
enabled us to observe temporal variations in electricity 
demand, especially at load troughs and peaks. Reflecting this, 
the model can capture short-term fluctuations and cyclical 
consumption patterns, indicating that it has great potential to 
identify time-related and nonlinear characteristics of load 
signals. The normalized error between the predicted and 
actual quantities is displayed in the lower portion of the 
figure. There is no evident pattern of systematic departure in 
the error distribution, which is uniform and roughly 
symmetric around the zero axis. This indicates there is no 
systemic bias in the model. 

Figure 10 examines the association between the actual 
and predicted load. With a correlation coefficient of R = 
0.99634, the linear regression line fits the data very well, 
demonstrating a high degree of agreement between the 
predicted and actual values. The large R-value indicates the 
model's ability to faithfully capture complex consumption 
behavior. In general, the regression line indicates that the 
proposed model has strong reliability for practical load 
demand control and performs well across a wide range of load 
demand from real data, with strong statistical coherence with 
the real data. 

 
Figure 9. Performance of the proposed method for load prediction 

 

 
Figure 10. Regression analysis of the  actual and predicted load 

4.6 Performance evaluation in day-ahead price (DAP) 
forecasting 

Figure 11 shows that the proposed method is highly 
effective at forecasting the day-ahead price. By comparing the 
actual and predicted price curves, it is evident that the system 
has successfully reconstructed price fluctuations. This is 
especially important in competitive energy markets with 
significant price sensitivity, where even small price 
movements can have exaggerated effects on buying behavior. 
A second important characteristic that illustrates the model's 
potential to learn complex economic and temporal features is 
its ability to capture both nonlinear dynamics and periodic 
behavior in price time series. The normalized error (forecast 
vs. actual price) is shown in the lower part of the figure. The 
low amplitude and symmetric spread of errors support the 
idea that the model is stable and not biased toward any price 
level, while showing low-amplitude errors, especially during 
price-making price fluctuations. As seen in Figure 12, the 
comparison is the day-ahead energy cost versus system 
production. The correlation coefficient (R = 0.99863) of the 
regression line we computed is almost perfect, which, as seen 
below, shows that we can accurately replicate the price levels 



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311 

 

we see in the real world. In other words, the model predicts 
absolute numbers and also the overall tendency. The model's 
predictions show no apparent systematic bias, as evidenced 
by the regression curve's intercept of around 0.0037, which is 
small in the context of energy market prices. Real-time and 
operational forecasting situations benefit significantly from 
this level of accuracy in estimating variable pricing values. In 
general, the analysis of Figure 11 and Figure 12 shows that 
the suggested model is a viable tool for maximizing electricity 
trading strategies in day-ahead markets since it produces 
extremely accurate predictions, successfully adjusts to 
market volatility, and maintains an impartial behavior. 

 
Figure 11. The proposed model's DAP effectiveness 

 

Figure 12. The regression plot between the DAP's actual and 
predicted values 

4.7 Comparative evaluation of prediction methods 
Table 2 provides a quantitative comparison of the 

suggested method, IDAOA-LSTM, with other comparable 
state-of-the-art models for PV and WT power prediction. 
Three common metrics are used to evaluate the performance: 
RMSE, MSE, and R². The suggested model much outperforms 
the best previous approach, GA-AWPSO-LSTM-GAM, which 
produced an RMSE of 0.055 and an MSE of 0.031, in PV power 
prediction, achieving an RMSE of 0.031 and an MSE of 0.0009. 
Additionally, the model's excellent ability to correctly 
reproduce fluctuations in PV production is confirmed by an 
R² of 0.98. Again, the suggested model outperforms the best 
reference model in wind power forecasting, with RMSE = 
0.021 and MSE = 0.0004 as compared to 0.064 and 0.037. In 

this case, the model's robustness and strong relationship over 
the whole range of real wind power outputs are supported by 
the R² value of 0.98. The simultaneous improvement across 
all three measures in both types of renewable energy sources 
is an essential result from Table 2, showing that the IDAOA-
LSTM model retains excellent statistical alignment while 
simultaneously lowering numerical prediction errors. These 
enhancements are the result of the LSTM architecture's 
intelligent layout and parameter optimization via the IDAOA 
approach, which enables it to learn complex, nonlinear 
patterns in renewable energy. 

Table 2. Performance evaluation for forecasting renewable energy 
(PV and WT Power) 

Method 
PVs WTs 

RMSE MSE R2 RMSE MSE R2 

LSTM[20] 0.099 0.065 0.85 0.112 0.077 0.80 

LSTM-
GAM[20] 

0.071 0.047 0.89 0.083 0.051 0.83 

PSO-
LSTM[20] 

0.066 
0.042 0.91 0.073 0.045 0.86 

GA-AWPSO-
LSTM[20] 

0.062 
0.039 0.93 0.071 0.042 0.88 

GRU-
BiLSTM[21] 

0.058 
0.034 0.94 0.067 0.039 0.89 

GAN[21] 0.057 
0.033 0.94 0.069 0.040 0.89 

GA-AWPSO-
LSTM-
GAM[20] 

0.055 
0.031 0.96 0.064 0.037 0.91 

IDAOA-
LSTM(propo
sed) 

0.031 
0.0009 0.98 0.021 0.0004 0.98 

   
 
Table 3. Performance analysis of MG, load, and DAP 

Method 
Load DAP 

RMSE MSE R2 RMSE MSE R2 

LSTM[20] 0.058 0.043 0.84 0.066 0.047 0.85 

LSTM-GAM[20] 0.67 0.049 0.86 0.059 0.042 0.88 

PSO-LSTM[20] 0.060 
0.045 0.91 0.058 0.042 0.91 

GA-AWPSO-
LSTM[20] 

0.043 
0.033 0.84 0.052 0.040 0.93 

GRU-
BiLSTM[21] 

0.035 
0.024 0.96 0.049 0.037 0.93 

GAN[21] 0.039 
0.030 0.95 0.041 0.033 0.94 

GA-AWPSO-
LSTM-GAM[20] 

0.029 
0.021 0.97 0.039 0.028 0.95 

IDAOA-
LSTM(proposed) 

0.024 
0.0005 0.99 0.013 0.0001 0.99 

 

The IDAOA-LSTM approach's prediction ability on two 
additional key parameters, load demand and DAP forecast, is 
studied in Table 3. This comparison uses the same metrics as 
benchmark approaches: R², MSE, and RMSE. The suggested 
method accurately predicts load patterns, with an RMSE of 
just 0.024, an R² of 0.99, and an extraordinarily low MSE of 
0.0005. These results outperform even the best-performing 
models, such as GA-AWPSO-LSTM-GAM (RMSE = 0.029, R² = 
0.97). The prediction of DAP by IDAOA-LSTM has a high 



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R²=0.99, RMSE=0.013, and MSE=0.0001 against the best 
benchmark model (GA-AWPSO-LSTM-GAM) that achieves an 
RMSE of 0.039 and R² = 0.95, showing a significant 
improvement. The R² value, which is close to 1, indicates that 
the proposed model's fit to the actual data is generally high. 
The small RMSE and MSE values, as shown in the table, exhibit 
how efficiently it mitigates prediction error. With these 
characteristics, IDAOA-LSTM is a reliable and practical model 
that can be applied in intelligent energy management 
systems.  

5. Conclusion  

In this paper, a new fusion model is proposed, which can 
improve the energy prediction accuracy of a microgrid by 
combining an IDAOA algorithm and an LSTM network. 
Essentially, modeling temporal data should exploit the 
strengths of deep learning. The adaptive determination of 
hyperparameters, including the number of nodes in the 
hidden layer, is also done via IDAOA. The proposed IDAOA-
LSTM model demonstrated high forecasting accuracy across 
key energy parameters in microgrid systems. For 
photovoltaic (PV) power prediction, the model achieved an 
RMSE of 0.031, and for wind turbine (WT) output, an RMSE of 
0.021. In forecasting electrical load demand and DAP, the 
model achieved RMSE values of 0.024 and 0.013, respectively. 
Across all prediction tasks, the model consistently achieved 
coefficient of determination (R²) values of 0.98 or higher, 
indicating strong alignment between predicted and actual 
values. These results corroborated the utility of the method 
developed herein for simulating and quantifying the 
nonlinear energy response of a structure in order to achieve 
accurate energy control decisions. The findings indicate 
potential for integrating deep learning architectures that 
predict challenges in microgrid and renewable-oriented 
problems into metaheuristic optimization at the upper level. 

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically regarding authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with research ethics policies. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the authors. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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https://doi.org/10.3390/en18040995
https://doi.org/10.1063/5.0236597
https://doi.org/10.1016/j.ecmx.2024.100828
https://doi.org/10.1080/15325008.2023.2217175
https://doi.org/10.3390/en16041883
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