Evolutionary Programming Research Articles

Angle stability improvement using optimised proportional integral derivative with filter controller

Load inconsistency has disrupted the power system, causing rotor angle fluctuation that leads to angle instability in the system. This research suggests an innovative proportional integral derivative with filter (PIDF)-based thyristor-controlled series compensator (TCSC) controller that utilise an evolutionary programming sine cosine algorithm (EPSCA) for hybrid optimisation to increase the angle stability of the power system. The challenge of the PIDF-TCSC design is transformed into an optimal control problem with respect to performance indices, such as the maximum imaginary part of system eigenvalues, damping ratio and damping factor, where another multi-objective function is utilised to determine the best stabiliser settings. Eigenvalue analysis is used to conduct the stability study in a linearised paradigm of the single-machine infinite-bus (SMIB) network. The resilience of the PIDF controller was tested using a SMIB power network under various operating circumstances. Simulation results are used to evaluate the system's effectiveness with the proposed optimised PIDF-TCSC controller to that of the system using the proportional integral derivative, proportional integral, and base case PIDF-TCSC approaches. The research findings demonstrate the efficacy of EPSCA in implementing PIDF-TCSC motif and its excellent resilient performance for improving power system stability as related to other strategies in various situations.

Effect of multi-unit and multi-type DG installation using integrated optimization technique in distribution power system planning

With the rise in load demand, improving the voltage profile and reducing line loss is vital to ensure reliable power delivery to the customer. However, increasing power plant generation capacity is limited by environmental and economic factors, requiring a careful assessment of locally optimal options. Distributed Generation (DG) installation into the electricity grid is one of the reliable remedial actions to ensure a smooth power delivery. Installation of DG requires an optimization process to identify the appropriate placement and sizing. Inaccurate sizing and placement of the DG installation may result to over-compensation or under-compensation phenomena. This paper proposes a novel approach termed the Integrated Immune Moth Flame Evolutionary Programming technique (IIMFEP) for optimizing the installation of DG sources in distribution systems. It handles various scenarios, including multi-DG single-type and multi-DG multi-type installations, with the main objective of minimizing power loss in the system. This technique employs a hybrid approach that combines elements of immune algorithms, moth flame optimization, and evolutionary programming to achieve more accurate and efficient results. Two cases were considered in this study termed Case 1 and Case 2. Results in Case 1 discovered that the optimal sizing and placement of four Type III DGs exhibit the lowest power loss worth 2.74 kW (98.78 % reduction) for the 69-Bus RDS, while for the 118-Bus RDS the power loss is 319.89 kW (75.36 % reduction). In Case Study 2, the combination of DG Types I and III provided the highest power loss reduction. With one DG Type I and two DG Type III units installed, power loss was reduced by 97.15 % to 6.41 kW for the 69-Bus RDS and by 62.01 % to 493.21 kW for the 118-Bus RDS. The proposed IIMFEP managed to alleviate the setback experienced in the traditional EP, AIS and MFO which found to be stuck at local optimum. The IIMFEP method is compared to Moth Flame Optimization, Artificial Immune System and Evolutionary Programming and validated using the IEEE 69-Bus and 118-Bus Radial Distribution Systems, resulting in outstanding performance.

Data-driven evolutionary programming for evaluating the mechanical properties of concrete containing plastic waste

Plastic waste (PW) has emerged as a global environmental concern due to its detrimental impact on ecosystems and human health. Traditional concrete heavily relies on natural aggregates like sand, gravel, and crushed stone, whose extraction leads to environmental degradation, including habitat destruction and resource depletion. Recently, the use of PW in concrete has gained attention as a sustainable alternative to these conventional aggregates. By incorporating PW as a partial replacement for natural aggregates, the construction industry can reduce its reliance on finite resources while also addressing the issue of PW. However, despite its potential environmental benefits, the incorporation of PW into concrete has primarily been explored through experimental studies, which are often time-consuming and resource-intensive. Therefore, this study aims to optimize the utilization of waste plastic in concrete through machine learning (ML) techniques, specifically Multi-Expression Programming (MEP) and Gene Expression Programming (GEP). A comprehensive literature review was conducted to compile a database for evaluating the compressive strength (CS) and tensile strength (TS) of PW concrete. The most influential parameters, such as plastic (P), gravel (G), water (W), cement (C), sand (S), and age (A), were considered as inputs in the models' development. The models developed were thoroughly evaluated using multiple statistical measures. Additionally, sensitivity analysis was conducted to discern and highlight influential factors that have a significant impact on the predicted outcomes. The findings indicate that both MEP (CS_R2 = 0.88, and TS_R2 = 0.89) and GEP (CS_R2 = 0.87, and TS_R2 = 0.88) models performed well, with MEP demonstrating slightly superior performance. Sensitivity analysis highlights the significant influence of cement (25.63 % and 24.53 %) and plastic (22.4 % and 23.44 %) on concrete strength properties. Furthermore, the equations provided by GEP and MEP models are simple to use from a practical perspective. Overall, this study contributes to sustainability efforts by promoting the incorporation of waste materials in concrete mixtures, thereby reducing reliance on cement.

Imperative Genetic Programming

Genetic programming (GP) has a long-standing tradition in the evolution of computer programs, predominantly utilizing tree and linear paradigms, each with distinct advantages and limitations. Despite the rapid growth of the GP field, there have been disproportionately few attempts to evolve ’real’ Turing-like imperative programs (as contrasted with functional programming) from the ground up. Existing research focuses mainly on specific special cases where the structure of the solution is partly known. This paper explores the potential of integrating tree and linear GP paradigms to develop an encoding scheme that universally supports genetic operators without constraints and consistently generates syntactically correct Python programs from scratch. By blending the symmetrical structure of tree-based representations with the inherent asymmetry of linear sequences, we created a versatile environment for program evolution. Our approach was rigorously tested on 35 problems characterized by varying Halstead complexity metrics, to delineate the approach’s boundaries. While expected brute-force program solutions were observed, our method yielded more sophisticated strategies, such as optimizing a program by restricting the division trials to the values up to the square root of the number when counting its proper divisors. Despite the recent groundbreaking advancements in large language models, we assert that the GP field warrants continued research. GP embodies a fundamentally different computational paradigm, crucial for advancing our understanding of natural evolutionary processes.

Microsolvation of a Proton by Ar Atoms: Structures and Energetics of ArnH+ Clusters.

We present a computational investigation on the structural arrangements and energetic stabilities of small-size protonated argon clusters, Ar nH +. Using high-level ab initio electronic structure computations, we determined that the linear symmetric triatomic ArH +Ar ion serves as the molecular core for all larger clusters studied. Through harmonic normal-mode analysis for clusters containing up to seven argon atoms, we observed that the proton-shared vibration shifts to lower frequencies, consistent with measurements in gas-phase IRPD and solid Ar-matrix isolation experiments. We explored the sum-of-potentials approach by employing kernel-based machine-learning potential models trained on CCSD(T)-F12 data. These models included expansions of up to two-body, three-body, and four-body terms to represent the underlying interactions as the number of Ar atoms increases. Our results indicate that the four-body contributions are crucial for accurately describing the potential surfaces in clusters with n> 3. Using these potential models and an evolutionary programming method, we analyzed the structural stability of clusters with up to 24 Ar atoms. The most energetically favored Ar nH + structures were identified for magic size clusters at n = 7, 13, and 19, corresponding to the formation of Ar-pentagon rings perpendicular to the ArH +Ar core ion axis. The sequential formation of such regular shell structures is compared to ion yield data from high-resolution mass spectrometry measurements. Our results demonstrate the effectiveness of the developed sum-of-potentials model in describing trends in the nature of bonding during the single proton microsolvation by Ar atoms, encouraging further quantum nuclear studies.

Pan-Evo: The Evolution of Information and Biology's Part in This.

Many people wonder whether biology, including humans, will benefit or experience harm from new developments in information such as artificial intelligence (AI). Here, it is proposed that biological and non-biological information might be components of a unified process, 'Panevolution' or 'Pan-Evo', based on four basic operations-innovation, transmission, adaptation, and movement. Pan-Evo contains many types of variable objects, from molecules to ecosystems. Biological innovation includes mutations and behavioural changes; non-biological innovation includes naturally occurring physical innovations and innovation in software. Replication is commonplace in and outside biology, including autocatalytic chemicals and autonomous software replication. Adaptation includes biological selection, autocatalytic chemicals, and 'evolutionary programming', which is used in AI. The extension of biological speciation to non-biological information creates a concept called 'Panspeciation'. Panevolution might benefit or harm biology, but the harm might be minimal if AI and humans behave intelligently because humans and the machines in which an AI resides might split into vastly different environments that suit them. That is a possible example of Panspeciation and would be the first speciation event involving humans for thousands of years. This event will not be particularly hostile to humans if humans learn to evaluate information and cooperate better to minimise both human stupidity and artificial simulated stupidity (ASS-a failure of AI).

Evolutionary Ensemble Learning for EEG-Based Cross-Subject Emotion Recognition.

Electroencephalogram (EEG) has been widely utilized in emotion recognition due to its high temporal resolution and reliability. However, the individual differences and non-stationary characteristics of EEG, along with the complexity and variability of emotions, pose challenges in generalizing emotion recognition models across subjects. In this paper, an end-to-end framework is proposed to improve the performance of cross-subject emotion recognition. A novel evolutionary programming (EP)-based optimization strategy with neural network (NN) as the base classifier termed NN ensemble with EP (EPNNE) is designed for cross-subject emotion recognition. The effectiveness of the proposed method is evaluated on the publicly available DEAP, FACED, SEED, and SEED-IV datasets. Numerical results demonstrate that the proposed method is superior to state-of-the-art cross-subject emotion recognition methods. The proposed end-to-end framework for cross-subject emotion recognition aids biomedical researchers in effectively assessing individual emotional states, thereby enabling efficient treatment and interventions.

Comparison of boosting and genetic programming techniques for prediction of tensile strain capacity of Engineered Cementitious Composites (ECC)

Plain concrete is weak against tension and has low Tensile Strain Capacity (TSC) which significantly affects its long-term performance. To overcome this issue, Engineered Cementitious Composites (ECC) were developed by incorporating polymer fibres in the cement matrix which increases ductility and provides higher TSC than plain concrete and they have emerged as a viable alternative to brittle plain concrete. This study is conducted in an attempt to develop empirical prediction models for TSC prediction of ECC without requiring extensive experimental procedures. For this purpose, two evolutionary programming techniques known as Multi Expression Programming (MEP), Gene Expression Programming (GEP) along with two boosting-based techniques: AdaBoost and Extreme Gradient Boosting (XGB) were developed using data collected from published literature. The gathered dataset had seven input parameters including water-to-binder ratio, sand, fibre content, cement, fly ash, superplasticizer, and age etc. and only one output parameter i.e., TSC. The error assessment of developed models was done using correlation coefficient, Mean Absolute Error (MAE), and Objective Function (OF) etc. and the error comparison showed that XGB has the highest accuracy having the least OF value of 0.081 as compared to 0.11 of AdaBoost, 0.13 of GEP, and 0.16 of MEP. Shapley additive analysis was conducted on the XGB model since it proved to be the most accurate, and the results highlighted that fibre content, age, and water-to-binder ratio are the most important features to predict TSC of ECC.

Embedded Real-Swarm Evolutionary Programming Technique for Intelligent Load Curtailment Strategy

Some traditional optimization techniques are inaccurate and failed to reach their optimal solutions since the solutions normally stuck at local optimal. Thus, any optimization technique cannot be generalized as a reliable optimizer since some optimization techniques are unique to solve optimization problems. This may also occur in power system optimization problem. Load curtailment is one of the important issues in power systems since its approach can help control the power system loss. In general, it is termed as loss minimization so that the delivery of electricity to the consumers can be smoothened. This paper proposes a new optimization technique, Embedded Real Swarm Evolutionary Programming (ERSEP) for identify contingencies occurrence in power system. ERSEP is the integration of real mutation swarm operator with the traditional evolutionary programming (EP) which aims to produce better results in terms of achieving lower optimal solution. Comparative studies were conducted to observe the advantages of ERSEP over the traditional. Results exhibited that the proposed ERSEP outperformed the traditional EP in achieving lower optimal solution validated on IEEE 30-Bus Reliability Test System (RTS). Significant results deduced from this study revealed that total transmission loss reduction worth 52.83% was achieved by EP, 54.09% solved by PSO and 74.09% by ERSEP in Case 1 for chosen load condition. In Case 2, ERSEP maintains to achieve the highest loss reduction worth 54.97%, while EP achieved 51.03% and PSO achieved 52.98% loss reduction. ERSEP maintains to achieve highest loss reduction worth 61.63%, while EP achieved 51.03% and PSO achieved 52.98% loss reduction. This implies that ERSEP is superior in all cases to reach the lowest minimized transmission loss.

Reactive Power Management in Loss and Voltage Control via Integrated Clonal Accelerated Evolutionary Programming

Optimal Reactive Power Dispatch (ORPD) plays a crucial role in maintaining voltage stability, enhance power transfer capability, improve system efficiency, regulate voltages, manage congestion, facilitate renewable energy integration, and achieve cost savings in power systems. This paper presents a new optimization technique for optimal reactive power management in power transmission system, called Integrated Clonal Accelerated Evolutionary Programming (ICAEP) algorithm to optimize the reactive power to be dispatched by the generator buses under 3 scenarios with cases. The ICAEP was developed based on hybridization of the traditional Artificial Immune System (AIS) and Evolutionary Programming (EP). The two cases demonstrate the effect of reactive load increment at the chosen load buses; while the three scenarios represent the ORPD schemes which indicate the involvement of generator buses either 3 generators, 4 generators or 5 generators. Implementation of ICAEP outperformed AIS and EP in both objective functions either in minimum voltage maximization or power loss minimization, involving all the cases under the three scenarios. The performance of the ICAEP is evaluated on the IEEE 30-bus test system. The results would be beneficial to power system operators and planning expansion and knowing the status of their systems in their utilities. The developed optimization engine is also robust and feasible for further optimization problem solving initiatives.

Impact of Under Voltage Load Shedding Approach for Voltage Security Control in Power Quality Environment

Contingencies in power system are an ever-present problem for electrical engineers. They may cause the system to have low voltages due to active and reactive power deficiencies. Engineers shold consider the many solutions to approach this problem. The solution has to be appropriate to the contingency faced so as to be able to solve the issue without major damage to a power system. A drastic measure that can be used is by removing low voltage loads or ‘shedding’ the problematic loads. This method of Under Voltage Load Shedding is done by shedding or ‘islanding’ buses that have fallen to a predetermined minimum voltage for a predetermined time to prevent a cascade of blackouts in the widespread power system. The method to automate the process is by using two optimization techniques, Evolutionary Programming (EP) and Particle Swarm Optimization (PSO). This paper proposes a new hybrid algorithm, named Integrated Chaotic Swarm Based-Evolutionary Programming Optimization (ICSBEP) Technique for Voltage Security Control using Under Voltage Load Shedding (UVLS) approach. Voltage security is indicated by the reduction in voltage stability index, FVSI. In this study, EP, PSO and ICSBEP optimizations algorithms were developed and tested on a IEEE 30-bus reliability test system (RTS). Comparative studies were conducted to observe the advantages of the hybrid algorithm over traditional EP and PSO algorithms. The results obtained from the study can help manage the power quality of the system in ensuring that the customer receive secure electricity supply.

Intelligent Composite Compensation Under Load Variation in Power Transmission System.

The power transmission system is in a stressed condition due to the increasing electricity demand. This stress, exacerbated by the deregulated power system environment, necessitates an urgent additional supply to maintain system adequacy. One important initiative to alleviate the transmission burden which meets the load demand can be rectified by composite compensation scheme. This paper showcases intelligent composite compensation under varying loads, emphasizing loss minimization. The approach integrates a loss control scheme involving Distributed Generation (DG) and Optimal Reactive Power Dispatch (ORPD) with multi-DG installation termed composite compensation, employing a novel optimization technique called Integrated Cloning Accelerated Mutation Evolutionary Programming (ICAMEP). The study identifies optimal locations and sizes for composite compensation in the power transmission system, demonstrating its superiority over traditional optimization techniques namely the evolutionary programming (EP) and artificial immune systems (AIS). Results are demonstrated for four cases involving single DG, 3 DGs and composite compensation validated on IEEE 30-Bus Reliability Test System (RTS). ICAMEP is superior over EP and AIS in achieving the highest loss reduction.

Integrated Index Vector Method and Hybrid Ant Lion Chaotic Evolutionary Programming Optimization (HALCEP) Technique for Loss Minimization in Distribution System

Distribution system is the final section of the electrical power system, apart from the transmission and generation system. The distribution system acts as the interface that connects the high-voltage network to the low-voltage consumer service point. Consequently, the distribution system contributes the most of the overall losses in the electrical power system. Hence, evolutionary computation was introduced to accomplish a reduction of the previously said losses. The evolutionary computation involves optimization techniques to allocate distributed generation (DG) to the distribution system. Unfortunately, several optimization techniques are not capable of achieving accurate results and are trapped at local optima. This paper presents the Integrated Index Vector Method and Hybrid Ant Lion Chaotic Evolutionary Programming Optimization (HALCEP) technique for loss minimization in a distribution system. In this study, Evolutionary Programming (EP), Ant Lion Optimization (ALO) and HALCEP optimization engines are developed. The validation process was simulated on the IEEE 33-bus radial distribution system (RDS) model. Comparative studies were performed to gain a clear observation of the advantage of the developed HALCEP over the conventional EP and the ALO techniques, effectively showing its capability to outperform them.

Particle Swarm Optimization (PSO) And Evolutionary Programming (EP) Technique for Optimal Placement and Sizing DG for Minimizing Loss in IEEE-30 Bus System

In recent years, most growing nations worldwide have experienced an unavoidably rising demand for electricity, which may result in a dropping of the voltage profile and a reduction in system stability, both of which have the potential to overload the power generation system significantly. One of the ways to reduce loss system network in this study is by distributed generation (DG) allocation, which the DG optimal location and sizing are the two most significant considerations for integration of DG. Improper placement and DG sizing in the power system not only result in increased total power losses but also affect the electrical system’s capability to be function properly. This paper provides a comparative analysis of two meta- heuristic optimization techniques, that is, Particle Swarm Optimization (PSO) and Evolutionary Programming (EP), to examine the optimal placement and sizing of distributed-generation (DG) for photovoltaic systems with the aim of minimizing the losses in interconnected distributed generation, IEEE-30 bus system. The objective function of this study is minimization the power loss with considered some constraints which are voltage limits and DG sizing limits are being covers in this study. The optimization issue has been solved by working with MATLAB/m-files software. The outcomes derived from the simulation results in this study demonstrated that PSO performance of two units of DG is better compared to EP algorithm. The voltage profile was improved drastically, and the power loss was reduced as lowest as 17.4486MW in the first case, 17.4368MW in the second case, and 17.4179MW in the third case.

Optimal sizing and placement of capacitors in the isolated microgrid throughout the day considering the demand response program

Reactive power compensation (RPC) is a big problem during power system operation. Parenthetically, capacitor allocation and sizing may be the only convenient solution for RPC of power systems. The loss sensitivity factor (LSF) is applied here for finding the optimum capacitor position. This paper presents quasi-oppositional fast convergence evolutionary programming (QOFCEP), fast convergence evolutionary programming (FCEP), and evolutionary programming (EP) for the optimum location and sizing of shunt capacitors in the isolated microgrid (MG) for minimizing total real power loss throughout the day with and without the demand response program (DRP). The 33-node, 69-node, and 118-node isolated MGs have been studied to authenticate the efficacy of the suggested approach. Each MG includes small hydro power plants (SHPPs), solar PV plants (SPVPs), wind turbine generators (WTGs), diesel generators (DGs), and plug-in electric vehicles (PEVs).

Search and Rescue Optimization for Combined Economic Load and Emission Dispatch

The goal of combined economic and emission dispatch (CEED) in the power system is to solve the economics management of generators in order to achieve both minimum fuel prices and pollution levels while meeting load demands and operating limits. The Search and Rescue (SAR) optimization methodology is developed in this study to address the CEED problem, and the results gained are compared with the Evolutionary Programming and Flower Pollination Algorithm methods. Those analyses are able to evaluate the effectiveness as well as the rate of convergence of the methods under consideration. In general, the CEED problem is initially considered a bi-objective problem that has been turned into a single objective function by the use of the price penalty element in its solution. Both solutions were tested on an IEEE 10-Generator 39-Bus System, which has a valve point impact with transmission loss. MATLAB is additionally utilized to run modeling for the evaluated system, with each system subjected to three separate load demands. The results reveal that the SAR technique performs better because it generates resilient and effective solutions to the CEED problem with the lowest fuel price, greenhouse gas emissions, CEED price, and power loss.

Investigation and Optimization of Biosorbent Capacities of Some Plants Used in Daily Life

In this study, sage, chamomile, and tarragon leaves, which are used as spices and consumed as beverages in daily life, were considered as different biosorbents that can be used in water purification by biosorption. At the same time, the effects of the parameters of initial dye concentration (10-200 mg/L), temperature (20-50 ⁰C) and contact time (0-120 min) on biosorption capacity were investigated. The biosorption processes were found to follow Freundlich isotherm and pseudo-second order (PSO) reaction kinetics. In the study, the process was also modeled using multi-tree evolutionary computation based automatic programming (AP) methods. The methods used initial dye concentration, temperature, and contact time as variables. According to the simulation results, these methods obtained nonlinear mathematical models of the processes with R^2 values as high as 0.99 for each biosorbent. By providing the most accurate models to accurately predict biosorption capacity, this study will make a significant contribution to the field of water treatment using experimental and AP methods.

Minimize Total Cost and Maximize Total Profit for Power Systems with Pumped Storage Hydro and Renewable Power Plants Using Improved Self-Organizing Migration Algorithm

This study presents the application of an improved self-organizing migration algorithm (ISOMA) for minimizing the total electricity production expenditure (TEPE) and maximizing the total electricity sale profit (TPRF) for hydrothermal power systems (HTPS) without and with renewable energies. Two power system configurations were employed to test the real efficiency of ISOMA while dealing with two objective functions. In the first configuration, there was one thermal power plant and one hydropower plant, while in the second configuration, wind and solar energy were both connected to the first system. The results achieved in the first configuration with the first objective function indicated that ISOMA not only outperformed SOMA according to all comparison criteria but was also superior to other methods such as evolutionary programming (EP), acceleration factor-based particle swarm optimization (AFPSO), and accelerated particle swarm optimization (APSO). The evaluation of the results achieved by ISOMA in the second configuration with the objective function of maximizing the TPRF revealed that ISOMA could reach better profits than SOMA in terms of maximum, mean and minimum TPRF values over fifty trial runs. As a result, it was concluded that pumped storage hydropower plants are very useful in integrating with renewable power plants to cut total cost for thermal power plants and in reaching the highest profit for the whole system. Also, ISOMA is a suitable algorithm for the considered problem.

Optimization of Microphone Placement for Audio-based Modeling of Construction Jobsites

Heavy equipment is a crucial resource in the construction industry. Recent studies have shown that analyzing the sound patterns generated by construction machinery can be an effective way to monitor their performance and detect potential operational issues. However, construction jobsites are complex environments that require consideration of multiple factors when creating an audio-based model. To perform efficient audio-based modeling of jobsites, it is essential to optimize the number and placement of microphones to capture the sound emitted by all the operating machines and achieve optimal sound quality. To address this challenge, we developed two optimization methods: (a) an integer programming model that guarantees finding the optimal placement of microphones, and (b) an evolutionary programming model, a heuristic approach more suited to larger problem instances. We evaluated the effectiveness of these models in five different case studies from construction jobsites. Our results showed that the developed models require a reasonable number of microphones to achieve the desired sound quality, demonstrating their satisfactory performance. Notably, both approaches exhibited similar performance in terms of the required number of microphones needed to cover all the machinery.

Integration of Multiple Distributed Generation Sources in Radial Distribution System Using a Hybrid Evolutionary Programming-Firefly Algorithm

This paper presents an approach for the optimal integration of multiple distributed generation (DG) sources in a radial distribution system. The integration of DG sources poses various challenges such as can lead to higher power losses caused by reverse power flow, voltage exceeding secure limits, voltage stability, power quality, and economic operation. To address these challenges, a hybrid algorithm is proposed which combines the benefits of both Evolutionary Programming and Firefly Algorithm. The proposed hybrid Evolutionary - Firefly Algorithm is employed for the determination of the optimal size of the DG sources. The objective of the proposed algorithm is to minimize the total system power losses and improve the voltage profile. The algorithm considers various constraints including the DG capacity limits and voltage limits. A comprehensive case study is conducted on a radial distribution system to demonstrate the effectiveness of the proposed approach. The simulation results show that the hybrid algorithm can find the optimal size and location of DG sources while achieving the desired system performance. The integration of multiple DG sources leads to a significant reduction in power losses and improved voltage profile. Furthermore, the proposed approach provides a flexible framework for the optimal integration of DG sources in radial distribution systems, allowing for the accommodation of different types and capacities of DG sources. The proposed technique is tested on the IEEE Reliability Test systems, specifically the IEEE 69-bus. The combination of DG at bus 61 and bus 27 yields a loss reduction index of 94%.