1. Introduction

This paper is an extension of work originally presented in 4th International Conference on Electrical and Electronics Engineering [1]. The purpose of this work is solving economic load dispatch problem with a lot of constraints through with new optimization technique Vortex Search Algorithm.

  Economic load dispatch of a power system is very important in terms of control and planning of that power system. Main goal of ELD is distributed total demand power among the committed thermal generation units with minimum production cost by satisfying set of equality and inequality constraints. If ELD problem is not solved for thermal power plants, demand power may be generated very costly. ELD problem can be basically modeled second order (quadratic) function [2].  However, this function may became more complex, non-smooth and non-convex with some constraints such as valve point loading effect, ramp rate limits, transmission line losses and prohibited zones.

Economic load dispatch plays very big role for operated power plants. For this reason, a lot of researcher studied this issue. A number of optimization techniques developed and applied to ELD problem. Quadratic Programming [3], Linear Programming [4], Non-Linear Programming [5], Lambda Iteration Method [6] etc. techniques were used for solving ELD problem. These traditionally techniques gives good results for basic ELD problem but these techniques may poor results when constraints and complexity are increased.

Together with the advances in the computer sciences, a lot of random search optimization techniques developed and used [7]. Different Evolution [8], Particle Swarm Optimization [9], Genetic Algorithm [10], Artificial Bee Colony [11], Harmony Search [12], Bacterial Foraging Optimization [13], Firefly Algorithm [14], Ant Colony Optimization [15] etc. are some of these techniques. User defined parameters are necessary for these optimization techniques. If the parameters are not chosen properly, the results obtained from these techniques may not be good results.

The organization of this paper as follows: Economic load dispatch, main objective of ELD, constraints of ELD and mathematical express of ELD are described in Section 2. Vortex Search Algorithm and its mathematical model are described in Section 3. Using test system, its parameters, obtained results and figures are described in Section 4. Finally evaluation of this paper is briefed in Section 5.

2. Economic Load Dispatch

There are a lot of operating cost for thermal power plants such as fuel cost, personal fees etc.. In these costs the biggest share is fuel cost of thermal generation units. For this reason solving economic load dispatch problem for thermal power plants is necessity. Main objective of economic load dispatch is keep the total fuel cost as minimum level while meet the total demand power. Basically defined cost function of ELD as a quadratic function as follows:

2.1.  Valve Point Loading Effect

Due to opening stream valves at the power systems losses are increased. This effect is called valve point loading effect. Due to system losses are increased wit valve point loading effect, total cost value is increased. Above equation has sinusoidal terms due to valve point loading effect. This situation can be seen in Figure 1. This transformed equation is expressed as follows:

            F_i = a_i + b_i × P_i + c_i ×  + |e_i × sin(f_i × (  – P_i))       (2)

F_i represents resulting fuel cost value, P_i represent power of thermal generator, a_i, b_i, c_i are cost coefficients and e_i, f_i are valve point loading coefficients of thermal generator unit i.

Total cost value of system is obtained by summed cost values of every thermal generation units.

Figure 1 With and without valve point effect

2.2.  Generators Limits

Thermal generators units must operate maximum and minimum power range. This power range can be different for different units:

                                         P_i,max ≥ P_i ≥ P_i,min                                    (3)

Pi,min and Pi,max are represent minimum generator limit and maximum generator limit of unit i.

2.3.  Power Balance

Total generated power at the thermal power plants meet the demand power by consumers. For this reason transmission line losses must be considered.  The total generated power obtained sum of total demand power and total transmission line losses.

Transmission line losses is calculated as follows:

                  P_loss = P_iB_ijP_j + B_0iP_i + B₀₀             (4)

Total generated power is calculated as follows:

                                       P_i = P_d + P_loss                                  (5)

N represent total thermal power plant. Pd and Ploss represent total demand power by consumer and total transmission line losses respectively. Bij, B0i and B00 are transmission loss coefficients.

2.4.  Ramp Rate Limits

While a thermal generator unit is operating at a certain point, the operating point can only be increased to a certain level determined by the up ramp rate limit or decreased to a certain level determined by the down ramp rate limit.

This situation is shown as follows:

URi represents the up-ramp rate limit, DRi represent down ramp rate limit,   is previous generated power and Pi present generated power of unit i.

2.5.  Prohibited Zone

In some cases, thermal generation units do not worked and do not want to be worked some reasons such as mechanical corruption some particular power range (prohibited zone). These conditions can be expressed as follows:

j represents number of prohibited zones of unit i and j=2, 3, 4 …ni.   represents lower limit and  represents  upper limit of jth prohibited zone. Prohibited zone effect is shown in Figure 2.

3. Vortex Search Algorithm

Vortex search algorithm is a new optimization technique and inspired by stirring liquid materials.[17,18]. VSA is very influential and handy technique for solving economic load dispatch problem.  problem. As a result of using an extensible step size modification arrangement a good balancing explorative and exploitative behavior of the search are obtained [18]. Vortex patterns can be represented in two dimensional space as a lot of nested circuits. The biggest and outer circuit is starting circuit of search space. The center of this circuit is calculated as follows:

Figure 2 Shown of prohibited zones [16]

Upperlimit and lowerlimit are maximum and minimum constraints of the problem. A lot of candidate solutions are constituted into the outer circuit. The initial standard deviation is accepted as radius of this outer circuit and calculated as follows:

                          µ₀ = (upperlimit + lowerlimit) / 2                   (10)

               σ₀ = (max (upperlimit) – min (lowerlimit)) / 2        (11)

Generated candidate solutions must be controlled for ensure these solutions within the maximum and minimum limits of the problem. If these candidate solutions are not into the search space, they must be shifted into the search space. Some candidate solutions, which are not into the search space, shifted into the search space using equation as follows:

             = lowerlimitⁱ + (upperlimitⁱ –lowerlimitⁱ)×rand    (12)

After this step a candidate solution, which is the best solution into the search space, is selected. This best solution is represented s’.  This solution is memorized and current center μ0 is shifted to s’. New candidate solutions are constituted around this new center. All of candidate solutions are compared with previous best solution. If there is a better solution than s’, it is selected as a new best solution [19]. This situation continues each iteration step. Radius of the circuits must be decreased every iteration. For this reason inverse gamma function (gammaincinv) is used and new radius is calculated every iteration as follows:

                       rt = σ0 × (1 / x) × gammaincinv(x, a_t)               (13)

a_t is changeable parameter and it dependent a₀, t and MaxItr. This function shown as follows:

a_t = a₀ – (t / MaxItr)                 (14)

Where t represents iteration number,  MaxItr  represents  maximum iteration number. Due to cover the all search space a₀ is chosen 1. Outline flowchart of VSA method is shown in Figure 3:

4. Test System and Results

Vortex search algorithm was proposed and used for solving economic load dispatch problem. Six generation unit power system was selected. VSA algorithm was applied to this system considering various constraints. Each cases the number of iteration is limited to 1000 for obtained good solutions.

Case1 constraints are ramp rate limits and transmission losses;

Case2 constraints are ramp rate limits, prohibited zones and transmission losses;

Case3 constraints are transmission losses, valve point loading effect and ramp rate limits;

For every case transmission line losses coefficients are same and given as follows:

B=10^-4 ×

B₀=10^-4 ×

B₀₀=0.056

4.1.  Case 1: ELD with Ramp Rate

For this case two different constraints, which are ramp rate limits and transmission line losses, applied to system. Cost coefficients, ramp rate limits data and maximum – minimum limits of generators are shown in Table 1. Results of VSA was given Table 2 with different optimization techniques. Convergence behavior of VSA for this case was shown Figure 4. For this case selected power is 1263MW.

Table 1 Data of Case 1

Table 2 Results for Case 1

Figure 3 Outline flowchart of VSA

Results of vortex search algorithm compared with PSO, CPSO and WIPSO techniques from [20]. It is clear that from the Table 2 proposed VSA method has capable of the finding best solutions and minimum cost value. Figure 4 is shown convergence behavior of VSA for this case.

Figure 4 Convergence behavior of VSA for Case1

4.2.  Case 2: ELD with Prohibited Zone

For this case three different constraints, which are ramp rate limits, prohibited zones and transmission line losses, applied to system. Cost coefficients was given in Table 3. Prohibited zone ranges and maximum – minimum limits of generators were given in Table 4. Ramp rate limits was given in Table 5. Convergence behavior of VSA for this case was shown Figure 5. 1263 MW power was selected for demand power.  Results of VSA and other techniques results are shown in Table 6.

Table 3 Cost Coefficients

Table 4 Limits and Prohibited Zones of Generators

Table 5 Ramp Rate Limits

Table 6 Results for Case 2

According to given results from Table 6, proposed VSA method has better cost value when compared with the MFO, PSO, GA techniques from [21].

Figure 5 is shown convergence behavior of VSA for this case.

Figure 5 Convergence behavior of VSA for Case 2

4.3.  Case 3: ELD with Valve Point Loading Effect

For this case three different constraints, which are transmission line losses, valve point loading effect and ramp rate limits, applied to system. Cost coefficients and valve point loading effect coefficients are given in Table 7. Obtained results were given in Table8 and compared with different methods. Convergence behavior of VSA for this case was shown Figure 6. 1263 MW power was selected for demand power.

Results of VSA and other techniques results was shown in Table 8. Maximum and minimum limits of generators are same with Table 4 and ramp rate limits are same with Table 5. Demand power is selected 1263 MW for this case.

Table 7 Valve point effect and cost coefficients

Table 8 Results for Case 3

It is obviously seen that from the Table 8 VSA, method gave best cost value when compared with   from PSO, CPSO, WIPSO and MRPSO techniques from [22].

Figure 6 is shown convergence behavior of VSA for this case

Figure 6 Convergence behavior of VSA for Case 3

5. Conclusion

In this paper vortex search algorithm was applied to six generator power system for solving economic load dispatch problem. ELD problem was became more complex and more difficult problem with valve point loading effect, ramp rate limits, transmission line losses and prohibited zones constraints. Three different situation were analyzed and for first case minimum cost value was found 15448 $, for second case minimum cost value was found 15447 $, for third case minimum cost value was found 15746 $. Obtained results from VSA compared with another techniques from the literature. These results clearly show that VSA is very capable, feasible and effective method for solving non smooth and very complex economic load dispatch problem.

1. Saka, I. EKE, S. S. Tezcan, M. C. Taplamacioglu., “Economic Load Dispatch Using Vortex Search Algorithm” in 4^th International Conference on Electrical and Electronics Engineering, Ankara Turkey, 2017.
2. Sen. H. D. Mathur, “A New Approach to Solve Economic Dispatch Problem Using A Hybrid ACO–ABC–HS Optimization Algorithm”, Electrical Power and Energy Systems, 78, 735-744, 2016.
3. S. Coelho, V. C. Mariani, “Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization with Valve-Point Effect”. IEEE Trans. Power Syst., 21, 989-996, 2006.
4. Farag, S. Al-Baiyat, T. C. Cheng, “Economic Load Dispatch Multi Objective Optimization Procedures Using Linear Programming Techniques” IEEE Trans. Power Syst., 10, 731-738, 1995.
5. Papageorgiou, E. Fraga, “A Mixed Integer Quadratic Programming Formulation for the Economic Dispatch of Generators with Prohibited Operating Zones” Electr. Power Syst. Res., 77, 1292-1296, 2007.
6. L. Chen, S. C. Wang, “Branch-and-Bound Scheduling for Thermal Generating Units”, IEEE Transactions on Energy Conversion, 8(2), 184–189, 1993.
7. Bhui, N. Senroy, “A Unified Method for Economic Dispatch with Valve Point Effects” in IEEE Int. Con. Power Systems, 1-5, 2016.
8. Balamurugan, S. Subramanian, “Differential Evolution-Based Dynamic Economic Dispatch of Generating Units with Valve-Point Effects,” Electric Power Components and Systems, 36, 828-843, 2008.
9. Sriyanyong, “An Enhanced Particle Swarm Optimization for Dynamic Economic Dispatch Problem Considering Valve-Point Loading,” in Proc. the Forth IASTED International Conference on Power and Energy Systems (AsiaPES 2008), 167-172, 2008.
10. L. Chiang, “Genetic-Based Algorithm for Power Economic Load Dispatch” IET Gener. Trans. Distrib., 1, 261-269, 2007.
11. Hemamalini, S. P. Simon, “Artificial Bee Colony Algorithm for Economic Load Dispatch Problem with Non-Smooth Cost Functions” Electr. Power Compo. Syst., 38, 786-803, 2010.
12. C. Liang, J. R. C. Juarez, “A Normalization Method for Solving the Combined Economic and Emission Dispatch Problem with Meta-Heuristic Algorithms”, Int. J. Electr. Power Energy Syst., 54, 163-186, 2014.
13. Vijay, “Intelligent Bacterial Foraging Optimization Technique to Economic Load Dispatch Problem”, Int. J. Soft Comput. Eng., 2, 55-59, 2012.
14. S. Yang, S. S. S. Hosseini, A. H. Gandomi, “Firefly Algorithm for Solving Non-Convex Economic Dispatch Problems with Valve Loading Effect”, Appl. Soft Comput., 12, 1180-1186, 2012.
15. Pothiya, I. Ngamroo, W. Kongprawechnon, “Ant Colony Optimisation for Economic Dispatch Problem with Non-Smooth Cost Functions”, Int. J. Electr. Power Energy Syst., 32, 478-487, 2010.
16. Saka, “Economic Load and Emission Dispatch Analysis at Power Systems”, M. Sc. Thesis, Gazi University, Ankara, 2017.
17. Dogan, T. Olmez, “A New Metaheuristic for Numerical Function Optimization: Vortex Search Algorithm”, Information Sciences, 293, 125-145, 2015.
18. Dogan B., T. Olmez, “Vortex Search Algorithm for the Analog Active Filter Component Selection Problem”, International Journal of Electronics and Comminications, 69, 1243-1253, 2015.
19. Saka, I. Eke, S. S. Tezcan, M. C. Taplamacioglu, “Application of Vortex Search Algorithm to Economic Load Dispatch Including Transmission Losses with Valve-Point Loading Effect” in 1st International Mediterranean Science and Engineering Congress, Adana Turkey, 2016.
20. Singh, Y. Kumar, “Economic Load Dispatch Using MRPSO with Generator Ramp Rate Limits Constraint” in Int. Con. Comp. Int. and Com. Networks, 632-637, 2012.
21. Trivedi, A. H. Ranpariya, A. Kumar, P. Jangir, “Economic Load Dispatch Problem with Ramp Rate Limits and Prohibited Operating Zones Solve using Levy Flight Moth-Flame Optimizer” in Int. Conf. Energy Efficient Technologies for Sustainability, 442-447, 2016.
22. Singh, Y. Kumar, “Economic Load Dispatch with Valve Point Loading Effect and Generator Ramp Rate Limits Constraint Using MRPSO”, International Journal of Advanced Research in Computer Engineering & Technology, 2, 1472-1477, 2013.

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Crossref Citations

1. Vikas Thammanna Gowda, Landis Humphrey, Aiden Kadoch, YinBo Chen, Olivia Roberts, "Multi Attribute Stratified Sampling: An Automated Framework for Privacy-Preserving Healthcare Data Publishing with Multiple Sensitive Attributes", Advances in Science, Technology and Engineering Systems Journal, vol. 11, no. 1, pp. 51–68, 2026. doi: 10.25046/aj110106
2. Kohinur Parvin, Eshat Ahmad Shuvo, Wali Ashraf Khan, Sakibul Alam Adib, Tahmina Akter Eiti, Mohammad Shovon, Shoeb Akter Nafiz, "Computationally Efficient Explainable AI Framework for Skin Cancer Detection", Advances in Science, Technology and Engineering Systems Journal, vol. 11, no. 1, pp. 11–24, 2026. doi: 10.25046/aj110102
3. Chiang Ling Feng, "Optimization of Sheet Material Layout in Industrial Production Using Genetic Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 10, no. 5, pp. 51–65, 2025. doi: 10.25046/aj100506
4. Marco I. Bonelli, Jiahao Liu, "Revolutionizing Robo-Advisors: Unveiling Global Financial Markets, AI-Driven Innovations, and Technological Landscapes for Enhanced Investment Decisions", Advances in Science, Technology and Engineering Systems Journal, vol. 9, no. 2, pp. 33–44, 2024. doi: 10.25046/aj090205
5. Rafi Zahedi, Amirhossein Ahmadian, Chen Zhang, Shashank Narayana Gowda, Kourosh SedghiSigarchi, Rajit Gadh, "Optimal Engagement of Residential Battery Storage to Alleviate Grid Upgrades Caused by EVs and Solar Systems", Advances in Science, Technology and Engineering Systems Journal, vol. 9, no. 2, pp. 01–08, 2022. doi: 10.25046/aj090201
6. Saidi Mohamed, Habib Cherif, Othman Hasnaoui, Jamel Belhadj, "Design and Comparative Analysis of Hybrid Energy Systems for Grid-Connected and Standalone Applications in Tunisia: Case Study of Audiovisual Chain", Advances in Science, Technology and Engineering Systems Journal, vol. 8, no. 3, pp. 144–153, 2023. doi: 10.25046/aj080316
7. Temsamani Khallouk Yassine, Achchab Said, Laouami Lamia, Faridi Mohammed, "Hybrid Discriminant Neural Networks for Performance Job Prediction", Advances in Science, Technology and Engineering Systems Journal, vol. 8, no. 2, pp. 116–122, 2023. doi: 10.25046/aj080213
8. Abdulrasaq Jimoh, Samson Oladayo Ayanlade, Emmanuel Idowu Ogunwole, Dolapo Eniola Owolabi, Abdulsamad Bolakale Jimoh, Fatina Mosunmola Aremu, "Metaheuristic Optimization Algorithm Performance Comparison for Optimal Allocation of Static Synchronous Compensator", Advances in Science, Technology and Engineering Systems Journal, vol. 8, no. 1, pp. 116–124, 2023. doi: 10.25046/aj080114
9. Jabrane Slimani, Abdeslam Kadrani, Imad EL Harraki, El hadj Ezzahid, "Long-term Bottom-up Modeling of Renewable Energy Development in Morocco", Advances in Science, Technology and Engineering Systems Journal, vol. 7, no. 5, pp. 129–145, 2022. doi: 10.25046/aj070515
10. Afsah Sharmin, Farhat Anwar, S M A Motakabber, Aisha Hassan Abdalla Hashim, "A Secure Trust Aware ACO-Based WSN Routing Protocol for IoT", Advances in Science, Technology and Engineering Systems Journal, vol. 7, no. 3, pp. 95–105, 2022. doi: 10.25046/aj070311
11. Ilhem Bouchriha, Ali Ben Ghanem, Khaled Nouri, "Optimization of the Sliding Mode Control (SMC) with the Particle Swarm Optimization (PSO) Algorithm for Photovoltaic Systems Based on MPPT", Advances in Science, Technology and Engineering Systems Journal, vol. 7, no. 1, pp. 100–106, 2022. doi: 10.25046/aj070110
12. Arakelyan Edik, Kosoy Anatoliy, Andryushin Alexander, Mezin Sergey, Yagupova Yulia, Leonov Maxim, Pashchenko Fedor, "Problems of Increasing the Intelligence of Algorithms for Optimal Distribution of the Current Load on the Combined Heat and Power Plant and Ways to Solve Them", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 5, pp. 369–374, 2021. doi: 10.25046/aj060542
13. Liang Chen, Mo-How Herman Shen, "A New Topology Optimization Approach by Physics-Informed Deep Learning Process", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 4, pp. 233–240, 2021. doi: 10.25046/aj060427
14. Abdulkarim Saleh Masoud Ali, Rozmie Razif Othman, Yasmin Mohd Yacob, Haitham Saleh Ali Ben Abdelmula, "An Efficient Combinatorial Input Output-Based Using Adaptive Firefly Algorithm with Elitism Relations Testing", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 4, pp. 223–232, 2021. doi: 10.25046/aj060426
15. Junho Chang, Mustafa Melih Pelit, Masaki Yamakita, "SLIP-SL: Walking Control Based on an Extended SLIP Model with Swing Leg Dynamics", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 3, pp. 84–91, 2021. doi: 10.25046/aj060309
16. Tamer Saraçyakupoğlu, "Usage of Additive Manufacturing and Topology Optimization Process for Weight Reduction Studies in the Aviation Industry", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 815–820, 2021. doi: 10.25046/aj060294
17. Yu-Chun Huang, "Analyze Performance of Enterprise Supervision System by Game Theory-Take the case of Tatung Management Rights Competition as Example", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 689–693, 2021. doi: 10.25046/aj060279
18. Khalil Ibrahim Mohammad Abuzanouneh, Khalil Hamdi Ateyeh Al-Shqeerat, "Development and Improvement of Web Services Selections using Immigrants Scheme of Multi-Objective Genetic Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 412–422, 2021. doi: 10.25046/aj060248
19. Musa Sulaiman Jibia, Abdussamad Umar Jibia, "Fetal Electrocardiogram Extraction using Moth Flame Optimization (MFO)-Based Adaptive Filter", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 303–312, 2021. doi: 10.25046/aj060235
20. Amany Khalil, Osama Tolba, Sherif Ezzeldin, "Design Optimization of Open Office Building Form for Thermal Energy Performance using Genetic Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 254–261, 2021. doi: 10.25046/aj060228
21. Abdelaziz Lberni, Malika Alami Marktani, Abdelaziz Ahaitouf, Ali Ahaitouf, "Multi-Objective Design of Current Conveyor using Optimization Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 154–160, 2021. doi: 10.25046/aj060218
22. Sk. Md. Masudul Ahsan, Aminul Islam, "Visual Saliency Detection using Seam and Color Cues", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 2, pp. 139–153, 2021. doi: 10.25046/aj060217
23. Subash Pokharel, Aleksandar Dimitrovski, "Ferromagnetic Core Reactor Modeling and Design Optimization", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 1, pp. 810–818, 2021. doi: 10.25046/aj060190
24. Jesus Aguila-Leon, Cristian Chiñas-Palacios, Carlos Vargas-Salgado, Elias Hurtado-Perez, Edith Xio Mara Garcia, "Particle Swarm Optimization, Genetic Algorithm and Grey Wolf Optimizer Algorithms Performance Comparative for a DC-DC Boost Converter PID Controller", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 1, pp. 619–625, 2021. doi: 10.25046/aj060167
25. Hendro Arieyanto, Andry Chowanda, "Classification of Wing Chun Basic Hand Movement using Virtual Reality for Wing Chun Training Simulation System", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 1, pp. 250–256, 2021. doi: 10.25046/aj060128
26. Broderick Crawford, Ricardo Soto, Gino Astorga, José Lemus-Romani, Sanjay Misra, Mauricio Castillo, Felipe Cisternas-Caneo, Diego Tapia, Marcelo Becerra-Rozas, "Balancing Exploration-Exploitation in the Set Covering Problem Resolution with a Self-adaptive Intelligent Water Drops Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 6, no. 1, pp. 134–145, 2021. doi: 10.25046/aj060115
27. Hoang Xuan Thinh, Pham Van Dong, Tran Ve Quoc, "A Study on the Tool Wear in Milling Process of the Gleason Spiral Bevel Gear", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 1402–1407, 2020. doi: 10.25046/aj0506169
28. Luisella Balbis, "Optimal Irrigation Strategy using Economic Model Predictive Control", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 781–787, 2020. doi: 10.25046/aj050693
29. Pearl Keitemoge, Daniel Tetteh Narh, "Effective Application of Information System for Purchase Process Optimization", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 594–605, 2020. doi: 10.25046/aj050673
30. Sergey Alekseevich Serebryansky, Alexander Vladimirovich Barabanov, "To the Question of Multi-Criteria Optimization of Aircraft Components in Order to Optimize its Life Cycle", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 408–415, 2020. doi: 10.25046/aj050649
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32. Simona Kirilova Filipova-Petrakieva, "Applications of the Heuristic Optimization Approach for Determining a Maximum Flow Problem Based on the Graphs’ Theory", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 175–184, 2020. doi: 10.25046/aj050621
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35. Rand Talib, Alexander Rodrigues, Nabil Nassif, "Energy Recovery Equipment and Control Strategies in Various Climate Regions", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 4, pp. 47–53, 2020. doi: 10.25046/aj050407
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37. Ayyoub El Berbri, Adil Saadi, Seddik Bri, "Design and Optimization of Dual-Band Branch-Line Coupler with Stepped-Impedance-Stub for 5G Applications", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 355–360, 2020. doi: 10.25046/aj050346
38. J. Vijay Fidelis, E. Karthikeyan, "Estimation of Influential Parameter Using Gravitational Search Optimization Algorithm for Soccer", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 340–348, 2020. doi: 10.25046/aj050344
39. Jesuretnam Josemila Baby, James Rose Jeba, "A Hybrid Approach for Intrusion Detection using Integrated K-Means based ANN with PSO Optimization", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 317–323, 2020. doi: 10.25046/aj050341
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47. Jalal Benallal, Lekbir Cherif, Mohamed Chentouf, Mohammed Darmi, Rachid Elgouri, Nabil Hmina, "A New Wire Optimization Approach for Power Reduction in Advanced Technology Nodes", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 140–146, 2019. doi: 10.25046/aj040617
48. Andrei Panteleev, Valentin Panovskiy, "Application of Open-Source Optimization Library “Extremum” to the Synthesis of Feedback Control of a Satellite", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 5, pp. 23–29, 2019. doi: 10.25046/aj040503
49. Houcine Marouani, Amin Sallem, Mondher Chaoui, Pedro Pereira, Nouri Masmoudi, "Multiple-Optimization based-design of RF Integrated Inductors", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 574–584, 2019. doi: 10.25046/aj040468
50. Jaya V. Gaitonde, Rajesh B. Lohani, "Material, Structural Optimization and Analysis of Visible-Range Back-Illuminated OPFET photodetector", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 485–502, 2019. doi: 10.25046/aj040459
51. Olfa Jedda, Ali Douik, "Optimal Discrete-time Sliding Mode Control for Nonlinear Systems Subject to Input Constraints", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 4, pp. 141–146, 2019. doi: 10.25046/aj040417
52. Ethmane Isselem Arbih Mahmoud, Mohamed Maaroufi, Abdel Kader Mahmoud, Ahmed Yahfdhou, "Optimization of Statcom in a Nouakchott Power System", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 2, pp. 333–339, 2019. doi: 10.25046/aj040242
53. Uttam S. Satpute, Diwakar R. Joshi, Shruti Gunaga, "Frequency-Based Design of Electric System for Off-shore Wind Power Plant (OWPP)", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 2, pp. 153–161, 2019. doi: 10.25046/aj040220
54. Gabriel Dämmer, Sven Gablenz, Alexander Hildebrandt, Zoltan Major, "Design of an Additively Manufacturable Multi-Material Light-Weight Gripper with integrated Bellows Actuators", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 2, pp. 23–33, 2019. doi: 10.25046/aj040204
55. Nikolay Starostin, Konstantin Mironov, "Strategies of the Level-By-Level Approach to the Minimal Route", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 1, pp. 268–281, 2019. doi: 10.25046/aj040126
56. Hiroyuki Yamamoto, Tomohiro Hayashida, Ichiro Nishizaki, Shinya Sekizaki, "Hypervolume-Based Multi-Objective Reinforcement Learning: Interactive Approach", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 1, pp. 93–100, 2019. doi: 10.25046/aj040110
57. Masahiro Kanazaki, Yusuke Yamada, Masaki Nakamiya, "Multi-Objective Path Optimization of a Satellite for Multiple Active Space Debris Removal Based on a Method for the Travelling Serviceman Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 479–488, 2018. doi: 10.25046/aj030656
58. Chika Yinka-Banjo, Babatunde Opesemowo, "Metaheuristics for Solving Facility Location Optimization Problem in Lagos, Nigeria", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 319–323, 2018. doi: 10.25046/aj030639
59. Mohammad Harun Rashid, Lixin Tao, "Parallelizing Combinatorial Optimization Heuristics with GPUs", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 265–280, 2018. doi: 10.25046/aj030635
60. Wiem Zouari, Ines Alaya, Moncef Tagina, "A Comparative Study of a Hybrid Ant Colony Algorithm MMACS for the Strongly Correlated Knapsack Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 6, pp. 1–22, 2018. doi: 10.25046/aj030601
61. Jamal Al Sadi, "Designing Experiments: 3 Level Full Factorial Design and Variation of Processing Parameters Methods for Polymer Colors", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 5, pp. 109–115, 2018. doi: 10.25046/aj030515
62. Ola Surakhi, Mohammad Khanafseh, Yasser Jaffal, "An enhanced Biometric-based Face Recognition System using Genetic and CRO Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 3, pp. 116–124, 2018. doi: 10.25046/aj030316
63. Mohammad Hossain, Sameer Abufardeh, Sumeet Kumar, "Frameworks for Performing on Cloud Automated Software Testing Using Swarm Intelligence Algorithm: Brief Survey", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 252–256, 2018. doi: 10.25046/aj030229
64. Laud Charles Ochei, Christopher Ifeanyichukwu Ejiofor, "A Model for Optimising the Deployment of Cloud-hosted Application Components for Guaranteeing Multitenancy Isolation", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 174–183, 2018. doi: 10.25046/aj030220
65. An-Ting Cheng, Chun-Yen Chen, Bo-Cheng Lai, Che-Huai Lin, "Software and Hardware Enhancement of Convolutional Neural Networks on GPGPUs", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 2, pp. 28–39, 2018. doi: 10.25046/aj030204
66. Uttara Sawant, Robert Akl, "Adaptive and Non Adaptive LTE Fractional Frequency Reuse Mechanisms Mobility Performance", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 511–520, 2018. doi: 10.25046/aj030162
67. Sahbi Marrouchi, Nesrine Amor, Moez Ben Hessine, Souad Chebbi, "Theoretical Investigation of Combined Use of PSO, Tabu Search and Lagrangian Relaxation methods to solve the Unit Commitment Problem", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 357–365, 2018. doi: 10.25046/aj030144
68. André Richter, Ines Hauer, Martin Wolter, "Algorithms for Technical Integration of Virtual Power Plants into German System Operation", Advances in Science, Technology and Engineering Systems Journal, vol. 3, no. 1, pp. 135–147, 2018. doi: 10.25046/aj030117
69. Mario Brcic, Nikica Hlupic, Nenad Katanic, "Distributing the computation in combinatorial optimization experiments over the cloud", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 6, pp. 136–144, 2017. doi: 10.25046/aj020617
70. Kornkanok Phoksawat, Massudi Mahmuddin, "Hybrid Ontology-based knowledge with multi-objective optimization model framework for Decision Support System in intercropping", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 3, pp. 1363–1371, 2017. doi: 10.25046/aj0203172
71. Riadh Essaadali, Said Aliouane, Chokri Jebali and Ammar Kouki, "Optimization of Multi-standard Transmitter Architecture Using Single-Double Conversion Technique Used for Rescue Operations", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 3, pp. 73–81, 2017. doi: 10.25046/aj020311