1. Introduction

Integrated Inductors are of paramount importance elements, layout-optimization for spiral inductors has been the focus issue of several studies for the last few years, as for application, the four main characteristics that are required for the design of spiral inductors are: high inductance, high current capability, energy density, and low losses, with the inductors properties being identified by its geometrical and technological parameters [1].

For the sizing of spiral inductors, the designer should consider three main parameters [2], [3], the inductance value which is one of the most sensitive parameters, then, the quality factor (Q), and finally the self-resonant frequency (SRF).

Many works have been conducted for the sake of modeling and optimizing of spiral inductors. Formulation, modeling, and implementation remain the main steps for designing an integrated inductor [4], [5]. However, to ameliorate the optimization, the operation could be repeated many times till an acceptable solution is found.

Metaheuristic’s techniques are especially applied to the optimal sizing of analog circuits [6], such techniques have proven to be efficient in solving difficult problems because they necessitate less time to converge and yield better solutions.

In this field, the methods mostly used are EA: ‘Evolutionary Algorithms ’ [7], such as the Differential Evolution (DE) Algorithm [8],  and the Genetic Algorithm (GE) [9], [10], but in the last two decades, a new group of nature-inspired heuristic optimization algorithms have been introduced as SI: ‘Swarm Intelligence Techniques’, such as Ant Colony Optimization (ACO) [11], [12], Gravitational Search Algorithm (GSA) [13],  Artificial Bee Colony (ABC) [14], Dragonfly Algorithm (DA) [15], Particle Swarm Optimization (PSO) [16], Grey Wolf Optimizer (GWO) [17], and Bacterial Foraging Optimization (BFO) [18].

Nevertheless, for the sake of achieving the optimal sizing of the (RF) spiral inductors, the Differential Evolution (DE) is to be the focus technique in this paper since it has been widely used in circuit design in the last decade.

In order to design circular and square spiral inductors for operating frequencies around 2.5 GHz, the inductor π-model has been embedded in the improvement device.

The next sections of the paper layout introduce as follows: Section 2 is devoted to the descriptions of the inductor π-model used, afterward, section 3 provides the synopsis of the DE

algorithm, while the optimal values of DE parameters have been determined by a proposed technique. Then, section 4 highlights the inductor sizing-optimization method, the technological parameters, and the design constraints as well, besides, the optimization results are presented, where analytical results obtained with DE are investigated by ADS momentum simulation software. Last and not least, the conclusion is offered in section 5.

2. Planar Spiral Inductors

All the shapes of spiral inductor known by four main geometrical parameters, the spacing between lines (s), the number of turns (n), the line width (w), and the outer length of a side (d_out), while the inner length of a side (d_in) defined by: d_in = (d_out – 2.(n .(s + w) – s)).

There are other important geometry parameters such the inductor length, while: L = 4.n.d_avg for the square shape, and L = 4.n.d_avg  for the circular shape, then, the inductor area:  A=d_out², and finally, the average diameter: d_avg = 0.5.(d_out + d_in).

Layouts of the circular and the square inductor have been showing respectively in Figure 1 and Figure 2 [19].

Figure 1: Layout of the Circular Integrated Inductor

2.1. The electrical Model of Integrated Inductors

It is important, thus, to present the expressions of the electrical model components for the inductor π-model, Figure 3 presented the electrical circuit for this type, while, C_s, C_si, C_ox, R_s, and R_si are  respectively the substrate capacitance,  the series capacitance between the spiral and the metal underpass, the substrate-oxide capacitance,  the series resistance, and the substrate resistance, these parameters  are determined by equations (1 2,3,4,5,6,7,8, 9):

Figure 2: Layout of the Square Integrated Inductor

Figure 3: Integrated Inductor Electrical π -Model

where (t) is the turn thickness, (t_ox) is the oxide thickness between the spiral and the substrate, (σ_m) is the conductivity of the metal,  (ω) is the frequency, (t_{ox, M1-M2}) is the oxide thickness between the spiral and the under-pass, (ε_ox) is the oxide permittivity, (G_sub) is the substrate conductance per unit area, (C_sub) is the substrate capacitance per unit area,  (h_sub) is the substrate height, (σ_sub)  is the substrate conductivity, (δ) is the skin depth, (µ) is the magnetic permeability of free space, and finally, (R_sh) is the sheet resistance.

Figure 4: The Parallel π-Equivalent Circuit of Integrated Inductors

A similar inductor model has been shown in Figure 4, the quality factor (Q) was calculated by equations (10) and (11), where (C_p) is the shunt capacitance, and (R_p) is the shunt resistance.

2.2. Inductance Ls

The model of the inductance L_s for the square inductor is expressed [19], [20] in equation (12):

The expression of the inductance L_s for the circular inductor is given in equation (13) [21]:

The coefficients c_i, β, and α_i are not depending on the technology but on the structure of the inductor. With ϼ is the fill ratio, inductances in nH, and dimensions in μm.

The expression of the inductance for a given frequency (f) for two ports [20] defined as follow:

2.3. The Quality factor (Q)

The quality factor is presented as follows:

An ideal inductor has an infinite Quality factor [19].

When the peak magnetic energy is the same as the electric energy, the Q-Factor is equal to zero, this phenomenon is defined as the self-resonant frequency phenomena.

The energy stockpiled in the inductor is attached to the imaginary part of the input admittance (Y_in), whereas the real part of (Y_in) is proportional to the energy dissipated in              resistances, with this approach is abridged to [20]:

3. The Differential Evolution Algorithm

It is possible to say that the DE algorithm, as is the genetic algorithm, is a population-based using identical operators’ mutation, crossover, and selection. However; what makes the genetic algorithms yield a better solution is the fact that it builds on the crossover operation while the DE builds on the mutation one [8].

At the beginning of the DE process, the population of the n-pop solution vectors is randomly selected. This population is then ameliorated by stratifying mutation, crossover, and selection operators. First, the algorithm uses the mutation process as its search mechanism. Then, the DE uses crossover (recombination) operators, and the child vector that takes parameters from one parent more than the other. Afterward, a selection process is carried out in order to change the parent vectors if their fitness is less than of the newly generated child vectors. This three-stage process is repeated until a better solution is found [22].

The principal steps of the DE algorithm are defined mathematically as follows:

3.1. Mutation

For each objective vector x_{j, k} ,a mutant vector is generated by (18):

where ?, ?₁, ?₂, ?₃ ∈ {1, 2,…, ??} are arbitrary chosen and must be different   from each other. In equation (18), (β) is the scaling factor which affects the difference vector                                                   .

3.2. Crossover

The trial vector is produced by the mixture of the parent vector with the mutated vector:

where (P_c) is the crossover probability parameter.

3.3. Selection

The comparison between a parent and its identical offspring called the selection and can be expressed as:

where g_(x) is the objective function value of the trial vector. The DE algorithm can be declared in 1:

3.4. The DE Algorithm Parametrization

     To determine the optimal values of DE parameters, the Ackley function presented in equation (21) was investigated for 100 population and 1000 number of iterations.

The Ackley function has one global minimum at:                                              f ( x_j ) = 0; for x_j = ( 0 , … , 0 ).

The function evaluated on x_j ∈ [ − 32, 32] for all                                                  (j = 1 , … , 32) .

Figure 5 displays the variation of fitness convergence according to the crossover probability P_c and the upper bound of the scaling factor beta_max (with the lower bound of the scaling factor-beta _min equal to 0,1). The cost function versus the number of iterations presented in Figure 6.

From Figure 5, the values of DE parameters that gave the best convergence are presented in Table 1.

4. Inductors Sizing

In the following section, we aim to maximize the Q-Factor for a specific value of the inductance for two structures, square and circular, by combining the inductor π-model and the DE optimization procedure. Afterward, simulations with ADSEM are adopted.

Figure 5: Convergence Rate versus the Crossover Probability and the Upper Bound of the Scaling Factor, with beta_min=0.1.

4.1. Constraints of the study

To minify the parasitic phenomena [20], [23], the liaison between geometry parameters in (22) is well respected as a sort of included design-rules [20], [23].

Figure 6: The Cost Function versus the Number of Iterations for the Ackley Function.

Table 1: Parameters Values of the Differential Evolution Algorithm.

• The SRF Constraint

The condition for a minimum self-resonant frequency which   SRF  SRF_min can be formed as [20]:

4.2. Optimization Procedure

The goal of this optimization is to find the optimum geometrical parameters of the spiral inductor to get a higher value of Q-Factor, the problem can be formulated as follows:

The objective function for the DE was defined as the following:

where (s_i) is the penalty coefficient, and P(x) is the sum of constraints.

Constraints g₈(x), g₉(x), g₁₀(x), and g₁₁(x) are boundary constraints, as result, they can be examined, while the DE was not allowed to generate a candidate vector farther these limitations.

Equations of constraints g₄(x), g₅(x), g₆(x), and g₇(x) have been shown in Table 2.

4.3.  Results and Discussions

In the following, we will be adopting a sizing of square and circular inductors, with distinct values of the inductance Ls_req in the field beyond 2.5 GHz, as shown in Table 3 the technological and physical parameters have been well presented, while Table 4 represents the geometry parameter boundaries.

The details of the optimization have been presented in Table 5 and Table 6. On aim to verify our procedure, Figure 7 gives the cost function versus the number of iterations for square inductors, in this case, the constraint for minimum self– resonant frequency is added as SRF_min=22 GHz. The optimization results of the maximum Q-Factor and area (A) for both circular and square inductors versus the   inductance obtained using   the DE algorithm are presented in Figure 8.

The Q-Factor versus frequency for each value of the inductance has been shown in Figure 9 and Figure 10. The simulation using momentum software has also been shown in          Figure 11, Figure 12, Figure 13, and Figure 14.

The comparison between optimization results and simulations is presented in Table 7 and Table 8.

Table 2: Equations of Constraints.

Table 3: The values of technological parameters.

Table 4: Sizing Variables and their Allowable Ranges.

Table 5: Optimization Results of Circular Inductors using the DE Algorithm.

Table 6: Optimization Results of Square Inductors using the DE Algorithm.

Figure 7: The Objective Function versus Iterations Number for a Square Inductor.

Figure 8: The Quality Factor and Inductors Area versus Inductance.

Figure 9: The Quality Factor of Square Inductors versus Frequency.

Figure 10: The Quality Factor of Circular Inductors versus Frequency.

What the results show is that when the inductance value increases, the quality factor decreases, and the self-resonant frequency decreases as well.

However, the results are very good in terms of the circuit’s size, and the constraints are very robust.

The DE algorithm provides better results concerning the circuit’s size and has a faster convergence as shown in the results.

We can notice that the simulation of square inductors is very accurate, with an error below 8.50% for the inductance value, and 5.21% for the quality factor for L_s less than 11 nH. It is possible to explain the increase of the error when the value of inductance is greater than 11 nH,   in that   we  have taken  similar  limits  of geometrical parameters for all values of the inductance, when the value of L_s has augmented, the number of turns became higher and D_out increased with a small percentage, in such

circumstances, the quality factor decreases owing to the parasitic phenomena effects, this problem can be solved by increasing the parameters of the allowable range in the proportion of the outer diameter.

As for the circular inductor, generally, the error is below than 5.66% for inductance value, and 21.56% for the quality factor, Although, this type has the shortest perimeter, and with a circular configuration, a higher quality factor (Q) is obtained.    Yet, this type shows a response to the parasitic phenomena effects.

We notice through the simulation that the circular inductor is not significantly affected by parasitic phenomena in terms of the self-resonant frequency. From Figures 10 and 13, we observe that the inductor of L_s equal to 11 nH reaches its maximum of Q-Factor when f_{max ~} 2 GHz, the area on the left of f_max, is an area where the Q-Factor is fundamentally affected by the magnetic induced losses, skin and proximity effects, and the DC resistance [24],[25]. On the opposite side of f_max, in addition to the preceding effects, the Q-Factor is also affected by the substrate noise coupling [23]. The evaluated SRF equal to 10.1 GHz, and the SRF obtained via simulation equal to 8.5 GHz, at this time, the                         Q-Factor is equal to 0, starting from this point, the peak magnetic energy is less than the electric energy, due to the perturbation of this last because of the parasitic phenomena.

The layout constraints for circular inductors required extensive research, in order to mitigate the parasitic phenomena effects.

Moreover, the degradation of the Q-Factor can be seen more clearly for square inductors, from Figures 9 and 11, for L_s equal to 11 nH, the Q-Factor equal to 0 when the evaluated SRF equal to 15.59 GHz and the SRF obtained via simulation equal to 7   GHz, we conclude that this type is extremely influenced by the parasitic phenomena.

Table 7: Comparison between Optimization Results and Momentum Simulations for Circular Inductors.

Table 8: Comparison between Optimization Results and Momentum Simulations for Square Inductors.

Figure 11: Simulation of the Quality Factor versus Frequency in Momentum for Square Inductors.

Figure 12: Simulation of the Inductance versus Frequency in Momentum for Square Inductors.

Figure 13: Simulation of the Quality Factor versus Frequency in   Momentum for Circular Inductors.

Figure 14: Simulation of the Inductance versus Frequency in Momentum for Circular Inductors.

5. Conclusion

For dealing with the optimal sizing of spiral inductors for (RF) circuits, we proposed on this paper an application of the Differential Evolution (DE) algorithm. Two inductor structures have been optimized i.e. shape square and shape circular, with a maximum Q-Factor, a maximum self-resonant frequency (SRF), and a minimum surface area. The performances of optimized inductors showed good results in terms of the Q-Factor, with the square inductor presenting a higher SRF and a smaller area (A) than the circular one.

The π-model does not allow for the assimilation of noises parasitic effects in a good way, leading to a lower SRF value, that is why we are focusing on using the double π-model, instead, for the integrated inductors optimal sizing.

1. J. M. Lopez-Villegas, J. Samitier, C. Cane, P. Losantos, J. Bausells, “Improvement of the quality factor of RF integrated inductors by layout optimization,” IEEE Transactions on Microwave Theory and Techniques, 48(1), 76–83, 2000, https://doi.org/10.1109/22.817474
2. H. M. Hsu, K. Y. Chan, H. C. Chien, H. C. Kuan, “Analytical design algorithm of planar inductor layout in CMOS technology,” IEEE Transactions on Electron Devices, 55(11), 3208–3213, 2008, https://doi.org/10.1109/TED.2008.2004248
3. J. N. Burghartz, B. Rejaei, “On the design of RF spiral inductors on silicon,” IEEE Transactions on Electron Devices, 50(3), 718–729, 2003, https://doi.org/10.1109/TED.2003.810474
4. Y. Yorozu, M. Hirano, K. Oka, Y. Tagawa, “Improvement of the quality factor of RF integrated inductors by layout optimization,” IEEE Transactions on Microwave Theory and Techniques, 48(1), 76–83, 2000, https://doi.org/10.1109/22.817474
5. S. Abi, H. Bouyghf, A. Raihani, B. Benhala, “Swarm intelligence optimization techniques for an optimal RF integrated spiral inductor design,” in 2018 International Conference on Electronics, Control, Optimization and Computer Science (ICECOCS), Kenitra, Morocco, 1–7, 2018, https://doi.org/10.1109/ICECOCS.2018.8610524
6. P. Siarry, Z. Michalewicz, Advances in metaheuristics for hard optimization, Natural Computing Series, Springer, 2008.
7. M. Crepinsek, S. H. Liu, M. Mernik, “Exploration and exploitation in evolutionary algorithms: A survey,” ACM Computing Surveys, 45(3), Article 35, 2013, https://doi.org/10.1145/2480741.2480752
8. R. Storn, K. Price, “Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization, 11(4), 341–359, 1997, https://doi.org/10.1023/A:1008202821328
9. A. El Beqal, B. Benhala, I. Zorkani, “A Genetic algorithm for the optimal design of a multistage amplifier,” International Journal of Electrical and Computer Engineering, 10(1), 129–138, 2020, http://doi.org/10.11591/ijece.v10i1.pp129-138
10. M. Mitchell, An introduction to genetic algorithms, The MIT Press, 1998.
11. B. Benhala, “Sizing of an inverted current conveyors by an enhanced ant colony optimization technique,” in 2016 Conference on Design of Circuits and Integrated Systems (DCIS), Granada, Spain, 1–5, 2016, https://doi.org/10.1109/DCIS.2016.7845271
12. L. Kritele, B. Benhala, I. Zorkani, “Ant Colony Optimization for Optimal Low-Pass Filter Sizing,” in: E. G. Talbi, A. Nakib. (Eds.), Bioinspired Heuristics for Optimization, Studies in Computational Intelligence, Springer, Cham, 283–299, 2019, https://doi.org/10.1007/978-3-319-95104-1_18
13. E. Rashedi, H. Nezamabadi, S. Saryazdi, “GSA: A gravitational search algorithm,” Information Sciences, 179(13), 2232–2248, 2009, https://doi.org/10.1016/j.ins.2009.03.004
14. C. J. Lin, M. L. Huang, “Modified artificial bee colony algorithm for scheduling optimization for printed circuit board production,” Journal of Manufacturing Systems, 44(1), 1–11, 2017, https://doi.org/10.1016/j.jmsy.2017.04.006
15. S. Mirjalili, “Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems,” Neural Computing and Applications, 27(4), 1053–1073, 2016, https://doi.org/10.1007/s00521-015-1920-1
16. B. Benhala, P. Pereira, A. Sallem, Focus on swarm intelligence research and applications, Nova Science Publishers, 2017.
17. S. Mirjalili, S. M. Mirjalili, A. Lewis, “Grey wolf optimizer,” Advances in Engineering Software, 69, 46–61, 2014, https://doi.org/10.1016/j.advengsoft.2013.12.007
18. K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control,” IEEE control systems Magazine, 22(3), 52–67, 2002, https://doi.org/10.1109/MCS.2002.1004010
19. C. P. Yue, C. Ryu, J. Lau, T. H. Lee, S. S. Wong, “A physical model for planar spiral inductors on silicon,” in International Electron Devices Meeting, Technical Digest, San Francisco, USA, 155–158, 1996, https://doi.org/10.1109/IEDM.1996.553144
20. S. S. Mohan, M. del Mar Hershenson, S. P. Boyd, T. H. Lee, “Simple accurate expressions for planar spiral inductances,” IEEE Journal of Solid-State Circuits, 34(10), 1419–1424, 1999, https://doi.org/10.1109/4.792620
21. B. Rejaei, J. L. Tauritz, P. Snoeij, “A predictive model for si-based circular spiral inductors,” in Topical Meeting on Silicon monolithic integrated circuits in RF systems, Ann Arbor, 148–154, 1998, https://doi.org/10.1109/SMIC.1998.750210
22. D. Karaboga, B. Akay, “A comparative study of Artificial Bee Colony algorithm,” Applied Mathematics and Computation, 214(1), 108–132, 2009, https://doi.org/10.1016/j.amc.2009.03.090
23. P. Pereira, M. H. S. Fino, F. V. Coito, M. V. Neves, “RF integrated inductor modeling and its application to optimization-based design,” Analog Integrated Circuits and Signal Processing, 73, 47–55, 2011, https://doi.org/10.1007/s10470-011-9682-x
24. J. Aguilera, R.Berengue, Design and test of integrated inductors for RF applications, Dordrecht: Kluwer Academic Publishers, 2004.
25. Y. Cao , R. A. Groves, X. Huang, N. D. Zamdmer, and al, “Frequency-independent equivalent-circuit model for on-chip spiral inductors,” IEEE Journal of Solid-State Circuits, 38(3), 419–426. 2003, https://doi.org/10.1109/JSSC.2002.808285

Citations by Dimensions

Citations by PlumX

Google Scholar

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. Basharat Jamil, Lucía Serrano-Luján, José Manuel Colmenar, "On the Prediction of One-Year Ahead Energy Demand in Turkey using Metaheuristic Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 7, no. 4, pp. 79–91, 2022. doi: 10.25046/aj070411
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. Athraa Ali Kadhem, Noor Izzri Abdul Wahab, Ahmed Abdalla, "The Contribution of Wind Energy Capacity on Generation Systems Adequacy Reliability using Differential Evolution Optimization Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 331–340, 2020. doi: 10.25046/aj050640
33. 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
34. Ihsan Mizher Baht, Petre Marian Nicolae, Ileana Diana, Nameer Baht, "Analysis of Green Building Effect on Micro grid Based on Potential Energy Savings and BIM", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 6, pp. 30–35, 2020. doi: 10.25046/aj050604
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
36. Pham Van Bach Ngoc, Bui Trung Thanh, "Dynamics Model and Design of SMC-type-PID Control for 4DOF Car Motion Simulator", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 557–562, 2020. doi: 10.25046/aj050369
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
40. Noraziah Adzhar, Yuhani Yusof, Muhammad Azrin Ahmad, "A Review on Autonomous Mobile Robot Path Planning Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 236–240, 2020. doi: 10.25046/aj050330
41. Vasiliy Olonichev, Boris Staroverov, Maxim Smirnov, "Dynamic Objects Parameter Estimation Program for ARM Processors Based Adaptive Controllers", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 3, pp. 34–40, 2020. doi: 10.25046/aj050305
42. Ricardo Simões Santos, António João Pina da Costa Feliciano Abreu, Joaquim José Rodrigues Monteiro, "Using Metaheuristics-Based Methods to Provide Sustainable Market Solutions, Suitable to Consumer Needs", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 2, pp. 399–410, 2020. doi: 10.25046/aj050252
43. Hind El Hassani, Nour- Eddine Boutammachte, Sanae El Hassani, "Optimization of Low Temperature Differential Stirling Engine Regenerator Design", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 2, pp. 272–279, 2020. doi: 10.25046/aj050235
44. Nguyen Tuan Anh, Hoang Thang Binh, Tran The Tran, "Optimization of the Stabilizer Bar by Using Total Scores Method", Advances in Science, Technology and Engineering Systems Journal, vol. 5, no. 1, pp. 431–435, 2020. doi: 10.25046/aj050155
45. Temitayo Olayemi Olowu, Mohamadsaleh Jafari, Arif Sarwat, "A Multi-Objective Voltage Optimization Technique in Distribution Feeders with High Photovoltaic Penetration", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 377–385, 2019. doi: 10.25046/aj040648
46. Mohd Razif Idris, Imad Mokhtar Mosrati, "Optimization of the Electrical Discharge Machining of Powdered Metallurgical High-Speed Steel Alloy using Genetic Algorithms", Advances in Science, Technology and Engineering Systems Journal, vol. 4, no. 6, pp. 255–262, 2019. doi: 10.25046/aj040632
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. Mustafa Saka, Ibrahim Eke, Suleyman Sungur Tezcan, Muslum Cengiz Taplamacioglu, "Analysis of Economic Load Dispatch with a lot of Constraints Using Vortex Search Algorithm", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 6, pp. 151–156, 2017. doi: 10.25046/aj020619
70. 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
71. Hossein Soleymani, Amin Hasanvand, "Estimation of Power System Stabilizer Parameters Using Swarm Intelligence Techniques to Improve Small Signal Stability of Power System", Advances in Science, Technology and Engineering Systems Journal, vol. 2, no. 4, pp. 139–144, 2017. doi: 10.25046/aj020419
72. 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
73. 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