Optimization of Core–Shell Nanoparticles Using a Combination of Machine Learning and Ising Machine

Machine‐learning‐based optimization techniques are widely used for designing complex materials. However, an efficient search for the complex systems, where a combinatorial explosion occurs in the materials search space, is still challenging. Core–shell nanoparticles (CSNPs) are an example of a complex system with a high degree of freedom owing to their complicated structure and multiple constituent materials. In this study, a new black box optimization technique is developed. In this method, the structure of the CSNPs is optimized using an Ising machine and their constituent materials are selected using Bayesian optimization with the optical properties of the materials as the “descriptors”. Aiming for applications to i‐line photolithography, the authors search for CSNPs that are transparent to ultraviolet light of wavelength 355–375 nm and opaque to visible light of wavelength 400–830 nm. The transmittance spectra of the nanoparticles are obtained using a Mie theory calculator. The proposed nanoparticles with the best optical properties have a multilayered structure with a radius of approximately 40 nm and an outer shell composed of either Mg or Pb. The results indicate that a combination of various optimization techniques is more efficient in discovering the better complex materials.


Introduction
In recent years, there has been an increasing demand for materials with high performance and functionality.Therefore, various types of elements [1] and raw materials with different structures [2] have been combined to synthesize such materials.However, owing to the extremely large search space of materials, it is difficult to discover the optimal materials for various objectives.
An example of a complex highperformance material is core-shell nanoparticles (CSNPs).CSNPs have a high degree of freedom and are composed of two or more materials; hence, they have a higher potential of performance than nanoparticles composed of a single material.CSNPs have a variety of applications and can be used as catalysts, [1] biomaterials, [2] and electromagnetic wave-absorbing materials. [3][6][7] However, the optical properties of CSNPs strongly depend on their underlying structure and constituent materials. [4]Thus, the design of CSNPs need to be optimized using appropriate techniques depending on the desired applications.
Exhaustive searches [5] have been conducted and various machine-learning models [6] have been explored to design the optimal CSNPs.However, these techniques require pre-evaluation and large datasets.Black box optimization [8] is an optimization technique that is commonly used to design materials based on small datasets.Bayesian optimization [9][10][11] is an example of a black box optimization method, which is used to efficiently find materials with the optimal target properties from a pool of candidate materials.Note that appropriate numerical "descriptors" are required to characterize the candidate materials when Bayesian optimization is performed.For example, various compositional descriptors [12] have been proposed to quantify compositional information.For compositional descriptors, by converting information from the periodic table of single elements and the results of DFT calculations into statistical values such as weighted means and variances by composition, the compositional information of candidate materials can be expressed as a higher-dimensional numerical vector.The first step in Bayesian optimization is to train a Gaussian process regression (GPR) model on an initial small dataset.Next, a promising candidate is selected from prepared candidates by the trained GPR model.Subsequently, the target properties of the selected candidate are evaluated using simulations or experiments, and this new data is added to the existing training dataset of the GPR model.Finally, the GPR model is retrained on the expanded dataset to obtain new candidates.15][16][17][18][19][20] However, owing to the vast search space of materials, the material candidate causes a combinatorial explosion.In such cases, it is impossible to list all candidates in advance, although list-up of them is necessary for Bayesian optimization.To overcome this issue, factorization machine with quantum annealing (FMQA) [21] was developed, which is a black box optimization algorithm [22][23][24] based on Ising machines. [25]FMQA facilitates faster candidate selection by using binary representation for the material search space during the optimization process.Black box optimization based on Ising machines has been used to design complex materials such as metamaterials, [21] materials with a layered photonic structure, [26] materials with different chemical structures, [27] printed circuit boards, [28] and photonic crystals. [29]However, FMQA is not suitable for optimization problems where the candidate materials represented by descriptors are listed in advance.
Thus, different optimization techniques have both advantages and disadvantages, and it is important to choose a technique in accordance with the requirements of the material to be designed.For example, both the structure and constituent materials of CSNPs need to be optimized.In this study, FMQA is more suitable for optimizing the structure which is caused by a combinatorial explosion and Bayesian optimization is better for optimizing the constituent materials which is necessary to use prepared descriptors.Thus, we combined the two methods for optimizing the design of CSNPs (see Figure 1).In particular, we focused on CSNPs that are transparent to ultraviolet light of wavelength 355-375 nm and opaque to visible light of wavelength 400-830 nm.CSNPs with these optical properties were designed for applications in i-line photolithography, which requires ultraviolet light of wavelength 365 nm. [30]Note that the visible spectrum typically ranges from 400 to 830 nm.These CSNPs can be used to develop membranes and paints that selectively transmit light of different wavelengths, such as those required in camera modules.The optical properties of the CSNPs were evaluated using a Mie theory calculator as described in Experimental Section.
The remainder of this article is organized as follows.In the next section, the efficiency of structural optimization using FMQA is compared with that of random optimization.In addition, the results of our proposed optimization method, which combines the FMQA and Bayesian techniques, are presented.Moreover, we investigate the impact of the outer shell material on the absorption peak in the extinction spectrum of the CSNPs.The outer shell of the proposed CSNPs with the best optical properties was composed of either Mg or Pb, which however, is not suitable materials for the production and applications; therefore, the criteria for selecting suitable alternative materials are also presented.Furthermore, the optical properties of CSNPs consisting of two outer shells composed of the same material are discussed because this structure is relatively easy to manufacture and is promising in usage.In addition, the experimental feasibility of the found CSNPs is discussed.Finally, the conclusions of this study and the method used to calculate the transmittance spectra of the CSNPs are presented.

Structural Optimization Using FMQA
In this study, FMQA was used to optimize the structure of the CSNPs.We designed CSNPs consisting of a single core and four Figure 1.Process flow of the proposed optimization method obtained by combining factorization machine with quantum annealing (FMQA) and Bayesian optimization.In the inner loop, procedure from (i-1) to (i-4) is repeated, and FMQA was used to optimize the structure of the core-shell nanoparticles (CSNPs) using Ising machines.In the outer loop, procedure from (o-1) to (o-4) is repeated, and Bayesian optimization was used to select the constituent materials of the CSNPs with the corresponding optical properties as the descriptors.
outer shells.Different core radii (i.e., 20, 50, 75, and 100 nm) and shell thicknesses (i.e., 2, 4, 6, and 8 nm) were considered for the candidate CSNPs.In addition, four materials were selected using Bayesian optimization as the optimal materials for the core and shells, as explained in the next section.The FMQA requires that the structure and material arrangement should be represented by binary variables.As shown in Table 1, the candidate values of the core radius, shell thickness, and materials of the core and shells are described by two binary variables respectively.Thus, the size and material for core and each shell can be determined by four binary variables (Figure 1), and the target CSNPs can be described by 20 bits.Note that all the number of candidates is 104 8576.
To optimize the structure of the CSNPs using FMQA, we introduce figure of merit (FOM) based on transmittance spectra of the CSNPs.The transmittance as a function of wavelength λ, TðλÞ, was calculated using a Mie theory calculator, as described in Experimental Section.Based on the calculated TðλÞ, the FOM was evaluated as where S 1 and S 2 are given by respectively, and w 1 = 20 (i.e., 375 À 355) and w 2 = 430 (i.e., 830 À 400). Figure 2 illustrates the relationship between these parameters.S 1 =w 1 and S 2 =w 2 are the weighted areas of the transparent and opaque regions of the spectrum, respectively.In this study, our objective was to select the CSNPs with the low FOM as much as possible.
In FMQA, the candidate selection is performed using an Ising machine.In this study, we used the Amplify Annealing Engine by Fixstars Amplify Corporation, [31] which is a GPU-based Ising machine.Note that the D-Wave quantum annealer [32] can also be used for our optimization problem.However, since the QPU in the quantum annealer is not a fully connected graph, embedding in fully connected graphs is necessary to solve FM.In contrast, GPU-based Ising machines can handle fully connected graphs of huge number of bits without embedding.Thus, we decided to use a GPU-based Ising machine in anticipation of handling optimization of more complex CSNPs in the future.In addition, since quantum annealing is not used in this study, FMQA is simply used as the name of the algorithm.First, 10 different structures (bit sequences) were randomly generated, which formed the initial dataset.Next, the FOM of these structures was evaluated.Finally, black box optimization was performed for 100 cycles using FMQA.Three independent trials were conducted, following which we selected the structure with the best (i.e., lowest) FOM among 330 evaluated structures.Note that each of the structures were composed of four pre-selected materials.
We studied 10 test cases, each corresponding to four randomly selected materials, and results are shown in Figure 3. Figure 3a shows the minimum FOM value (among the three trials) as a function of the number of optimization cycles for each case.Except for case 4, the FOM values of all the cases converged within approximately 70 cycles.For case 4, a structure with a sufficiently low FOM was obtained only after 100 cycles.However, a better structure was not obtained even when the optimization was performed for 200 cycles.Thus, based on these results, we fixed the total number of structural optimization cycles to be 100.
Figure 3b compares the best FOM values obtained using FMQA and random optimization for the 10 test cases.In random optimization, the structures were randomly generated throughout the 100 cycles, unlike in FMQA, where they were randomly generated only during the initial step.For all the cases, FMQA yielded structures with a lower FOM than random optimization, indicating that FMQA can be used to optimize the structure of CSNPs efficiently.

Combined FMQA and Bayesian Optimization of CSNPs
In the structural optimization by FMQA, four types of materials for the core and shells are needed.Bayesian optimization was performed to select the four most promising materials out of the 70 candidates as shown in Table 2.Although it is possible to use only FMQA to optimize the CSNPs using the binary representations of the 70 materials, the optical properties of CSNPs strongly depend on the optical properties of the constituent materials.Thus, the performance of the optimization algorithm is expected to improve significantly when the optical properties  of the constituent materials are used as the descriptors.Because FMQA does not use descriptors, we used Bayesian optimization and defined the desired optical properties as the descriptors of the material selection problem.The descriptors were defined by a 26D vector consisting of the optical constants of the four materials.Specifically, the refractive indices and extinction coefficients of the four materials in the wavelength range 300-900 nm were averaged and discretized into 50 nm intervals.A total of 916 895 combinations are possible when four materials are selected from 70 candidates.The descriptors for all the candidates were calculated before performing Bayesian optimization.The FOM defined while performing FMQA was used as the objective function.The PHYSBO package [11] was used to perform Bayesian optimization with the expected improvement (EI) as an acquisition function.Ten material combinations were randomly generated as part of the initial dataset, and the total number of Bayesian optimization cycles was set to 350.
Figure 4 shows the optimization results obtained by combining FMQA for structural optimization and Bayesian optimization for material selection.Figure 4a shows the best FOM value as a function of the number of Bayesian optimization cycles for three independent trials.The FOM decreased steadily as the number of cycles increased.The top 30 CSNPs yielded by our optimization method are listed in Table 3.These CSNPs shared the following characteristics: 1) the core radius was 20 nm; 2) the outer shell had a thickness of 2 nm and was composed of either Mg or Pb; and 3) the radius of the CSNPs was approximately 40 nm.The transmittance spectrum of the best CSNP is shown in Figure 4b.This CSNP has desirable optical properties because it not only had high transmittance (>0.8) at %365 nm but also low transmittance (<0.2) across a wide wavelength band in the visible region.
In this study, we cannot conclude that Bayesian optimization is the optimal outer loop optimization method although it shows higher optimization performance.In the outer loop, it is sufficient to perform black box optimization using materials descriptors, and thus other surrogate model-based optimization methods can also be adopted.

Impact of Outer Shell Material on the Absorption Peaks
Figure 4c shows the extinction (absorption þ scattering), absorption, and scattering efficiencies of the best CSNP as functions of wavelength.The extinction spectrum was mainly dominated by absorption.This absorption is caused by surface plasmon resonance, which is well known in nanoparticles composed of metals such as Au. [33,34]Some studies have reported that the position of the absorption peak is redshifted as the particle size increases or as standardized shell thickness by the core size decreases. [35]hus, the position of the absorption peak can be fitted to the desired wavelength by controlling the core and particle sizes.However, the desired CSNPs need to be opaque to visible light in the wide wavelength range 400-830 nm.Therefore, to achieve our objective, it is necessary to not only optimize the position but also the width of the absorption peak and the scattering coefficient.
To confirm that our optimization technique can control the width of extinction peak, we investigated the extinction spectra of the CSNPs for different particle sizes and shell materials.We calculated the extinction spectra of "single-shell" CSNPs consisting of a vacuum core of radius R p ¼ 5, 20, 40, and 60 nm and a single outer shell of thickness 2 nm.Different shell materials were considered for comparison, namely, Mg, Pb, Al, Ag, and V.
Figure 5 shows the extinction efficiency as a function of wavelength for different R p and shell materials and a schematic of the single-shell structure.The extinction spectra of the Mg and Pb CSNPs were very similar.The absorption peak for R p ¼5 nm was located at approximately 200 nm for both Mg and Pb, and the peak was redshifted with increasing R p .Similarly, the absorption peak for R p ¼40 nm was located at approximately 600 nm for both Mg and Pb.The redshift in the peak position with increasing R p was also confirmed for the Al and Ag CSNPs.However, for the Al CSNPs, the absorption peak at 600 nm (i.e., R p ¼ 60 nm) was too broad, and there was a shoulder peak near 365 nm.This is not desired, as the CSNPs are supposed to be transparent to light of wavelength 365 nm.By contrast, in case of the Ag CSNPs, the peak at 600 nm (i.e., R p ¼ 20 nm) was too sharp and did not span the desired region in the visible spectrum.Furthermore, the extinction spectra of the V CSNPs exhibited a high extinction efficiency or absorbance at low wavelengths.These results indicate that our proposed optimization method can indeed select the appropriate materials based on the widths of the corresponding absorption peaks.

Criteria for Selecting Alternative Outer Shell Materials
The optimization results presented in the previous section establish Mg and Pb to be the best materials for the outermost shell of the CSNPs.However, these elements are not suitable for industrial production and applications because of their high reactivity and toxicity.Therefore, we explored alternative materials to construct the desired CSNPs.
The position of the absorption peak in the extinction spectrum is generally believed to strongly depend on the relative permittivity of the constituent material of the CSNPs as well as the relative permittivity of the background medium.To this end, we adopted the Maxwell-Garnett approximation, [36] which is an effective medium approximation that describes the permittivity of composite materials.Using this approximation, the effective relative complex permittivity (ε eff Þ of a composite material for low particle volume fraction can be estimated using where ε p is the permittivity of the particles, ε s is the permittivity of the medium, and f v is the volume fraction of the particles.Equation ( 4) can be rewritten as where Re denotes the real part of ε eff , and ε p can be decomposed into real and imaginary parts, such that ε p ¼ ε 0 þ iε 00 .From Equation ( 5), we observe that the imaginary part of ε eff is maxi- In this study, we calculate a low concentration of CSNPs (i.e., 5 vol%) in vacuum, as described in Experimental Section.Thus, here, we consider the condition with a low volume fraction of particles in vacuum (i.e., f v ≃ 0 and ε s ¼ 1), Therefore, the absorption peak in the extinction spectrum of the CSNP occurs at the wavelength corresponding to ε 0 ¼ À2.We calculated the dielectric functions of Mg and Pb using their optical constants, which are refractive index nðλÞ and extinction coefficient kðλÞ, as shown in Figure 6a,b.For comparison, the dielectric functions of Al, Ag, and V are also shown in Figure 6c-e, respectively.The dielectric functions of Mg and Pb behaved quite similarly, and ε 0 ¼ À2 corresponded to a wavelength of %200 nm for both the elements.By contrast, ε 0 ¼ À2 corresponded to a much shorter wavelength (i.e., higher energy) than 200 nm for Al, and a much longer wavelength of %350 nm for Ag.These results are consistent with the absorption peak positions of the CSNPs with a core radius of 5 nm, as shown in Figure 5.For V, the wavelength corresponding to ε 0 ¼ À2 was similar to that for Mg and Pb; however, the behavior of ε 00 with wavelength differed significantly from that of Mg and Pb.Note that ε 00 is related to optical absorption, and the value of ε 00 at 365 nm for V was higher than that for Mg and Pb.This is because of the higher absorbance at 365 nm in the extinction spectrum of V compared to that in the extinction spectrum of Mg or Pb, as shown in Figure 5e.
These results imply that materials exhibiting ε 0 ¼ À2 at 200 nm and ε 00 ≃ 0 at 365 nm are suitable alternatives to Mg and Pb.Unfortunately, despite our thorough literature search, we were unable to find any materials with these properties.Consequently, although it is limited to proposing design guidelines, CSNPs could be optimized for higher stability and easier production based on these design guidelines.

Extinction Efficiency of Double-Shell CSNPs
In this section, we discuss the properties of "double-shell" CSNPs, which consist of two shells composed of the same material.Such CSNPs are relatively easier to manufacture and have several potential applications.However, no double-shell CSNPs were obtained among the top 30 CSNPs proposed by our optimization method, as seen in Table 3.Five double-shell CSNPs composed of either Mg or Pb were obtained when the search was extended to the top 40 CSNPs, as shown in Table 4. Figure 7a,b shows the transmittance and extinction spectrum of the CSNP corresponding to rank 40, respectively.This CSNP consisted of a KCl core of radius 52 nm, an inner Mg shell of thickness 2 nm, a second KCl shell of thickness 2 nm, and an outermost Mg shell of thickness 2 nm.Interestingly, the transmittance spectrum of the double-shell CSNP of rank 40 is similar to the target transmittance spectrum, which exhibited a slightly higher transmittance in the visible spectral region than that of the best CSNP (see Figure 4).The extinction spectrum of the double-Mg-shell CSNP exhibited two peaks owing to absorption; in addition, its scattering efficiency was higher than that of the best CSNP.Therefore, the better performance of the double-Mg-shell CSNP is mainly owing to the extinction efficiency in the 400-830 nm wavelength band.The previous results indicate that it is possible to design CSNPs with a sufficiently low FOM by controlling the width and position of the absorption peaks.To this end, we calculated the extinction efficiency of double-Mg-shell CSNPs with the following characteristics: the thickness of the inner and outer Mg shells was fixed at 2 nm; the radius of the CSNPs was fixed at 50 nm; and the radius (R i ) of the inner Mg shell was varied, such that R i ¼ 15, 25, and 35 nm. Figure 7c shows a schematic of the double-shell structure focused only on Mg.In this structure, instead of KCl, the optical constants of vacuum were used for the core and second sell.Figure 7d shows the extinction efficiency of the double-Mg-shell CSNPs as a function of wavelength for different R i .Two peaks were observed due to the double Mg shells.When the distance between the two Mg shells was large (i.e., R i was small), a strong peak was observed at longer wavelengths; whereas, when the distance between the two Mg shells was small (i.e., R i was large), a strong peak was observed at shorter wavelengths.For R i ¼25 nm, two equally prominent peaks were observed in the extinction spectrum.Such a double-peak structure can span a wide range of wavelengths, leading to high opaque in the desired spectral band.Thus, the desired CSNPs can be obtained by tuning the distance between the metallic shells.These findings show that our optimization optimal CSNP proposed in Table 3.In contrast, the CSNP ranked 30th in the top ranking is considered to have higher experimental synthesizability.For the core of this CSNP, it has been reported that ZnO nanoparticles with a size of 72 nm can be synthesized. [37]In addition, according to ref. [38], some nanoparticles can be coated with Pb by photodeposition.Therefore, we believe that synthesizing this CSNP and measuring their photonic properties is the next promising future perspective as experimental feasibility.However, even if this CSNP can be synthesized and has better photonic properties, we cannot eliminate the problem that it is not suitable for practical use due to the presence of Pb in the outer shell.

Conclusion
In this study, we designed the CSNPs using black box optimization.To this end, we proposed a new technique by combining Bayesian optimization and FMQA.FMQA was used to optimize the structure of the CSNPs using Ising machines and Bayesian optimization was performed to select the constituent materials of the CSNPs.The CSNPs designed in this study were transparent to ultraviolet light of wavelength 355-375 nm and opaque to visible light of wavelength 400-830 nm in accordance with the target optical properties.The CSNPs with the best optical properties yielded by our optimization technique had the following characteristics: core radius of 20 nm; outer shell composed of either Mg or Pb with a thickness of 2 nm; and total radius of approximately 40 nm.The CSNPs designed using our proposed method have a complex structure and material arrangement, which would be otherwise impossible to generate without a machine-learningbased optimization method.However, these CSNPs are not suitable for production and applications because their outer shell is composed of Mg or Pb which have high reactivity and toxicity; therefore, we explored the criteria for selecting alternative materials.We found that if for a material the real part of the relative permittivity is -2 at 200 nm and the imaginary part is nearly 0 at 365 nm, then it possesses the target optical properties.Furthermore, we found that a double-shell structure is more likely to achieve the target optical properties.Thus, our proposed optimization method can be used to extract a variety of structures from a vast search space, which in turn can be used to design the desired CSNPs.In contrast, to design practical nanoparticles, we should perform optimization calculations that include not only the constituent materials and structures of nanoparticles, but also many conditions such as experimental complexity, size variation of the manufactured particles, toxicity, and stability.Since our proposed optimization method can treat large search spaces, it is highly possible to design practical nanoparticles including a complex optimization of such conditions, and this is an important goal in the near future.
In recent years, several machine-learning-based optimization techniques have been developed for material design.Our results indicate that a combination of multiple optimization methods depending on the target properties is more efficient for discovering the appropriate materials from a vast search space.Moreover, owing to the rapid expansion of the material search space, such a combination of algorithms is becoming increasingly more necessary.

Experimental Section
Mie Theory Calculations of the Transmittance Spectrum: The transmittance spectrum of the CSNPs was obtained using Scattnlay, [39] a Mie theory calculator.Note that the optical constants of the constituent materials, namely, the refractive index nðλÞ and extinction coefficient kðλÞ, are necessary for this calculation.We obtained the values of these constants from the public database refractiveindex.info [40]by applying the following conditions: 1) inorganic material; 2) wavelength range 300-900 nm; and 3) experimental data.The sources of the optical constant data used in this study are provided in Table S1, Supporting Information.The absorption ðQ abs ðλÞÞ and scattering ðQ sca ðλÞÞ efficiencies were evaluated for the wavelength range 355-830 nm for a single CSNP in vacuum.Using these values, the extinction efficiency Q ext ðλÞ can be obtained as Assuming that the CSNPs were dispersed uniformly in the medium, the transmittance TðλÞ was calculated using where S is the cross-sectional area of the CSNP, C is the number density of the CSNPs, and L is the optical path length.In this study, S was calculated using the particle radius; C was calculated assuming an equivalent particle volume density of 5 vol%; and L = 1 μm.Note that the interactions between neighboring CSNPs were not considered in this calculation.

Figure 2 .
Figure 2. Parameters for calculating the structural figure of merit (FOM) of CSNPs.The desired CSNPs correspond to a large value of S 1 =w 1 and small value of S 2 =w 2 .

Figure 3 .
Figure 3. a) Best FOM values obtained using the FMQA method for structural optimization.Note that three independent trials were conducted, but only the best case is shown here.The dotted line indicates the switching point from random optimization to FMQA.The colors indicate different cases, each corresponding to four randomly selected materials.Note that, in some cases, the number of selected materials is three because overlap limitation is not imposed in the selection of the four materials.b) Comparison of the best FOM values yielded by FMQA and random optimization for each case.The transmittance spectrums with best FOM value obtained by FMQA and random sampling are summarized in Figure S1, Supporting Information.

Figure 4 .
Figure 4. a) Best FOM values obtained using the combined FMQA and Bayesian optimization method for three independent trials.The dotted line indicates the switching point from random optimization to FMQA.b) Transmittance spectrum of the best CSNP composed of MgH 2 , BaF 2 , KCl, and Mg.The dotted line indicates the target wavelength for i-line photolithography.c) Extinction (scattering þ absorption), scattering, and absorption efficiencies of the best CSNP as functions of wavelength.

Figure 5 .
Figure 5. Extinction efficiency of single-shell CSNPs as a function of wavelength for different vacuum core radius R p and shell material: a) Mg, b) Pb, c) Al, d) Ag, and e) V.The thickness of the metallic shell was fixed to be 2 nm for all cases.f ) Schematic of the single-shell structure.

Figure 7 .
Figure 7. Optical properties of double-shell CSNPs composed of Mg ranked 40th: a) transmittance spectrum and b) extinction (scattering þ absorption), scattering, and absorption efficiencies as functions of wavelength.The dotted line in (a) indicates the target wavelength for i-line photolithography.In this double-shell structure, the core and second shell are KCl.c) Schematic of the double-shell structure focused only Mg.Instead of KCl, the optical constants of vacuum were used for the core and the second shell.d) Extinction efficiency as a function of wavelength for different inner Mg shell radius R i for the structure illustrated in (c).

Table 1 .
Binary representations of the core radius, shell thickness, and constituent material of the CSNPs.

Table 2 .
Candidate materials for the desired CSNPs.

Table 3 .
Top 30CSNPs yielded by the proposed optimization technique.