esa-sceva/satcom-chunk-collection huggingface dataset:
# Computational Aspects of \(L_{0}\) Linking in the Rasch Model
## 5 Empirical Example  
We now illustrate \(L_{0}\) linking in the Rasch model using an empirical dataset. The dataDIF dataset from the R package equateIRT (Version 1.0.0; [53; 54]) was selected for this purpose. The dataset contains 20 dichotomous items and three groups, each with 1000 subjects. For illustration, only Groups 1 and 2 were linked using the Rasch model.  
As in the Simulation Study (see Section 4), the Rasch model was fitted using the sirt::xzirt() function from the R package sirt (Version 4.2-106; [52]). The optimization of \(L_{0}\) linking was performed using the stats::nlminb() function, with R code specifically written for this paper, available at [[https://osf.io/un604](https://osf.io/un604)]([https://osf.io/un604](https://osf.io/un604)) (accessed on 20 February 2025).  
The average standard error of item difficulty differences was 0.126. The mean ability difference between Group 1 and Group 2, obtained from MM linking based on the \(L_{2}\) loss function, was 0.482. Slight deviations from this estimate were observed with different specifications of the \(L_{0}\) linking function. For the ratio loss function, the mean estimate based on \(\varepsilon=0.01\) was 0.535. Empirical choices of the \(\varepsilon\) parameter, specifically \(\varepsilon_{0.2}\) and \(\varepsilon_{0.4}\), were also explored. For the ratio loss function, the estimates for \(\varepsilon_{0.2}=0.064\) and \(\varepsilon_{0.4}=0.024\) yielded mean differences of 0.518 and 0.520, respectively. The mean estimate based on the Gaussian loss function was 0.537, with estimates for \(\varepsilon_{0.2}=0.072\) and \(\varepsilon_{0.4}=0.031\) yielding 0.519 and 0.517, respectively.  
DIF effects for the 20 items were also computed based on the estimated mean difference of 0.520, obtained with \(\varepsilon_{0.4}\) and the ratio loss function. Figure 5 displays the DIF effects along with their 95% confidence intervals. Item 1 exhibited a significantly positive DIF effect (0.798, with a standard error of 0.112), while DIF effects for the remaining 19 items did not significantly differ from 0.
## 2 Explaining BBRefinement
### The Principle of BBRefinement
That process has several beneficial consequences. Firstly, larger objects are downscaled, and smaller ones are upscaled to fit the resolution, so that  
Figure 3: The figure shows crops that cannot be refined by the naive way because a crop includes multiple objects, usually of the same class. Note that precise labeling of such images is a hard task, even for humans. all objects have the same scale, which is much more effective than training a network for multiscale detection. Second, one image from the dataset yields multiple boxes. In the case of COCO, a standard detector uses 0.2M images (one image as an input), while BBRefinement uses 1.7M images (one box as an input). In addition, a standard detector downscales the input images to a specific resolution to fit GPU memory, so that many pixels are thrown out. BBRefinement does not use non-object parts from the image, but it allows us to use more pixels from the object due to a weaker downsample. Third, due to mixture data usage, BBRefinement obtains information about the object's detected class and center. Although such data may be imprecise, it is a piece of prior information that makes the task more accessible. It is necessary to take into account that BBRefinement is placed on top of an object detector, which may be imprecise. As a result, the data fed into BBRefinement may be ambiguous. Therefore, the crops taken during the inference should not be extracted precisely, but should be surrounded by padding. The same process is used during training, where, in addition, we also distort the center by random shifts. Such augmentation is visualized in Figure 6.  
Figure 4: Scheme of the BBRefinement architecture. Orange blocks represent convolutional layers, gray blocks represent fully connected layers. \(f_{1},...,f_{k}\) represent the layers of the sub-network \(\mathbb{F}\), \(g_{1},...,g_{j}\) represent layers of the sub-network \(\mathbb{G}\). Figure 5: The figure illustrates the proposed prediction pipeline. A generic object detector processes an image, and then the detected boxes are taken from the original image, updated by BBRefinement, and taken as the output predictions. BBRefinement consists of a standard convolutional backbone (e.g., EfficientNet) marked by the orange color and fully connected layers marked by the white color. ‘\(\times\)’ represents the dot-product operation. A detailed description of BBRefinement is given in Section 2.2.
# Mechanical and Dielectric Properties of Aligned Electrospun Fibers
## 2 Molecular Orientation and System Configurations of Nanofibers
### Molecular Orientation of Nanofibers  
High orientation of polymer molecular chains along the fiber axis and aligned electrospun fibers have important consequences in the field of carbon fiber-reinforced nanocomposites. The electrospun fibers are generally stronger than traditional fibers because of their higher orientation of macromolecular polymer chains along the fiber axis. The polymer jet under the influence of an electrostatic field experiences a high degree of molecular orientation due to high elongation strains and shear forces. As explained later, in Section 2.2, System Configuration to Align Fibers, optimal speed of fiber collecting drum brings about better alignment. In addition, optimal speed of collecting drum causes maximum molecular orientation. Beyond the optimal speed, the orientation can decrease slightly. According to [PERSON] and [PERSON] (2004), twisted yarns of higher degree of molecular orientation resulted in better mechanical properties [99]. The degree of orientation can be quantified by the X-ray diffraction analysis of the samples. The nitrile group in PAN is oriented in approximately perpendicular to the draw direction. The absorbance of perpendicular polarization showed nitrile-stretching vibration with strong dichroism, and therefore better orientation. A twist angle of 11\({}^{\circ}\) in as-spun PAN fiber improved the initial modulus and ultimate strength of 2.6 GPa and 56 MPa, respectively, to 2.2 times and 2.9 times, respectively. Molecular orientation results in better mechanical properties in general, Young's modulus in particular, of the resulting carbon fibers [101; 102]. [PERSON] et al. (2010) studied the effects of electrospun polymers on oriented morphology and tensile properties. The lower the diameter of the fibers, the higher the modulus and strength of the fibers. They observed that finer fibers have enhanced properties because of gradual ordering of molecular chains and increase in crystallinity [103]. [PERSON] et al. (2010) noticed that the modulus and tensile properties of polycarbonate (PCL) fibers increased significantly when the fiber diameter was reduced to below 500 nm. The molecular orientation improves gradually as the fiber diameter is reduced. Moreover, [PERSON] et al. (2013) concluded that electrospun PAN fibers have better mechanical properties at lower diameters [104]. [PERSON] et al. (2011) observed that the strength of the carbonized nanofibers at 800 \({}^{\circ}\)C increased by 100% when the diameter was reduced from 800 to 200 nm [105]. For composite applications, a decrease in diameter of fiber at the nanoscale level can improve mechanical properties as the specific reinforcement area per unit mass increases. [PERSON] et al. (2009) observed self-aligned bundled fibers of polyphenylene-g-polystyrene/poly (a-caprolactone) (PP-g-PS/PCL) when blended with polystyrene (PS) or polymethyl methacrylate (PMMA). This is because of the unique molecular architecture of PP-g-PS/PCL and its interaction with PS or PMMA [106].
## 4 Leak Detection Technologies
### Software-Based Methods
#### 4.2.3 Water Balance Method  
Water balance, mass balance, or water audit is the most employed technique for quantifying total water losses and leakage in a network. This approach is based on the principle of mass conservation, which asserts that the amount of fluid that enters a pipe section must either remain in the section or exit it [22]. To identify a leak, the water balance method compares the amount of water introduced into the distribution network to the sum of the water consumed or used components, with any significant difference indicating the presence of a leak beyond an established tolerance level [60]. The accuracy of the mass balance technique is dependent on precise measurement of the mass flowing into and out of a pipeline [61]. The primary limitation of the water audit technique is its reliance on the assumption of steady-state conditions. This means that the volumes being balanced must be calculated over a longer time interval to prevent false alarms [62]. Additionally, while the water balance method is effective in quantifying total water losses, it is limited in pinpointing the exact locations of leaks in the network. As such, it is often necessary to complement this approach with other active leakage detection methods.
## 2 Theory
### Harmonic Approximation (HA)  
Harmonic approximation, commonly known as four-point method, approximates the Fourier transform based on the idea that only four data points per modulation cycle provide the correct phase and amplitude of a sinusoidal signal [(42)]. This method is fast, but only valid for sinusoidal stimulation. For the experimental LIT data, the four-point method and the Fourier transform computes the amplitude and phase angle data from the recorded temperature-time history of each pixel, then stored in the form of 2D matrices and converted to amplitude and phase images. If \(\mathrm{S_{1}}\), \(\mathrm{S_{2}}\), \(\mathrm{S_{3}}\), and \(\mathrm{S_{4}}\) are four equidistant thermal images, as shown in Figure 3, in a constant period, then the amplitude (A) and phase (\(\varnothing\)) images can be expressed by Equations (9) and (10), respectively [(43; 44)].  
\[\mathrm{A=}\sqrt{(\mathrm{S_{1}}-\mathrm{S_{3}})^{2}+(\mathrm{S_{2}}-\mathrm{ S_{4}})^{2}} \tag{9}\]  
Figure 2: Principle of data acquisition and processing by fast Fourier transform.
# Domination and Independent Domination in Extended Supergrid Graphs +
## 2 Preliminaries
Note that we use \((1,1)\) to denote the coordinates of the upper-left-most vertex of a (grid, supergrid, triangular supergrid) graph in the figures. For example, Figure 3a-c shows \(G_{8\times 9}\), \(R_{8\times 9}\) and \(T_{8\times 9}\), respectively. Notice that \(G_{m\times n}\), \(R_{m\times n}\), and \(T_{m\times n}\) are not paths; hence, \(m,n\geqslant 2\). Without loss of generality, we assume that \(n\geqslant m\geqslant 2\) for these rectangular graphs. A path in an extended supergrid graph is called a _horizontal_ (respectively, _vertical_) _path_ if all of its edges are horizontal (respectively, vertical) edges. For instance, the arrow lines in Figure 3b depict a horizontal path \(P_{9}\). In [28; 34], the domination number \(\gamma(R_{m\times n})\) and the independent domination number \(\gamma_{\text{ind}}(R_{m\times n})\) of \(R_{m\times n}\) are computed as follows:  
**Lemma 2** (see [28; 34]). : \(\gamma(R_{m\times n})=\gamma_{\text{ind}}(R_{m\times n})=\lceil\frac{m}{3} \rceil\lceil\frac{n}{3}\rceil\)_._  
The complexities of the domination and independent domination problems on rectangular triangular-supergrid graphs remain open. In this paper, we provide a tight upper bound of \(\gamma(T_{m\times n})\) and \(\gamma_{\text{ind}}(T_{m\times n})\). To simplify notation, for a dominating set \(D\) of graph \(G\) and the subgraph \(H\) of \(G\), we denote the restriction from \(D\) to \(H\) as \(D_{\lfloor H}\). In our method, a partition may be made on a rectangular triangular-supergrid graph which is split into two disjoint parts, and is defined below. **Definition 1**. : _Let \(T\) be a rectangular triangular-supergrid graph. The separation operation on \(T\) is to divide \(T\) into two vertex-disjoint rectangular triangular-supergrid subgraphs \(T_{1}\) and \(T_{2}\), that is, \(V(T)=V(T_{1})\cup V(T_{2})\) and \(V(T_{1})\cap V(T_{2})=\emptyset\). If a separation consists of a set of horizontal edges, it is called vertical, and if it consists of a set of vertical edges, it is called horizontal. For example, the bold vertical (respectively, horizontal) dashed line in Figure 3c represents a vertical (respectively, horizontal) separation on \(T_{8\times 9}\) divided into \(T_{8\times 3}\) and \(T_{8\times 6}\) (respectively, \(T_{3\times 9}\) and \(T_{5\times 9}\))._
# Parallel Agent-Based Framework for Analyzing Urban Agricultural Supply Chains
## 7 Discussion  
The development of simulation tools for analyzing urban agricultural supply chains presents significant challenges, particularly in terms of balancing model complexity, data availability, computational demands, and real-world applicability. Our proposed framework, which integrates agent-based modeling (ABM) with discrete event simulation (DES) and incorporates an approximate optimistic parallel execution strategy, represents a step forward in tackling these challenges.  
While our simulator captures key decision-making dynamics among farmers, vendors, and consumers, we acknowledge the inherent trade-offs in behavioral modeling. Real-world consumer behavior is influenced by a wide range of factors--cultural, economic, and situational--which are difficult to capture in their entirety, particularly when working with limited or aggregated data. To mitigate this, we implemented a range of agent profiles (e.g., risk-aware farmers, seasonal fairground workers, and family budget consumers) that allow for more complex behaviors than purely random or rule-based actions. Nonetheless, we recognize the value of further sophistication and have identified this as a priority for future work, including the exploration of reinforcement learning techniques to enable adaptive and evolving behaviors.  
A major limitation in modeling informal or semi-formal food markets is the scarcity of fine-grained, high-resolution datasets--particularly concerning purchasing patterns and household-level consumption dynamics. To address this, we relied on the most complete data sources available for Santiago, Chile, and the sixth region of Chile, including historical price data and national consumption surveys.  
A recurrent concern in deploying complex simulation systems is the technical barrier to entry. While our simulator was evaluated on a 32-core machine to assess performance under large-scale configurations, the framework supports both sequential and optimized low-cost parallel executions. The dual implementation of atomic and grouped event strategies enables users to adjust the level of computational granularity according to their hardware capacity. Additionally, the model's modular design and configuration files allow for easy customization without modifying the source code, thus reducing the expertise required for its use.
## 2 Seismic Analysis of Liquid Storage Tanks
### Hydrodynamic Analysis
#### 2.2.2 Convective Pressure Distribution  
To estimate the convective pressure, a cylindrical coordinate system \((\xi,\ \zeta,\ \theta)\) is used as shown in Figure 3:  
\[\xi=r/R \tag{5}\]  
\[\zeta=z/H \tag{6}\]  
where \(r\) is the radial distance, \(z\) is the height, \(R\) is the tank radius, and \(H\) is the fluid height.  
The convective pressure \(p_{c}\) can be expressed as follows [38]:  
\[p_{c}(\xi,\zeta,\theta)=C_{cn}(\xi,\zeta)\cdot\rho\ R\ \tilde{u}_{cn}\text{cos}(\theta) \tag{7}\]  
where \(C_{cn}(\xi,\zeta)\) is the non-dimensional convective pressure distribution coefficient, \(\rho\) is the fluid density, \(\tilde{u}_{cn}\) is the acceleration of the \(n\)-th convective mass mode, and \(\theta\) is the angular position. The coefficient \(C_{cn}(\xi,\zeta)\) is computed using the following expression:  
\[C_{cn}(\xi,\zeta)=\sum_{n=1}^{\infty}\frac{2\text{cosh}(\lambda_{n}\gamma\zeta )\ J_{1}(\lambda_{n}\xi)}{(\lambda_{n}^{2}-1)\ J_{1}(\lambda_{n})\text{cosh}( \lambda_{n}\gamma)} \tag{8}\]  
where \(J_{1}(\cdot)\) is the first-order Bessel function, \(\gamma=H/R\) is the height-to-radius ratio, and \(\lambda_{n}\) is the \(n\)-th root of the Bessel function. The first three roots are approximately \(\lambda_{1}=1.841\), \(\lambda_{2}=5.331\), and \(\lambda_{3}=8.536\), corresponding to the fundamental and higher-order modes of sloshing.
# On Classical Solutions for A Kuramoto-Sinelshchikov-Velarde-Type Equation
## 2 Proof of Theorem 1, under the Assumptions (2) and (4)
It follows from (31) that  
\[ \begin{split}\frac{d}{dt}\left\|\partial_{x}^{2}u(t,\cdot) \right\|_{L^{2}(\mathbb{R})}^{2}+\frac{\beta^{2}}{2}\left\|\partial_{x}^{4}u( t,\cdot)\right\|_{L^{2}(\mathbb{R})}^{2}\\ \leq C(T)\left(1+(1+D_{1})\left\|\partial_{x}u\right\|_{L^{ \infty}((0,T)\times\mathbb{R})}^{2}+\frac{1}{D_{1}}\left\|\partial_{x}u\right\| _{L^{\infty}((0,T)\times\mathbb{R})}^{4}\right)\end{split}  \tag{32}\]  
We prove (28). Thanks to (18), (26) and (32),  
\[\left\|\partial_{x}u\right\|_{L^{\infty}((0,T)\times\mathbb{R})}^{2}\leq C(T) \sqrt{\left(1+(1+D_{1})\left\|\partial_{x}u\right\|_{L^{\infty}((0,T)\times \mathbb{R})}^{2}+\frac{1}{D_{1}}\left\|\partial_{x}u\right\|_{L^{\infty}((0,T )\times\mathbb{R})}^{4}\right)}.\]  
Hence,  
\[\left(1-\frac{C(T)}{D_{1}}\right)\left\|\partial_{x}u\right\|_{L^{\infty}((0, T)\times\mathbb{R})}^{4}-C(T)\left(1+D_{1}\right)\left\|\partial_{x}u \right\|_{L^{\infty}((0,T)\times\mathbb{R})}^{2}-C(T)\leq 0.\]  
Choosing  
\[D_{1}=2C(T), \tag{33}\]  
we have that  
\[\frac{1}{2}\left\|\partial_{x}u\right\|_{L^{\infty}((0,T)\times\mathbb{R})}^{ 4}-C(T)\left\|\partial_{x}u\right\|_{L^{\infty}((0,T)\times\mathbb{R})}^{2}-C (T)\leq 0,\]  
which gives (28). Finally, (29) follows from (28), (32) and (33). **Lemma 5**: _Fix \(T>0\). There exists a constant \(C(T)>0\), such that_  
\[\beta^{2}\left\|\partial_{x}^{2}u(t,\cdot)\right\|_{L^{2}(\mathbb{R})}^{2}+ \int_{0}^{t}\left\|\partial_{t}u(s,\cdot)\right\|_{L^{2}(\mathbb{R})}^{2}ds \leq C(T), \tag{34}\]  
_for every \(0\leq t\leq T\)._  
Let \(0\leq t\leq T\). Multiplying (17) by \(2\partial_{t}u\), an integration on \(\mathbb{R}\) gives  
\[ \begin{split}\beta^{2}\frac{d}{dt}\left\|\partial_{x}^{2}u(t, \cdot)\right\|_{L^{2}(\mathbb{R})}^{2}&+2\left\|\partial_{t}u(t, \cdot)\right\|_{L^{2}(\mathbb{R})}^{2}\\ =&-2\kappa\int_{\mathbb{R}}(\partial_{x}u)^{2} \partial_{t}udx-2q\int_{\mathbb{R}}(\partial_{x}u)^{3}\partial_{t}udx\\ &-2r\int_{\mathbb{R}}(\partial_{x}u)^{4}\partial_{t}udx-2\delta \int_{\mathbb{R}}\partial_{x}^{3}u\partial_{t}udx-2\mu\int_{\mathbb{R}} \partial_{x}^{2}u\partial_{t}udx.\end{split}
## 4 Materials and Methods
### Antibacterial Activity  
The microdilution technique [78; 79] was used by reducing resazurin (7-hydroxy-3\(H\)-phenoxazin-3-one-10-oxide) for antibacterial tests and TTC (2,3,5-triphenyltetrazolzolium chloride) for antifungal tests. All tests were performed in triplicate. The samples were tested against strains purchased commercially from Cefar Diagnostic Ltd.a: _Escherichia coli_ (CCCD-E005), _Staphylococcus aureus_ (CCCD-S009), _Klebsiella pneumoniae_ (CCCD-K003) _Pseudomonas aeruginosa_ (CCCD-P004), _Proteus mirabilis_ (CCCD-P001), _Staphylococcus epidermidis_ (CCCD-S010), _Enterococcus faecalis_ (CCCD-E002), _Salmonella enterica_ (CCCD-S003), _Serratia marcescens_ (CCCD-S005), _Bacillus subtilis_ (CCCD-B005), _Candida albicans_ (CCCD-CC001), _Candida tropicalis_ (CCCD-CC002), _Candida parapysilosis_ (CCCD-CC004). The assay was performed in 96-well microplates with 100 \(\upmu\)L of double-concentrated microbial inoculum (5 \(\times\) 10\({}^{5}\) CFU/mL--bacteria and 5 \(\times\) 10\({}^{3}\) CFU/mL--fungi) and 100 \(\upmu\)L of the sample to be tested. The positive control used for bacteria was levofloxacin 0.25 mg/mL, and terbinafine 0.4 mg/mL for fungi. As a negative control, 100 \(\upmu\)L of the microbial inoculum and 100 \(\upmu\)L of 10% DMSO were inserted. For sterility control, 100 \(\upmu\)L of the sterile culture medium used to prepare the inoculum [Mueller Hinton broth for bacteria (beef extract--2.0 g/L; casamino acid--17.5 g/L; starch--1.5 g/L) and Sabouraud broth for fungi (dextrose--20 g/L; petpune--10g/L)] was added.  
The microplates were then incubated at 37 \({}^{\circ}\)C for 24 h (bacteria) and 48 h (fungi) in a BOD incubator. After this period, 30 \(\upmu\)L of resazurin was added to all wells of the antibacterial activity assay plates, and 30 \(\upmu\)L of TTC was added to the wells of the antifungal activity assay plates. The plates were incubated again at 37 \({}^{\circ}\)C for 1 to 2 h to check the reduction of the inserted developers. For the antibacterial assay, the pink color is indicative of cell growth, i.e., no antimicrobial action, and for the antifungal assay, the red color indicates that there was no inhibition of microbial growth by the extract tested.  
For extracts with antimicrobial activity, the Minimum Inhibitory Concentration (MIC) was determined by successive dilutions of the samples with sterile distilled water. The concentration ranges used were 75, 37.5, 18.7, 9.4, 4.7, and 2.3 \(\upmu\)g/mL, where the lowest concentration of extract that managed to inhibit microbial growth was considered the MIC.
## 4 Experimental Study and Performance Benchmarking
### Number of Times the Algorithm Converged to the Optimal Solution
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{2}{c}{\(N_{C}\)**Obtained Using the New**} & \multicolumn{2}{c}{**Best \(N_{C}\) Obtained Using the**} \\  & **Hybrid Algorithm** & **Previous Three Algorithms** \\ \hline Rec-01 & 0 & 2 \\ Rec-03 & 0 & 8 \\ Rec-05 & 0 & 1 \\ Rec-07 & 0 & 10 \\ Rec-09 & 0 & 10 \\ Rec-11 & 0 & 10 \\ Rec-13 & 0 & 1 \\ Rec-15 & 0 & 2 \\ Rec-17 & 0 & 1 \\ \hline Car-01 & **10** & **10** \\ Car-02 & 9 & **10** \\ Car-03 & 1 & **10** \\ Car-04 & **10** & **10** \\ Car-05 & 2 & **10** \\ Car-06 & 4 & **10** \\ Car-07 & 7 & **10** \\ Car-08 & **10** & **10** \\ \hline Hel-02 & 0 & **10** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the N\({}_{c}\) found using the new hybrid algorithm and the previous three algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{2}{c}{\(N_{O}\)**Obtained Using the New**} & \multicolumn{2}{c}{**Best \(N_{O}\) Obtained Using the**} \\  & **Hybrid Algorithm** & **Previous Three Algorithms** \\ \hline Rec-01 & 0.00 & **18.00** \\ Rec-03 & 0.00 & **4.20** \\ Rec-05 & 0.00 & **3.00** \\ Rec-07 & 0.00 & **4.00** \\ Rec-09 & 0.00 & **3.00** \\ Rec-11 & 0.00 & **3.00** \\ Rec-13 & 0.00 & **2.00** \\ Rec-15 & 0.00 & **3.00** \\ Rec-17 & 0.00 & **6.80** \\ \hline Car-01 & 33.80 & 58.50 \\ Car-02 & 17.11 & **30.40** \\ Car-03 & 1.00 & **6.20** \\ Car-04 & 12.20 & **13.5** \\ Car-05 & 1.00 & **1.90** \\ Car-06 & 1.00 & **1.00** \\ Car-07 & 1.00 & **1.00** \\ Car-08 & 1.00 & **1.00** \\ \hline Hel-02 & 0.00 & **6.30** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of the \(N_{O}\) using the new hybrid algorithm and the previous three algorithms. performance compared to sharing fitness or the proposed algorithm. The reason that the proposed algorithm was able to achieve better performance than sharing fitness, CM, and the hybrid algorithm, was its utilization of a feature vector to separate the individuals into different clusters rather than a single value. In this section, the performance of the three algorithms was measured by their application to 18 benchmark PFSSP. Four indicators were used to measure the performance--(1) best optimal found, (2) mean value and standard deviation of the optimal solution found in 10 simulations, (3) number of simulations in which the algorithm converged to the best optimal solution, and (4) average number of best optimal solution found. The results indicated that the proposed algorithm had a better performance than the sharing fitness and CM, and also a hybrid algorithm created by combining the proposed algorithm and sharing fitness.