# Fine-Tuned Cardiovascular Risk Assessment: Locally Weighted Salp Swarm Algorithm in Global Optimization

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## Abstract

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## 1. Introduction

- This research introduces the Locally Weighted Salp Swarm Algorithm (LWSSA), an enhancement of the Salp Swarm Algorithm (SSA), which combines two mechanisms to mitigate issues like slow convergence and local optima.
- The LWSSA introduces a new Local Search (LS) Algorithm known as the “Locally Weighted approach” that guides the search process toward promising local regions, improving search efficiency by iteratively probing and refining high-quality solutions. This local search strategy is employed to refine individual solutions after each iteration of the optimization process.
- The LWSSA incorporates a mutation operator to inject randomness into the search process, enhancing its ability to escape local optima and explore the solution space more effectively.
- This research extends its contributions to practical applications by evaluating the LWSSA-XGBoost model for cardiovascular disease (CVD) risk assessment, showcasing its superior predictive performance.

## 2. Related Work

- For more accurate fine-tuning of solutions, the Salp Swarm Algorithm (SSA) incorporates the locally weighted approach as a local search tool. The method is able to better solve difficult optimization problems and converge more quickly because of the concentrated exploration.
- The implementation of the mutation scheme within the SSA adds an extra layer of randomness to the Salps, which in turn improves the latter’s capacity for conducting global searches. This helps to diversify the exploration process, which enables the algorithm to break free from local optimal solutions and investigate a wider range of possible solutions.
- The performance of the SSA’s global search is improved thanks to the synergistic effect of the combination of the locally weighted technique and the mutation scheme. The method is made more robust and successful in tackling difficult optimization problems with multiple local optima as a result of the integration of both strategies.

## 3. Preliminaries

#### Principles of Salp Swarm Optimization (SSA)

## 4. Proposed Algorithm

#### 4.1. Locally Weighted Approach ($LW$)

#### 4.2. Update Salp Followers’ Position

Algorithm 1: The developed Locally Weighted Approach |

For i = 1: $N$If random < 0.5: Randomly choose two positions ${y}_{{r}_{1}}^{t}$ and ${y}_{{r}_{2}}^{t}$ from ${pop}^{t}$ Calculate $weight$ for position i by Equation (6) Calculate $the\text{}random\text{}value\text{}Z\text{}based\text{}on\text{}\mathrm{L}\mathrm{e}\mathrm{v}\mathrm{y}\text{}\mathrm{f}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\text{}$ for position i by Equation (8) Calculate the new position ${ynew}_{i}$ of particle i by Equation (7) End For |

#### 4.3. LWSSA Optimization Scenario

Algorithm 2: The LWSSA |

Each search agent’s dimension (D), as well as its upper bound (ub) and lower bound (lb), as well as the evaluation fitness function (Fitness), as well as the maximum number of iterations (T), are input. Optimal individual (Food Location), and optimal cost function (Food Fitness) are the final results. According to Dimensions D, population size N, ub, lb, initial the Salp population. According to the fitness function, select the least costly individual in the population as the Food Fitness. while (stopping condition is not hold)compute w1 by Equation (2) for (all Salp (Salp Location))if ($i\le N/2$) thenUpdate the location of the Salp leaders by Equation (1) else Update the Location of the followers Salp by Equation (10) if (random < 0.5)Apply (LW) technique as Algorithm (2) Compute the value of the fitness of ${ynew}_{i}$ and reported it as NewFitness if (NewFitness < Food Fitness) thenUpdate the Food Location and Food Fitness endendend |

## 5. Experimental Results and Analysis

#### 5.1. Experiment 1: Benchmark Examination for the IEEE CEC 2021

#### 5.1.1. Comparison of LWSSA with Some SSA Variants

#### 5.1.2. Comparison of LWSSA with State-of-the-Art Competitors

#### 5.2. Experiment 2: Benchmark Examination for the IEEE CEC 2017

#### 5.3. LWSSA Computation Complexity

#### 5.4. Qualitative Analysis

#### 5.5. Demonstrated Effectiveness

- Population Division and Dynamic Mutation:
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- LWSSA approach: The LWSSA employs a unique population division strategy, categorizing individuals into leaders and followers. Leaders are updated using a specific equation, while followers undergo a distinct mutation strategy. This dynamic population management introduces a nuanced exploration–exploitation balance.
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- Contrast with existing algorithms: Unlike conventional algorithms with uniform population treatment, the LWSSA’s tailored approach enhances diversity within the population, fostering a more effective search process.

- Local Weight (LW) Technique:
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- LWSSA approach: The LWSSA introduces the LW technique, functioning as a form of local search with a 50% update probability for all individuals. This technique strategically enhances solutions and determines optimal locations, providing adaptability and responsiveness to the optimization process.
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- Contrast with existing algorithms: Many existing algorithms lack a dedicated local search strategy. The LWSSA’s integration of the LW technique contributes to its ability to navigate the search space dynamically.

- Robustness and Local Minima Avoidance:
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- LWSSA approach: The LWSSA demonstrates enhanced robustness, effectively avoiding local minima through its dynamic population strategies and local search capabilities.
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- Contrast with existing algorithms: Some existing algorithms may struggle in complex landscapes, leading to premature convergence to local minima. The LWSSA’s adaptability and strategic updates contribute to its robust performance.

- Convergence Speed and Solution Quality:
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- LWSSA approach: The LWSSA consistently exhibits superior convergence speed, rapidly approaching optimal solutions. This can be attributed to the innovative combination of population division, mutation, and the LW technique.
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- Contrast with existing algorithms: While many algorithms may converge more slowly or struggle to reach high-quality solutions, the LWSSA’s distinctive techniques contribute to its efficiency in reaching optimal outcomes.

- Versatility and Competitive Performance:
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- LWSSA approach: The LWSSA competes favorably against state-of-the-art Salps algorithm variants and advanced optimization algorithms, showcasing its versatility and competitiveness across diverse benchmark problems.
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- Contrast with existing algorithms: The LWSSA’s performance consistently outpaces existing solutions, substantiating its effectiveness in addressing a wide range of optimization challenges.

## 6. Risk Assessment Method for CVD Using LWSSA-XGBoost Model

#### 6.1. Dataset Description

#### 6.2. The XGBoost Method

#### 6.3. Objective Function and LWSSA-XGBoost Parameter Settings

#### 6.4. Methodology

#### 6.5. Measure of Performance

#### 6.5.1. Classification Evaluation Indicators Based on the Confusion Matrix

#### Accuracy

#### Precision

#### Recall

#### F1 Score

#### 6.5.2. ROC Area and AUC Area

#### 6.6. Analysis and Outcomes

#### 6.6.1. Comparison with Most Advanced Optimization Techniques

#### Average Run Time

#### 6.6.2. Comparing to ML Models Currently Used

#### 6.6.3. Evaluation of LWSSA Algorithm with Various Kinds of Datasets

ID | Dataset Name | No. Classes | No. Attributes | No. of Samples |
---|---|---|---|---|

DS1 | Zoo | 7 | 16 | 101 |

DS2 | Wine | 3 | 13 | 178 |

DS3 | Heart | 2 | 13 | 270 |

DS4 | Vehicle | 4 | 18 | 846 |

DS5 | Breastcancer | 2 | 9 | 699 |

DS6 | Soybean small | 4 | 35 | 47 |

DS7 | Spambase | 2 | 57 | 4601 |

DS8 | Dermatology | 6 | 34 | 366 |

DS9 | fri_c0_500_10 | 2 | 10 | 500 |

DS10 | fri_c0_1000_10 | 2 | 10 | 1000 |

DS11 | fri_c1_1000_10 | 2 | 10 | 1000 |

DS12 | Pc1 | 2 | 21 | 1109 |

DS13 | stock | 2 | 9 | 950 |

DS14 | CLEAN | 2 | 166 | 476 |

DS15 | Semeion | 10 | 256 | 1593 |

DS16 | Waveform | 3 | 40 | 5000 |

#### Test Accuracy and Precision Analysis

**Table 8.**Statistical outcome comparison, average test accuracy, and precision values for 20 runs for all methods.

ID | GWO-XGBoost | ISSA-XGBoost | ESSA-XGBoost | TVSSA-XGBoost | SSA-XGBoost | WOA-XGBoost | SSALEO-XGBoost | LWSSA-XGBoost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | Acc. | Preci. | |

DS1 | 1.000 | 1.000 | 1.000 | 1.000 | 0.964 | 0.905 | 1.000 | 1.000 | 0.876 | 0.811 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS2 | 1.000 | 1.000 | 1.000 | 1.000 | 0.994 | 0.995 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS3 | 0.877 | 0.876 | 0.888 | 0.887 | 0.852 | 0.854 | 0.885 | 0.884 | 0.840 | 0.813 | 0.870 | 0.871 | 0.884 | 0.883 | 0.889 | 0.888 |

DS4 | 0.820 | 0.820 | 0.816 | 0.816 | 0.791 | 0.785 | 0.813 | 0.814 | 0.805 | 0.804 | 0.808 | 0.808 | 0.819 | 0.820 | 0.826 | 0.826 |

DS5 | 0.970 | 0.963 | 0.971 | 0.964 | 0.965 | 0.959 | 0.971 | 0.964 | 0.968 | 0.962 | 0.969 | 0.962 | 0.972 | 0.965 | 0.971 | 0.964 |

DS6 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.940 | 0.910 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS7 | 0.958 | 0.956 | 0.956 | 0.954 | 0.950 | 0.949 | 0.956 | 0.954 | 0.955 | 0.953 | 0.956 | 0.954 | 0.957 | 0.956 | 0.958 | 0.955 |

DS8 | 0.987 | 0.987 | 0.991 | 0.990 | 0.989 | 0.989 | 0.984 | 0.983 | 0.973 | 0.971 | 0.986 | 0.985 | 0.994 | 0.993 | 0.989 | 0.989 |

DS9 | 0.964 | 0.957 | 0.959 | 0.959 | 0.901 | 0.901 | 0.954 | 0.954 | 0.946 | 0.946 | 0.949 | 0.949 | 0.960 | 0.960 | 0.974 | 0.964 |

DS10 | 0.903 | 0.901 | 0.897 | 0.897 | 0.883 | 0.883 | 0.897 | 0.897 | 0.892 | 0.893 | 0.895 | 0.895 | 0.902 | 0.902 | 0.904 | 0.904 |

DS11 | 0.957 | 0.955 | 0.954 | 0.953 | 0.945 | 0.944 | 0.954 | 0.953 | 0.950 | 0.949 | 0.954 | 0.952 | 0.959 | 0.958 | 0.961 | 0.959 |

DS12 | 0.959 | 0.873 | 0.959 | 0.883 | 0.948 | 0.760 | 0.959 | 0.892 | 0.955 | 0.864 | 0.957 | 0.876 | 0.959 | 0.878 | 0.961 | 0.886 |

DS13 | 0.988 | 0.988 | 0.988 | 0.988 | 0.968 | 0.968 | 0.989 | 0.989 | 0.976 | 0.976 | 0.987 | 0.987 | 0.990 | 0.990 | 0.991 | 0.991 |

DS14 | 0.969 | 0.970 | 0.969 | 0.970 | 0.965 | 0.967 | 0.969 | 0.970 | 0.967 | 0.968 | 0.967 | 0.967 | 0.969 | 0.970 | 0.970 | 0.970 |

DS15 | 0.972 | 0.974 | 0.973 | 0.975 | 0.967 | 0.968 | 0.958 | 0.961 | 0.957 | 0.960 | 0.959 | 0.962 | 0.962 | 0.964 | 0.974 | 0.976 |

DS16 | 0.872 | 0.872 | 0.868 | 0.868 | 0.869 | 0.870 | 0.867 | 0.867 | 0.869 | 0.870 | 0.867 | 0.868 | 0.872 | 0.872 | 0.876 | 0.876 |

#### Recall, Precision, F1 Score, and AUC Analysis

**Table 9.**Statistical outcomes of comparison, average recall, and F1 score values for 20 runs for all methods.

ID | GWO-XGBoost | ISSA-XGBoost | ESSA-XGBoost | TVSSA-XGBoost | SSA-XGBoost | WOA-XGBoost | SSALEO-XGBoost | LWSSA-XGBoost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | Recall | F1 Score | |

DS1 | 1.000 | 1.000 | 1.000 | 1.000 | 0.911 | 0.907 | 1.000 | 1.000 | 0.829 | 0.816 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS2 | 1.000 | 1.000 | 1.000 | 1.000 | 0.995 | 0.995 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS3 | 0.879 | 0.876 | 0.887 | 0.887 | 0.858 | 0.852 | 0.885 | 0.884 | 0.837 | 0.819 | 0.873 | 0.870 | 0.885 | 0.883 | 0.888 | 0.888 |

DS4 | 0.821 | 0.819 | 0.817 | 0.816 | 0.793 | 0.784 | 0.814 | 0.812 | 0.806 | 0.804 | 0.809 | 0.807 | 0.820 | 0.819 | 0.827 | 0.826 |

DS5 | 0.972 | 0.967 | 0.973 | 0.968 | 0.964 | 0.961 | 0.972 | 0.968 | 0.968 | 0.965 | 0.970 | 0.966 | 0.974 | 0.969 | 0.973 | 0.968 |

DS6 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.925 | 0.914 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

DS7 | 0.954 | 0.955 | 0.953 | 0.954 | 0.946 | 0.948 | 0.954 | 0.954 | 0.952 | 0.952 | 0.953 | 0.953 | 0.955 | 0.955 | 0.955 | 0.956 |

DS8 | 0.985 | 0.985 | 0.989 | 0.989 | 0.986 | 0.987 | 0.981 | 0.982 | 0.971 | 0.970 | 0.986 | 0.985 | 0.993 | 0.993 | 0.986 | 0.988 |

DS9 | 0.958 | 0.957 | 0.959 | 0.958 | 0.901 | 0.900 | 0.954 | 0.953 | 0.946 | 0.945 | 0.950 | 0.949 | 0.961 | 0.960 | 0.961 | 0.963 |

DS10 | 0.901 | 0.900 | 0.897 | 0.897 | 0.883 | 0.883 | 0.897 | 0.897 | 0.892 | 0.892 | 0.895 | 0.895 | 0.902 | 0.902 | 0.907 | 0.903 |

DS11 | 0.957 | 0.956 | 0.955 | 0.954 | 0.944 | 0.944 | 0.954 | 0.953 | 0.951 | 0.950 | 0.953 | 0.953 | 0.960 | 0.959 | 0.961 | 0.960 |

DS12 | 0.772 | 0.813 | 0.765 | 0.810 | 0.644 | 0.676 | 0.757 | 0.806 | 0.736 | 0.782 | 0.754 | 0.799 | 0.763 | 0.807 | 0.776 | 0.820 |

DS13 | 0.988 | 0.988 | 0.988 | 0.988 | 0.968 | 0.968 | 0.989 | 0.989 | 0.976 | 0.976 | 0.987 | 0.987 | 0.990 | 0.990 | 0.991 | 0.991 |

DS14 | 0.967 | 0.968 | 0.968 | 0.969 | 0.963 | 0.964 | 0.967 | 0.968 | 0.965 | 0.967 | 0.965 | 0.966 | 0.968 | 0.969 | 0.968 | 0.969 |

DS15 | 0.972 | 0.972 | 0.973 | 0.973 | 0.967 | 0.967 | 0.959 | 0.959 | 0.957 | 0.957 | 0.960 | 0.960 | 0.962 | 0.962 | 0.974 | 0.975 |

DS16 | 0.872 | 0.871 | 0.868 | 0.868 | 0.869 | 0.868 | 0.867 | 0.867 | 0.870 | 0.869 | 0.867 | 0.867 | 0.872 | 0.872 | 0.877 | 0.876 |

**Table 10.**Statistical outcomes of comparison, average fitness, and AUC values for 20 runs for all methods.

ID | GWO-XGBoost | ISSA-XGBoost | ESSA-XGBoost | TVSSA-XGBoost | SSA-XGBoost | WOA-XGBoost | SSALEO-XGBoost | LWSSA-XGBoost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | Fitness | AUC. | |

DS1 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0933 | 0.999 | 0.0000 | 0.998 | 0.1842 | 0.898 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 |

DS2 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0051 | 0.999 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 |

DS3 | 0.1240 | 0.879 | 0.1134 | 0.887 | 0.1484 | 0.858 | 0.1160 | 0.885 | 0.1807 | 0.837 | 0.1304 | 0.873 | 0.1167 | 0.885 | 0.1125 | 0.888 |

DS4 | 0.1809 | 0.936 | 0.1841 | 0.938 | 0.2165 | 0.927 | 0.1876 | 0.936 | 0.1958 | 0.935 | 0.1932 | 0.934 | 0.1814 | 0.938 | 0.1745 | 0.938 |

DS5 | 0.0329 | 0.972 | 0.0318 | 0.973 | 0.0386 | 0.964 | 0.0322 | 0.972 | 0.0350 | 0.968 | 0.0341 | 0.970 | 0.0310 | 0.974 | 0.0318 | 0.973 |

DS6 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0857 | 0.950 | 0.0000 | 1.000 | 0.0000 | 1.000 | 0.0000 | 1.000 |

DS7 | 0.0444 | 0.955 | 0.0463 | 0.953 | 0.0523 | 0.946 | 0.0460 | 0.954 | 0.0476 | 0.952 | 0.0465 | 0.953 | 0.0446 | 0.955 | 0.0452 | 0.954 |

DS8 | 0.0145 | 0.998 | 0.0107 | 0.998 | 0.0131 | 0.997 | 0.0184 | 0.998 | 0.0297 | 0.997 | 0.0152 | 0.998 | 0.0069 | 0.998 | 0.0123 | 0.998 |

DS9 | 0.0430 | 0.958 | 0.0415 | 0.959 | 0.0995 | 0.901 | 0.0465 | 0.954 | 0.0545 | 0.946 | 0.0510 | 0.950 | 0.0400 | 0.961 | 0.0365 | 0.964 |

DS10 | 0.0995 | 0.901 | 0.1033 | 0.897 | 0.1173 | 0.883 | 0.1030 | 0.897 | 0.1078 | 0.892 | 0.1048 | 0.895 | 0.0978 | 0.902 | 0.0968 | 0.903 |

DS11 | 0.0439 | 0.957 | 0.0464 | 0.955 | 0.0562 | 0.944 | 0.0467 | 0.954 | 0.0505 | 0.951 | 0.0472 | 0.953 | 0.0414 | 0.960 | 0.0401 | 0.961 |

DS12 | 0.1873 | 0.772 | 0.1899 | 0.765 | 0.3240 | 0.644 | 0.1944 | 0.757 | 0.2179 | 0.736 | 0.2006 | 0.754 | 0.1928 | 0.763 | 0.1803 | 0.776 |

DS13 | 0.0121 | 0.988 | 0.0119 | 0.988 | 0.0321 | 0.968 | 0.0113 | 0.989 | 0.0242 | 0.976 | 0.0134 | 0.987 | 0.0097 | 0.990 | 0.0087 | 0.991 |

DS14 | 0.0318 | 0.967 | 0.0313 | 0.968 | 0.0356 | 0.963 | 0.0318 | 0.967 | 0.0334 | 0.965 | 0.0340 | 0.965 | 0.0313 | 0.968 | 0.0308 | 0.968 |

DS15 | 0.0276 | 0.998 | 0.0269 | 0.997 | 0.0332 | 0.997 | 0.0412 | 0.996 | 0.0428 | 0.997 | 0.0403 | 0.996 | 0.0377 | 0.997 | 0.0255 | 0.998 |

DS16 | 0.1286 | 0.973 | 0.1319 | 0.970 | 0.1318 | 0.973 | 0.1333 | 0.974 | 0.1308 | 0.973 | 0.1329 | 0.972 | 0.1284 | 0.974 | 0.1237 | 0.974 |

## 7. Problematic Constraints and Difficulties

- Computational Overhead: Because of the increased complexity of the optimization process, the locally weighted technique and the mutation strategy could result in the introduction of additional computing overhead. This could result in a greater amount of processing time compared to some of the simpler forms of the Salp Swarm Algorithm, depending on the size of the problem and the number of iterations.
- Parameter Tuning: The success of the strategy that has been suggested is strongly dependent on the accurate tuning of parameters linked to the locally weighted strategy and the mutation scheme. Finding the ideal values for the parameters may need additional work and trial and error, particularly when dealing with a variety of distinct optimization situations.
- Sensitivity to Problem Characteristics: In the same way that the performance of any algorithm can be affected by the specifics of the optimization problems it is applied to, the performance of the suggested approach could be susceptible to those features. It is very useful in some circumstances, but its usefulness may vary depending on the nature of the problem and the structure it has.
- Comparative Performance: Comprehensive comparative studies are required so that an in-depth evaluation may be carried out to determine whether or not the proposed method is preferable to the various other Salp Swarm versions. This requires testing the algorithm on a wide variety of benchmark issues and contrasting its results with those of previously developed variants of the Salp Swarm Algorithm as well as other cutting-edge optimization strategies.

## 8. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Comparison of the LWSSA with Some Improved SSA Algorithms during 2500 Iterations (cec2021)

$\mathbf{F}$ | $\mathbf{Criteria}$ | $\mathbf{ESSA}$ | $\mathbf{HSSASCA}$ | $\mathbf{ISSA}$ | $\mathbf{\text{ISSA\_OBL}}$ | $\mathbf{SSALEO}$ | $\mathbf{\text{SSA-FGWO}}$ | $\mathbf{TVSSA}$ | $\mathbf{LWSSA}$ |

F1 | Avg | $1.498\times {10}^{3}$ | $2.274\times {10}^{10}$ | $3.879\times {10}^{3}$ | $9.531\times {10}^{2}$ | $2.966\times {10}^{3}$ | $4.288\times {10}^{3}$ | $4.774\times {10}^{3}$ | $\mathbf{1.000}\mathbf{\times}{\mathbf{10}}^{\mathbf{2}}$ |

Std | $1.885\times {10}^{7}$ | $6.973\times {10}^{9}$ | $3.712\times {10}^{3}$ | $1.276\times {10}^{3}$ | $2.158\times {10}^{3}$ | $3.153\times {10}^{3}$ | $3.518\times {10}^{3}$ | $\mathbf{0.000}$ | |

Med | $9.198\times {10}^{6}$ | $2.155\times {10}^{10}$ | $2.463\times {10}^{3}$ | $1.363\times {10}^{2}$ | $2.712\times {10}^{3}$ | $3.429\times {10}^{3}$ | $3.776\times {10}^{3}$ | $\mathbf{1.000}\times {10}^{2}$ | |

F2 | Avg | $7.151\times {10}^{8}$ | $1.781\times {10}^{12}$ | $4.128\times {10}^{5}$ | $3.056\times {10}^{5}$ | $4.184\times {10}^{5}$ | $5.496\times {10}^{5}$ | $2.925\times {10}^{5}$ | $\mathbf{1.100}\times {10}^{3}$ |

Std | $4.993\times {10}^{8}$ | $5.894\times {10}^{11}$ | $4.681\times {10}^{5}$ | $3.103\times {10}^{5}$ | $4.099\times {10}^{5}$ | $6.695\times {10}^{5}$ | $3.603\times {10}^{5}$ | $\mathbf{0.000}$ | |

Med | $6.395\times {10}^{8}$ | $1.816\times {10}^{12}$ | $1.922\times {10}^{5}$ | $2.053\times {10}^{5}$ | $2.847\times {10}^{5}$ | $1.909\times {10}^{5}$ | 1.345$\times {10}^{5}$ | 1.100$\times {10}^{3}$ | |

F3 | Avg | $3.502\times {10}^{8}$ | $4.753\times {10}^{11}$ | $2.295\times {10}^{5}$ | $1.188\times {10}^{5}$ | $1.949\times {10}^{5}$ | 2.151$\times {10}^{5}$ | 1.692$\times {10}^{5}$ | 7.002$\times {10}^{2}$ |

Std | $3.633\times {10}^{8}$ | 1.499$\times {10}^{11}$ | 2.206$\times {10}^{5}$ | 9.574$\times {10}^{4}$ | 1.844$\times {10}^{5}$ | 2.304$\times {10}^{5}$ | 2.379$\times {10}^{5}$ | 6.716$\times {10}^{2}$ | |

Med | 2.647$\times {10}^{8}$ | 4.791$\times {10}^{11}$ | 1.418$\times {10}^{5}$ | 8.691$\times {10}^{4}$ | 1.444$\times {10}^{5}$ | 1.104$\times {10}^{5}$ | 6.491$\times {10}^{4}$ | 7.002$\times {10}^{2}$ | |

F4 | Avg | 1.909$\times {10}^{3}$ | 1.233$\times {10}^{5}$ | 1.904$\times {10}^{3}$ | 1.912$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ |

Std | 4.635 | 1.719$\times {10}^{5}$ | 1.296 | 3.376 | 1.308 | 1.516 | 1.254 | $1.329$ | |

Med | 1.907$\times {10}^{3}$ | 3.900$\times {10}^{4}$ | 1.904$\times {10}^{3}$ | 1.911$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | |

F5 | Avg | 4.169$\times {10}^{5}$ | 5.002$\times {10}^{6}$ | 1.640$\times {10}^{5}$ | 9.883$\times {10}^{4}$ | 1.062$\times {10}^{5}$ | 1.350$\times {10}^{5}$ | 1.548$\times {10}^{5}$ | 2.555$\times {10}^{3}$ |

Std | 4.740$\times {10}^{5}$ | 5.063$\times {10}^{6}$ | 9.887$\times {10}^{4}$ | 7.492$\times {10}^{4}$ | 6.638$\times {10}^{4}$ | 9.461$\times {10}^{4}$ | 8.765$\times {10}^{4}$ | 5.437$\times {10}^{2}$ | |

Med | 3.010$\times {10}^{5}$ | 3.666$\times {10}^{6}$ | 1.507$\times {10}^{5}$ | 7.715$\times {10}^{4}$ | 9.471$\times {10}^{4}$ | 1.042$\times {10}^{5}$ | 1.379$\times {10}^{5}$ | 2.456$\times {10}^{3}$ | |

F6 | Avg | 1.346$\times {10}^{4}$ | 1.287$\times {10}^{7}$ | 2.017$\times {10}^{4}$ | 1.208$\times {10}^{4}$ | 1.060$\times {10}^{4}$ | 1.741$\times {10}^{4}$ | 2.514$\times {10}^{4}$ | 1.686$\times {10}^{3}$ |

Std | 9.198$\times {10}^{3}$ | 2.874$\times {10}^{7}$ | 1.716$\times {10}^{4}$ | 5.195$\times {10}^{3}$ | 7.099$\times {10}^{3}$ | 1.343$\times {10}^{4}$ | 1.530$\times {10}^{4}$ | 1.576$\times {10}^{2}$ | |

Med | 1.032$\times {10}^{4}$ | 8.938$\times {10}^{4}$ | 1.546$\times {10}^{4}$ | 1.013$\times {10}^{4}$ | 8.698$\times {10}^{3}$ | 1.365$\times {10}^{4}$ | 2.420$\times {10}^{4}$ | 1.606$\times {10}^{3}$ | |

F7 | Avg | 9.040$\times {10}^{5}$ | 3.593$\times {10}^{7}$ | 2.653$\times {10}^{5}$ | 1.688$\times {10}^{6}$ | 1.561$\times {10}^{5}$ | 4.767$\times {10}^{5}$ | 3.723$\times {10}^{5}$ | 2.796$\times {10}^{3}$ |

Std | 9.564$\times {10}^{5}$ | 6.567$\times {10}^{7}$ | 1.418$\times {10}^{5}$ | 6.874$\times {10}^{5}$ | 6.675$\times {10}^{4}$ | 4.554$\times {10}^{5}$ | 3.031$\times {10}^{5}$ | 3.971$\times {10}^{2}$ | |

Med | 5.997$\times {10}^{5}$ | 1.035$\times {10}^{7}$ | 2.114$\times {10}^{5}$ | 1.717$\times {10}^{6}$ | 1.435$\times {10}^{5}$ | 3.859$\times {10}^{5}$ | 2.905$\times {10}^{5}$ | 2.712$\times {10}^{3}$ | |

F8 | Avg | 2.326$\times {10}^{3}$ | 2.717$\times {10}^{3}$ | 2.315$\times {10}^{3}$ | 2.333$\times {10}^{3}$ | 2.337$\times {10}^{3}$ | 2.313$\times {10}^{3}$ | 2.315$\times {10}^{3}$ | 2.321$\times {10}^{3}$ |

Std | 4.287 | 6.736$\times {10}^{2}$ | 1.636$\times {10}^{1}$ | 1.752$\times {10}^{1}$ | 1.540$\times {10}^{1}$ | 1.653$\times {10}^{1}$ | 1.705$\times {10}^{1}$ | 1.423$\times {10}^{1}$ | |

Med | 2.326$\times {10}^{3}$ | 2.576$\times {10}^{3}$ | 2.303$\times {10}^{3}$ | 2.338$\times {10}^{3}$ | 2.338$\times {10}^{3}$ | 2.300$\times {10}^{3}$ | 2.303$\times {10}^{3}$ | 2.328$\times {10}^{3}$ | |

F9 | Avg | 2.944$\times {10}^{3}$ | 1.631$\times {10}^{4}$ | 2.606$\times {10}^{3}$ | 2.662$\times {10}^{3}$ | 2.621$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.622$\times {10}^{3}$ | 2.567$\times {10}^{3}$ |

Std | 1.498$\times {10}^{2}$ | 3.795$\times {10}^{3}$ | 3.427$\times {10}^{1}$ | 1.276$\times {10}^{2}$ | 5.598$\times {10}^{1}$ | 4.968$\times {10}^{4}$ | 6.926$\times {10}^{1}$ | 4.795$\times {10}^{1}$ | |

Med | 2.948$\times {10}^{3}$ | 1.678$\times {10}^{4}$ | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | |

F10 | Avg | 3.265$\times {10}^{3}$ | 6.061$\times {10}^{3}$ | 3.162$\times {10}^{3}$ | 3.307$\times {10}^{3}$ | 3.215$\times {10}^{3}$ | 3.170$\times {10}^{3}$ | 3.156$\times {10}^{3}$ | 3.132$\times {10}^{3}$ |

Std | 8.030$\times {10}^{1}$ | 1.312$\times {10}^{3}$ | 3.603$\times {10}^{1}$ | 1.440$\times {10}^{2}$ | 7.049$\times {10}^{1}$ | 4.920$\times {10}^{1}$ | 3.858$\times {10}^{1}$ | 1.452$\times {10}^{1}$ | |

Med | 3.258$\times {10}^{3}$ | 5.942$\times {10}^{3}$ | 3.157$\times {10}^{3}$ | 3.273$\times {10}^{3}$ | 3.221$\times {10}^{3}$ | 3.158$\times {10}^{3}$ | 3.142$\times {10}^{3}$ | 3.123$\times {10}^{3}$ | |

$\mathbf{F}\mathbf{r}\mathbf{i}\mathbf{e}\mathbf{d}\mathbf{m}\mathbf{a}\mathbf{n}\mathbf{A}\mathbf{v}\mathbf{g}.$ | 5.879 | 7.938 | 3.886 | 4.886 | 3.779 | 3.983 | 3.852 | 1.797 | |

$\mathbf{F}\mathbf{r}\mathbf{i}\mathbf{e}\mathbf{d}\mathbf{m}\mathbf{a}\mathbf{n}\mathbf{R}\mathbf{a}\mathbf{n}\mathbf{k}$ | 7.000 | 8.000 | 4.000 | 6.000 | 2.000 | 5.000 | 3.000 | 1.000 | |

Bold denotes to the best results. |

#### Appendix A.2. Wilcoxon Rank-Sum of the LWSSA vs. Some Improved SSA Algorithms on CEC2021

Fun | $\mathbf{ESSA}$ | $\mathbf{HSSASCA}$ | $\mathbf{ISSA}$ | $\mathbf{\text{ISSA\_OBL}}$ | $\mathbf{SSALEO}$ | $\mathbf{\text{SSA-FGWO}}$ | $\mathbf{TVSSA}$ |

1 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

2 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

3 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

4 | <0.05 | <0.05 | <0.05 | <0.05 | 0.15475248 | 0.61326587 | 0.3629539 |

5 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

6 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

7 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

8 | 0.91948423 | <0.05 | 0.22811625 | <0.05 | <0.05 | 0.05478402 | 0.23417446 |

9 | <0.05 | <0.05 | 0.74987697 | <0.05 | 0.52880743 | 0.83371254 | 0.63527561 |

10 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

#### Appendix A.3. Comparison between LWSSA and Some State-of-the-Art Algorithms during 2500 Iterations (cec2021)

$\mathbf{F}$ | $\mathbf{Criteria}$ | GBO | EGBO | SMA | PSO | EO | SADE | CLPSO | HPSO_TVAC | LWSSA |

F1 | Avg | 9.217$\times {10}^{2}$ | 1.499$\times {10}^{2}$ | 7.679$\times {10}^{3}$ | 2.137$\times {10}^{3}$ | 4.280$\times {10}^{7}$ | 1.000$\times {10}^{2}$ | 6.292$\times {10}^{6}$ | 1.754$\times {10}^{4}$ | 1.000$\times {10}^{2}$ |

Std | 1.415$\times {10}^{3}$ | 2.704$\times {10}^{2}$ | 3.384$\times {10}^{3}$ | 2.187$\times {10}^{3}$ | 1.346$\times {10}^{8}$ | 0.000 | 2.358$\times {10}^{7}$ | 6.309$\times {10}^{4}$ | 4.336$\times {10}^{14}$ | |

Med | 4.134$\times {10}^{2}$ | 1.000$\times {10}^{2}$ | 8.933$\times {10}^{3}$ | 1.453$\times {10}^{3}$ | 4.233$\times {10}^{3}$ | 1.000$\times {10}^{2}$ | 7.389$\times {10}^{4}$ | 2.327$\times {10}^{3}$ | 1.000$\times {10}^{2}$ | |

F2 | Avg | 1.122$\times {10}^{3}$ | 1.398$\times {10}^{9}$ | 9.045$\times {10}^{5}$ | 2.590$\times {10}^{5}$ | 6.700$\times {10}^{9}$ | 1.100$\times {10}^{3}$ | 2.040$\times {10}^{8}$ | 1.575$\times {10}^{8}$ | 1.100$\times {10}^{3}$ |

Std | 6.650$\times {10}^{1}$ | 7.657$\times {10}^{9}$ | 7.804$\times {10}^{5}$ | 3.880$\times {10}^{5}$ | 1.369$\times {10}^{10}$ | 0.000 | 5.861$\times {10}^{8}$ | 8.617$\times {10}^{8}$ | 6.938$\times {10}^{13}$ | |

Med | 1.101$\times {10}^{3}$ | 1.100$\times {10}^{3}$ | 6.705$\times {10}^{5}$ | 1.351$\times {10}^{5}$ | 2.509$\times {10}^{6}$ | 1.100$\times {10}^{3}$ | 9.251$\times {10}^{5}$ | 1.646$\times {10}^{4}$ | 1.100$\times {10}^{3}$ | |

F3 | Avg | 1.183$\times {10}^{5}$ | 1.183$\times {10}^{5}$ | 9.370$\times {10}^{3}$ | 2.991$\times {10}^{4}$ | 1.897$\times {10}^{9}$ | 7.000$\times {10}^{2}$ | 1.753$\times {10}^{8}$ | 1.554$\times {10}^{3}$ | 7.000$\times {10}^{2}$ |

Std | 6.442$\times {10}^{5}$ | 6.442$\times {10}^{5}$ | 1.662$\times {10}^{4}$ | 1.418$\times {10}^{5}$ | 2.781$\times {10}^{9}$ | 0.000 | 3.641$\times {10}^{8}$ | 3.196$\times {10}^{3}$ | 9.569$\times {10}^{2}$ | |

Med | 7.000$\times {10}^{2}$ | 7.000$\times {10}^{2}$ | 1.305$\times {10}^{3}$ | 7.000$\times {10}^{2}$ | 5.883$\times {10}^{7}$ | 7.000$\times {10}^{2}$ | 7.717$\times {10}^{6}$ | 7.000$\times {10}^{2}$ | 7.002$\times {10}^{2}$ | |

F4 | Avg | 1.907$\times {10}^{3}$ | 1.908$\times {10}^{3}$ | 1.905$\times {10}^{3}$ | 1.905$\times {10}^{3}$ | 1.907$\times {10}^{3}$ | 1.905$\times {10}^{3}$ | 1.913$\times {10}^{3}$ | 1.926$\times {10}^{3}$ | 1.904$\times {10}^{3}$ |

Std | 3.669 | 5.142 | 1.525 | 1.161 | 1.179$\times {10}^{1}$ | 7.251$\times {10}^{1}$ | 3.100$\times {10}^{1}$ | 1.612$\times {10}^{1}$ | 1.042 | |

Med | 1.906$\times {10}^{3}$ | 1.907$\times {10}^{3}$ | 1.903$\times {10}^{3}$ | 1.903$\times {10}^{3}$ | 1.903$\times {10}^{3}$ | 1.905$\times {10}^{3}$ | 1.906$\times {10}^{3}$ | 1.922$\times {10}^{3}$ | 1.904$\times {10}^{3}$ | |

F5 | Avg | 1.946$\times {10}^{4}$ | 1.280$\times {10}^{4}$ | 1.073$\times {10}^{5}$ | 5.173$\times {10}^{4}$ | 8.561$\times {10}^{4}$ | 5.156$\times {10}^{4}$ | 5.718$\times {10}^{4}$ | 5.280$\times {10}^{4}$ | 2.638$\times {10}^{3}$ |

Std | 1.119$\times {10}^{4}$ | 1.259$\times {10}^{4}$ | 4.806$\times {10}^{4}$ | 2.961$\times {10}^{4}$ | 4.972$\times {10}^{4}$ | 2.661$\times {10}^{4}$ | 2.007$\times {10}^{4}$ | 2.411$\times {10}^{4}$ | 6.982$\times {10}^{2}$ | |

Med | 1.944$\times {10}^{4}$ | 7.881$\times {10}^{3}$ | 1.053$\times {10}^{5}$ | 4.306$\times {10}^{4}$ | 6.680$\times {10}^{4}$ | 4.570$\times {10}^{4}$ | 5.562$\times {10}^{4}$ | 4.808$\times {10}^{4}$ | 2.548$\times {10}^{3}$ | |

F6 | Avg | 2.115$\times {10}^{3}$ | 3.107$\times {10}^{3}$ | 2.309$\times {10}^{3}$ | 1.788$\times {10}^{3}$ | 6.070$\times {10}^{3}$ | 1.672$\times {10}^{3}$ | 2.920$\times {10}^{3}$ | 2.163$\times {10}^{3}$ | 1.634$\times {10}^{3}$ |

Std | 5.474$\times {10}^{2}$ | 3.569$\times {10}^{3}$ | 8.531$\times {10}^{2}$ | 2.248$\times {10}^{2}$ | 2.584$\times {10}^{3}$ | 1.763$\times {10}^{2}$ | 1.306$\times {10}^{3}$ | 7.765$\times {10}^{2}$ | 9.759$\times {10}^{1}$ | |

Med | 2.013$\times {10}^{3}$ | 2.341$\times {10}^{3}$ | 2.006$\times {10}^{3}$ | 1.677$\times {10}^{3}$ | 5.359$\times {10}^{3}$ | 1.604$\times {10}^{3}$ | 2.649$\times {10}^{3}$ | 2.000$\times {10}^{3}$ | 1.604$\times {10}^{3}$ | |

F7 | Avg | 7.997$\times {10}^{3}$ | 4.270$\times {10}^{4}$ | 5.924$\times {10}^{4}$ | 1.203$\times {10}^{4}$ | 2.166$\times {10}^{5}$ | 2.068$\times {10}^{4}$ | 1.580$\times {10}^{5}$ | 1.678$\times {10}^{4}$ | 2.838$\times {10}^{3}$ |

Std | 5.292$\times {10}^{3}$ | 9.986$\times {10}^{4}$ | 2.737$\times {10}^{4}$ | 6.035$\times {10}^{3}$ | 6.129$\times {10}^{5}$ | 1.239$\times {10}^{4}$ | 7.703$\times {10}^{5}$ | 8.566$\times {10}^{3}$ | 7.969$\times {10}^{2}$ | |

Med | 7.122$\times {10}^{3}$ | 8.697$\times {10}^{3}$ | 5.601$\times {10}^{4}$ | 1.063$\times {10}^{4}$ | 6.654$\times {10}^{4}$ | 1.719$\times {10}^{4}$ | 1.648$\times {10}^{4}$ | 1.326$\times {10}^{4}$ | 2.611$\times {10}^{3}$ | |

F8 | Avg | 2.332$\times {10}^{3}$ | 2.337$\times {10}^{3}$ | 2.303$\times {10}^{3}$ | 2.362$\times {10}^{3}$ | 2.320$\times {10}^{3}$ | 2.318$\times {10}^{3}$ | 2.328$\times {10}^{3}$ | 2.339$\times {10}^{3}$ | 2.319$\times {10}^{3}$ |

Std | 8.092 | 4.241 | 6.499$\times {10}^{3}$ | 5.505$\times {10}^{1}$ | 1.135$\times {10}^{1}$ | 1.442$\times {10}^{1}$ | 2.165 | 8.417 | 1.403$\times {10}^{1}$ | |

Med | 2.334$\times {10}^{3}$ | 2.336$\times {10}^{3}$ | 2.300$\times {10}^{3}$ | 2.342$\times {10}^{3}$ | 2.324$\times {10}^{3}$ | 2.328$\times {10}^{3}$ | 2.328$\times {10}^{3}$ | 2.338$\times {10}^{3}$ | 2.327$\times {10}^{3}$ | |

F9 | Avg | 2.642$\times {10}^{3}$ | 2.622$\times {10}^{3}$ | 2.614$\times {10}^{3}$ | 2.715$\times {10}^{3}$ | 3.014$\times {10}^{3}$ | 2.605$\times {10}^{3}$ | 2.739$\times {10}^{3}$ | 2.647$\times {10}^{3}$ | 2.530$\times {10}^{3}$ |

Std | 1.117$\times {10}^{2}$ | 8.419$\times {10}^{1}$ | 4.880$\times {10}^{1}$ | 3.634$\times {10}^{2}$ | 5.436$\times {10}^{2}$ | 3.009$\times {10}^{1}$ | 3.289$\times {10}^{2}$ | 1.382$\times {10}^{2}$ | 4.661$\times {10}^{1}$ | |

Med | 2.600$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.601$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.738$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.602$\times {10}^{3}$ | 2.600$\times {10}^{3}$ | 2.500$\times {10}^{3}$ | |

F10 | Avg | 3.216$\times {10}^{3}$ | 3.208$\times {10}^{3}$ | 3.160$\times {10}^{3}$ | 3.278$\times {10}^{3}$ | 3.035$\times {10}^{3}$ | 3.164$\times {10}^{3}$ | 3.423$\times {10}^{3}$ | 3.298$\times {10}^{3}$ | 3.132$\times {10}^{3}$ |

Std | 6.647$\times {10}^{1}$ | 8.238$\times {10}^{1}$ | 4.418$\times {10}^{1}$ | 1.597$\times {10}^{2}$ | 7.140$\times {10}^{1}$ | 4.642$\times {10}^{1}$ | 9.664$\times {10}^{1}$ | 1.214$\times {10}^{2}$ | 1.581$\times {10}^{1}$ | |

Med | 3.213$\times {10}^{3}$ | 3.183$\times {10}^{3}$ | 3.149$\times {10}^{3}$ | 3.232$\times {10}^{3}$ | 3.017$\times {10}^{3}$ | 3.158$\times {10}^{3}$ | 3.443$\times {10}^{3}$ | 3.281$\times {10}^{3}$ | 3.123$\times {10}^{3}$ | |

$\mathbf{F}\mathbf{r}\mathbf{i}\mathbf{e}\mathbf{d}\mathbf{m}\mathbf{a}\mathbf{n}\mathbf{A}\mathbf{v}\mathbf{g}.$ | 4.690 | 4.366 | 5.845 | 4.988 | 6.541 | 3.359 | 6.807 | 6.162 | 2.243 | |

$\mathbf{F}\mathbf{r}\mathbf{i}\mathbf{e}\mathbf{d}\mathbf{m}\mathbf{a}\mathbf{n}\mathbf{R}\mathbf{a}\mathbf{n}\mathbf{k}$ | 4.000 | 3.000 | 6.000 | 5.000 | 8.000 | 2.000 | 9.000 | 7.000 | 1.000 | |

Bold denotes to the best results. |

#### Appendix A.4. Wilcoxon Rank-Sum of the LWSSA vs. Some State-of-the-Art Algorithms during 2500 Iterations

Fun | GBO | EGBO | SMA | PSO | EO | SADE | CLPSO | HPSO_TVAC |

1 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | 1 | <0.05 | <0.05 |

2 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | 1 | <0.05 | <0.05 |

3 | <0.05 | 0.821595 | <0.05 | 0.651998 | <0.05 | 1 | <0.05 | <0.05 |

4 | <0.05 | <0.05 | 0.266174 | <0.05 | 0.5809 | <0.05 | <0.05 | <0.05 |

5 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

6 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | 0.240346 | <0.05 | <0.05 |

7 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

8 | <0.05 | <0.05 | <0.05 | <0.05 | 0.931838 | 0.432254 | 0.301061 | <0.05 |

9 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

10 | <0.05 | <0.05 | 0.228116 | <0.05 | <0.05 | <0.05 | <0.05 | <0.05 |

#### Appendix A.5. Results from 2500 Iterations of the LWSSA vs. Some Salp Variants on IEEE CEC2017

F | Cr. | ESSA | HSSASCA | ISSA_OBL | ISSA | SSALEO | TVSSA | QSSALEO | LWSSA |

F1 | Avg | $9.03656\times {10}^{9}$ | $9.16426\times {10}^{11}$ | $2.01231\times {10}^{9}$ | $9.98052\times {10}^{3}$ | $3.30750\times {10}^{3}$ | $9.55185\times {10}^{3}$ | $4.01170\times {10}^{3}$ | $\mathbf{3.01336}\times {10}^{3}$ |

Std | $4.11154\times {10}^{9}$ | $1.12483\times {10}^{11}$ | $1.65616\times {10}^{9}$ | $9.68170\times {10}^{3}$ | $3.75111\times {10}^{3}$ | $7.32136\times {10}^{3}$ | $4.38525\times {10}^{3}$ | $3.63301\times {10}^{3}$ | |

Med | $7.67018\times {10}^{9}$ | $9.16077\times {10}^{11}$ | $1.53825\times {10}^{9}$ | $7.00016\times {10}^{3}$ | $2.58166\times {10}^{3}$ | $8.98747\times {10}^{3}$ | $2.79712\times {10}^{3}$ | $1.76476\times {10}^{3}$ | |

F2 | Avg | $1.41786\times {10}^{5}$ | $3.44395\times {10}^{5}$ | $7.17507\times {10}^{4}$ | $8.99510\times {10}^{4}$ | $2.50918\times {10}^{3}$ | $1.25908\times {10}^{5}$ | $1.58827\times {10}^{4}$ | $\mathbf{9.50716}\times {10}^{3}$ |

Std | $1.47078\times {10}^{4}$ | $8.52222\times {10}^{4}$ | $1.25022\times {10}^{4}$ | $1.82673\times {10}^{4}$ | $9.17320\times {10}^{2}$ | $4.60251\times {10}^{4}$ | $4.99559\times {10}^{3}$ | $3.35783\times {10}^{3}$ | |

Med | $1.40149\times {10}^{5}$ | $3.29620\times {10}^{5}$ | $7.08563\times {10}^{4}$ | $8.69489\times {10}^{4}$ | $2.41802\times {10}^{3}$ | $1.15600\times {10}^{5}$ | $1.47988\times {10}^{4}$ | $8.47643\times {10}^{3}$ | |

AF3 | Avg | $8.10472\times {10}^{2}$ | $1.93663\times {10}^{4}$ | $7.54794\times {10}^{2}$ | $5.65904\times {10}^{2}$ | $5.64657\times {10}^{2}$ | $5.82398\times {10}^{2}$ | $5.68846\times {10}^{2}$ | $\mathbf{5.60686}\times {10}^{3}$ |

Std | $8.32235\times {10}^{1}$ | $4.56035\times {10}^{3}$ | $7.79068\times {10}^{1}$ | $4.55730\times {10}^{1}$ | $5.50436\times {10}^{1}$ | $4.18799\times {10}^{1}$ | $4.55508\times {10}^{1}$ | $4.69864\times {10}^{1}$ | |

Med | $8.24397\times {10}^{2}$ | $1.87923\times {10}^{4}$ | $7.44610\times {10}^{2}$ | $5.64272\times {10}^{2}$ | $5.79414\times {10}^{2}$ | $5.87143\times {10}^{2}$ | $5.66641\times {10}^{2}$ | $5.57586\times {10}^{2}$ | |

F4 | Avg | $8.09324\times {10}^{2}$ | $1.13284\times {10}^{3}$ | $8.43132\times {10}^{2}$ | $\mathbf{7.99437}\times {10}^{2}$ | $8.24122\times {10}^{2}$ | $8.28960\times {10}^{2}$ | $8.51549\times {10}^{2}$ | $9.01785\times {10}^{2}$ |

Std | $2.79974\times {10}^{1}$ | $4.00484\times {10}^{1}$ | $4.25395\times {10}^{1}$ | $5.50168\times {10}^{1}$ | $4.39905\times {10}^{1}$ | $7.42270\times {10}^{1}$ | $2.36665\times {10}^{1}$ | $7.52235\times {10}^{1}$ | |

Med | $8.09432\times {10}^{2}$ | $1.14156\times {10}^{3}$ | $8.48338\times {10}^{2}$ | $8.07937\times {10}^{2}$ | $8.23360\times {10}^{2}$ | $8.03083\times {10}^{2}$ | $8.47238\times {10}^{2}$ | $9.06014\times {10}^{2}$ | |

F5 | Avg | $6.81917\times {10}^{2}$ | $7.24503\times {10}^{2}$ | $6.91499\times {10}^{2}$ | $6.63502\times {10}^{2}$ | $6.66724\times {10}^{2}$ | $\mathbf{6.65778}\times {10}^{2}$ | $6.74832\times {10}^{2}$ | $6.82869\times {10}^{2}$ |

Std | $1.02701\times {10}^{1}$ | $1.50459\times {10}^{1}$ | 7.28669 | $1.73109\times {10}^{1}$ | $1.14701\times {10}^{1}$ | $1.68224\times {10}^{1}$ | $1.26545\times {10}^{1}$ | $1.69733\times {10}^{1}$ | |

Med | $6.83101\times {10}^{2}$ | $7.22801\times {10}^{2}$ | $6.92164\times {10}^{2}$ | $6.64658\times {10}^{2}$ | $6.66304\times {10}^{2}$ | $6.64545\times {10}^{2}$ | $6.77293\times {10}^{2}$ | $6.85125\times {10}^{2}$ | |

F6 | Avg | $1.18583\times {10}^{3}$ | $1.95674\times {10}^{3}$ | $1.64099\times {10}^{3}$ | $1.09615\times {10}^{3}$ | $1.09556\times {10}^{3}$ | $1.11161\times {10}^{3}$ | $1.34477\times {10}^{3}$ | $\mathbf{1.10426}\times {10}^{3}$ |

Std | $6.58112\times {10}^{1}$ | $9.37910\times {10}^{1}$ | $1.55676\times {10}^{2}$ | $9.76494\times {10}^{1}$ | $7.48194\times {10}^{1}$ | $8.18462\times {10}^{1}$ | $1.26781\times {10}^{2}$ | $8.60101\times {10}^{1}$ | |

Med | $1.18845\times {10}^{3}$ | $1.96788\times {10}^{3}$ | $1.62038\times {10}^{3}$ | $1.08841\times {10}^{3}$ | $1.08852\times {10}^{3}$ | $1.11536\times {10}^{3}$ | $1.36312\mathrm{E}\times {10}^{3}$ | $1.09649\times {10}^{3}$ | |

F7 | Avg | $1.14113\times {10}^{3}$ | $1.43990\times {10}^{3}$ | $1.16850\times {10}^{3}$ | $1.17294\times {10}^{3}$ | $1.14861\times {10}^{3}$ | $\mathbf{1.10273}\times {10}^{3}$ | $1.16127\times {10}^{3}$ | $1.17958\times {10}^{3}$ |

Std | $4.33617\times {10}^{1}$ | $5.39006\times {10}^{1}$ | $3.59235\times {10}^{1}$ | $9.96923\times {10}^{1}$ | $4.24728\times {10}^{1}$ | $7.05031\times {10}^{1}$ | $4.27204\times {10}^{1}$ | $6.77353\times {10}^{1}$ | |

Med | $1.14793\times {10}^{3}$ | $1.43532\times {10}^{3}$ | $1.16384\times {10}^{3}$ | $1.15129\times {10}^{3}$ | $1.14807\times {10}^{3}$ | $1.09852\times {10}^{3}$ | $1.17641\times {10}^{3}$ | $1.17238\times {10}^{3}$ | |

F8 | Avg | $1.46443\times {10}^{4}$ | $3.74321\times {10}^{4}$ | $1.38950\times {10}^{4}$ | $1.14001\times {10}^{4}$ | $\mathbf{7.47256}\times {10}^{3}$ | $1.42571\times {10}^{4}$ | $1.09280\times {10}^{4}$ | $1.39525\times {10}^{4}$ |

Std | $2.36454\times {10}^{3}$ | $5.76418\times {10}^{3}$ | $1.84673\mathrm{E}\times {10}^{3}$ | $2.51992\times {10}^{3}$ | $2.72882\times {10}^{3}$ | $4.19994\times {10}^{3}$ | $1.80218\times {10}^{3}$ | $3.92527\times {10}^{3}$ | |

Med | $1.49006\times {10}^{4}$ | $3.67857\times {10}^{4}$ | $1.33979\times {10}^{4}$ | $1.22345\times {10}^{4}$ | $6.67854\times {10}^{3}$ | $1.44039\times {10}^{4}$ | $1.10557\times {10}^{4}$ | $1.35127\times {10}^{4}$ | |

F9 | Avg | $7.87305\times {10}^{3}$ | $1.52464\times {10}^{4}$ | $8.85248\times {10}^{3}$ | $7.84373\times {10}^{3}$ | $7.93135\times {10}^{3}$ | $8.02314\times {10}^{3}$ | $8.47217\times {10}^{3}$ | $\mathbf{7.29078}\times {10}^{3}$ |

Std | $7.23499\times {10}^{2}$ | $7.10918\times {10}^{2}$ | $1.06756\times {10}^{3}$ | $9.64341\times {10}^{2}$ | $9.57611\times {10}^{2}$ | $8.76859\times {10}^{2}$ | $9.78798\times {10}^{2}$ | $7.31876\times {10}^{2}$ | |

Med | $7.85331\times {10}^{3}$ | $1.53959\times {10}^{4}$ | $8.78094\times {10}^{3}$ | $7.66902\times {10}^{3}$ | $7.66004\times {10}^{3}$ | $8.23477\times {10}^{3}$ | $8.27706\times {10}^{3}$ | $7.33032\times {10}^{3}$ | |

F10 | Avg | $3.54871\times {10}^{3}$ | $1.62130\times {10}^{4}$ | $1.92676\times {10}^{3}$ | $1.50495\times {10}^{3}$ | $1.37232\times {10}^{3}$ | $1.46749\times {10}^{3}$ | $1.37368\times {10}^{3}$ | $\mathbf{1.32727}\times {10}^{3}$ |

Std | $1.65052\times {10}^{3}$ | $4.04847\times {10}^{3}$ | $2.29106\times {10}^{2}$ | $9.84397\times {10}^{1}$ | $7.03959\times {10}^{1}$ | $8.61959\times {10}^{1}$ | $7.15218\times {10}^{1}$ | $6.92137\times {10}^{1}$ | |

Med | $3.23887\times {10}^{3}$ | $1.57903\times {10}^{4}$ | $1.89588\times {10}^{3}$ | $1.50591\times {10}^{3}$ | $1.36892\times {10}^{3}$ | $1.45323\times {10}^{3}$ | $1.38586\times {10}^{3}$ | $1.32272\times {10}^{3}$ | |

F11 | Avg | $5.09616\times {10}^{8}$ | $4.18049\times {10}^{11}$ | $9.16145\times {10}^{8}$ | $5.41120\times {10}^{8}$ | $2.17013\times {10}^{8}$ | $6.09851\times {10}^{8}$ | $2.38139\times {10}^{8}$ | $\mathbf{1.73582}\times {10}^{6}$ |

Std | $2.70692\times {10}^{8}$ | $1.38807\times {10}^{11}$ | $4.53783\times {10}^{8}$ | $3.49198\times {10}^{8}$ | $1.31139\times {10}^{8}$ | $4.96511\times {10}^{8}$ | $1.53479\times {10}^{8}$ | $1.04780\times {10}^{6}$ | |

Med | $4.32410\times {10}^{8}$ | $4.17268\times {10}^{11}$ | $7.97665\times {10}^{8}$ | $4.77970\times {10}^{8}$ | $2.12643\times {10}^{8}$ | $4.97356\times {10}^{8}$ | $2.48229\times {10}^{8}$ | $1.68378\times {10}^{6}$ | |

F12 | Avg | $1.68125\times {10}^{8}$ | $2.19159\times {10}^{11}$ | $3.01884\times {10}^{4}$ | $2.03851\times {10}^{5}$ | $1.16566\times {10}^{5}$ | $2.16897\times {10}^{5}$ | $1.28671\times {10}^{5}$ | $\mathbf{1.07429}\times {10}^{4}$ |

Std | $2.24354\times {10}^{8}$ | $9.03048\times {10}^{10}$ | $1.12142\times {10}^{4}$ | $1.20097\times {10}^{5}$ | $6.37039\times {10}^{4}$ | $1.33391\times {10}^{5}$ | $9.49496\times {10}^{4}$ | $2.51347\times {10}^{3}$ | |

Med | $9.75892\times {10}^{7}$ | $2.10153\times {10}^{11}$ | $2.76593\times {10}^{4}$ | $1.64624\times {10}^{5}$ | $1.03117\times {10}^{5}$ | $1.95169\times {10}^{5}$ | $1.00876\times {10}^{5}$ | $1.01773\times {10}^{4}$ | |

F13 | Avg | $7.93422\times {10}^{6}$ | $8.91424\times {10}^{6}$ | $4.05799\times {10}^{5}$ | $2.24767\times {10}^{5}$ | $1.17258\times {10}^{5}$ | $1.94325\times {10}^{5}$ | $1.23123\times {10}^{5}$ | $\mathbf{1.73686}\times {10}^{3}$ |

Std | $7.12085\times {10}^{6}$ | $9.74291\times {10}^{6}$ | $2.80680\times {10}^{5}$ | $1.58367\times {10}^{5}$ | $8.70056\times {10}^{4}$ | $1.03172\times {10}^{5}$ | $9.41972\times {10}^{4}$ | $6.09089\times {10}^{1}$ | |

Med | $5.16878\times {10}^{6}$ | $5.38535\times {10}^{6}$ | $3.62468\times {10}^{5}$ | $2.01597\times {10}^{5}$ | $9.18832\times {10}^{4}$ | $1.61554\times {10}^{5}$ | $8.62047\times {10}^{4}$ | $1.74028\times {10}^{3}$ | |

F14 | Avg | $1.36685\times {10}^{7}$ | $3.63546\times {10}^{10}$ | $1.49138\times {10}^{4}$ | $1.11354\times {10}^{5}$ | $4.54213\times {10}^{4}$ | $9.23849\times {10}^{4}$ | $6.20934\times {10}^{4}$ | 2.76966 × 10^{3} |

Std | $1.56014\times {10}^{7}$ | $2.81518\times {10}^{10}$ | $5.58794\times {10}^{3}$ | $5.47972\times {10}^{4}$ | $2.31837\times {10}^{4}$ | $4.63380\times {10}^{4}$ | $4.58291\times {10}^{4}$ | $3.31537\times {10}^{2}$ | |

Med | $6.58964\times {10}^{6}$ | $2.79066\times {10}^{10}$ | $1.45733\times {10}^{4}$ | $1.03929\times {10}^{5}$ | $4.16434\times {10}^{4}$ | $7.66969\times {10}^{4}$ | $4.92331\times {10}^{4}$ | $2.71988\times {10}^{3}$ | |

F15 | Avg | $3.87651\times {10}^{3}$ | $6.36455\times {10}^{3}$ | $4.25149\times {10}^{3}$ | $3.50712\times {10}^{3}$ | $3.96245\times {10}^{3}$ | $3.56187\times {10}^{3}$ | $3.99024\times {10}^{3}$ | $\mathbf{3.43327}\times {10}^{3}$ |

Std | $4.38522\times {10}^{2}$ | $9.77898\times {10}^{2}$ | $5.06100\times {10}^{2}$ | $4.34234\times {10}^{2}$ | $5.45647\times {10}^{2}$ | $4.60965\times {10}^{2}$ | $4.73674\times {10}^{2}$ | $3.60364\times {10}^{2}$ | |

Med | $3.86743\times {10}^{3}$ | $6.04054\times {10}^{3}$ | $4.25893\times {10}^{3}$ | $3.47240\times {10}^{3}$ | $3.86245\times {10}^{3}$ | $3.53008\times {10}^{3}$ | $4.05225\times {10}^{3}$ | $3.37880\times {10}^{3}$ | |

F16 | Avg | $3.35283\times {10}^{3}$ | $8.99633\times {10}^{3}$ | $3.41636\times {10}^{3}$ | $3.47051\times {10}^{3}$ | $3.40178\times {10}^{3}$ | $3.53721\times {10}^{3}$ | $3.40178\times {10}^{3}$ | $\mathbf{3.10155}\times {10}^{3}$ |

Std | $3.06752\times {10}^{2}$ | $8.04598\times {10}^{3}$ | $2.98422\times {10}^{2}$ | $3.19347\times {10}^{2}$ | $3.04596\times {10}^{2}$ | $4.04267\times {10}^{2}$ | $3.04596\times {10}^{2}$ | $2.68766\times {10}^{2}$ | |

Med | $3.38986\times {10}^{3}$ | $6.12882\times {10}^{3}$ | $3.37638\times {10}^{3}$ | $3.51138\mathrm{E}\times {10}^{3}$ | $3.38707\times {10}^{3}$ | $3.60296\times {10}^{3}$ | $3.38707\times {10}^{3}$ | $3.12971\times {10}^{3}$ | |

F17 | Avg | $9.11523\times {10}^{6}$ | $7.05276\times {10}^{7}$ | $4.40012\times {10}^{6}$ | $2.28832\times {10}^{6}$ | $9.57515\times {10}^{5}$ | $2.15412\times {10}^{6}$ | $9.57515\times {10}^{5}$ | $\mathbf{6.90995}\times {10}^{3}$ |

Std | $4.75372\times {10}^{6}$ | $4.90121\times {10}^{7}$ | $2.19153\times {10}^{6}$ | $1.94567\times {10}^{6}$ | $6.53424\times {10}^{5}$ | $1.49028\times {10}^{6}$ | $6.53424\times {10}^{5}$ | $4.71762\times {10}^{3}$ | |

Med | $8.50410\times {10}^{6}$ | $6.40628\times {10}^{7}$ | $4.00712\times {10}^{6}$ | $1.76689\times {10}^{6}$ | $9.21205\times {10}^{5}$ | $1.83995\times {10}^{6}$ | $9.21205\times {10}^{5}$ | $5.81318\times {10}^{3}$ | |

F18 | Avg | $1.83085\times {10}^{6}$ | $1.78472\times {10}^{10}$ | $1.41295\times {10}^{5}$ | $1.59581\times {10}^{7}$ | $5.17783\times {10}^{6}$ | $1.60407\times {10}^{7}$ | $4.14719\times {10}^{6}$ | $\mathbf{2.14610}\times {10}^{3}$ |

Std | $2.66950\times {10}^{6}$ | $1.82443\times {10}^{10}$ | $7.81764\times {10}^{4}$ | $1.21002\times {10}^{7}$ | $5.60110\times {10}^{6}$ | $1.35824\times {10}^{7}$ | $5.83485\times {10}^{6}$ | $9.85921\times {10}^{1}$ | |

Med | $1.25293\times {10}^{6}$ | $1.24151\times {10}^{10}$ | $1.41243\times {10}^{5}$ | $1.20016\times {10}^{7}$ | $2.71450\times {10}^{6}$ | $1.22599\times {10}^{7}$ | $1.66892\times {10}^{6}$ | $2.11550\times {10}^{3}$ | |

F19 | Avg | $3.10711\times {10}^{3}$ | $4.23320\times {10}^{3}$ | $3.14930\times {10}^{3}$ | $3.29848\times {10}^{3}$ | $3.03626\times {10}^{3}$ | $3.33348\times {10}^{3}$ | $\mathbf{3.03626}\times {10}^{3}$ | $3.13075\times {10}^{3}$ |

Std | $3.20684\times {10}^{2}$ | $4.01035\times {10}^{2}$ | $3.22682\times {10}^{2}$ | $4.07341\times {10}^{2}$ | $3.01334\times {10}^{2}$ | $3.38872\times {10}^{2}$ | $3.01334\times {10}^{2}$ | $2.06599\times {10}^{2}$ | |

Med | $3.04765\times {10}^{3}$ | $4.27941\times {10}^{3}$ | $3.16749\times {10}^{3}$ | $3.31251\times {10}^{3}$ | $3.00510\times {10}^{3}$ | $3.37189\times {10}^{3}$ | $3.00510\times {10}^{3}$ | $3.08932\times {10}^{3}$ | |

F20 | Avg | $2.60058\times {10}^{3}$ | $2.98419\times {10}^{3}$ | $2.72520\times {10}^{3}$ | $\mathbf{2.54531}\times {10}^{3}$ | $2.63792\times {10}^{3}$ | $2.56892\times {10}^{3}$ | $2.65532\times {10}^{3}$ | $2.68525\times {10}^{3}$ |

Std | $4.67976\times {10}^{1}$ | $7.00936\times {10}^{1}$ | $8.38298\times {10}^{1}$ | $5.16031\times {10}^{1}$ | $5.83411\times {10}^{1}$ | $6.52628\times {10}^{1}$ | $9.57621\times {10}^{1}$ | $7.42052\times {10}^{1}$ | |

Med | $2.60226\times {10}^{3}$ | $2.96847\times {10}^{3}$ | $2.74358\times {10}^{3}$ | $2.53897\times {10}^{3}$ | $2.62657\times {10}^{3}$ | $2.55757\times {10}^{3}$ | $2.65628\times {10}^{3}$ | $2.69321\times {10}^{3}$ | |

F21 | Avg | $9.07504\times {10}^{3}$ | $1.70175\times {10}^{4}$ | $1.09582\times {10}^{4}$ | $9.38908\times {10}^{3}$ | $9.15415\times {10}^{3}$ | $9.21257\times {10}^{3}$ | $9.60887\times {10}^{3}$ | $\mathbf{8.94920}\times {10}^{3}$ |

Std | $2.71554\times {10}^{3}$ | $8.13669\times {10}^{2}$ | $9.28556\times {10}^{2}$ | $8.14791\times {10}^{2}$ | $2.45061\times {10}^{3}$ | $1.79573\times {10}^{3}$ | $2.21273\times {10}^{3}$ | $1.44719\times {10}^{3}$ | |

Med | $1.00121\times {10}^{4}$ | $1.71563\times {10}^{4}$ | $1.11692\times {10}^{4}$ | $9.39694\times {10}^{3}$ | $9.74711\times {10}^{3}$ | $9.38979\times {10}^{3}$ | $1.03739\times {10}^{4}$ | $8.93462\times {10}^{3}$ | |

F22 | Avg | $3.12543\times {10}^{3}$ | $3.81231\times {10}^{3}$ | $3.41873\times {10}^{3}$ | $\mathbf{2.97795}\times {10}^{3}$ | $3.25726\times {10}^{3}$ | $3.00084\times {10}^{3}$ | $3.17730\times {10}^{3}$ | $3.12742\times {10}^{3}$ |

Std | $8.78357\times {10}^{1}$ | $1.52531\times {10}^{2}$ | $1.91680\times {10}^{2}$ | $5.57378\times {10}^{1}$ | $1.18682\times {10}^{2}$ | $6.13483\times {10}^{1}$ | $1.36059\times {10}^{2}$ | $7.16808\times {10}^{1}$ | |

Med | $3.11586\times {10}^{3}$ | $3.79582\times {10}^{3}$ | $3.40470\times {10}^{3}$ | $2.97593\times {10}^{3}$ | $3.25904\times {10}^{3}$ | $3.00346\times {10}^{3}$ | $3.16339\times {10}^{3}$ | $3.15600\times {10}^{3}$ | |

F23 | Avg | $3.45961\times {10}^{3}$ | $4.05526\times {10}^{3}$ | $3.60986\times {10}^{3}$ | $3.15583\times {10}^{3}$ | $3.44325\times {10}^{3}$ | $\mathbf{3.13525}\times {10}^{3}$ | $3.23939\times {10}^{3}$ | $3.30224\times {10}^{3}$ |

Std | $1.35080\times {10}^{2}$ | $1.78941\times {10}^{2}$ | $1.48160\times {10}^{2}$ | $4.34247\times {10}^{1}$ | $9.09276\times {10}^{1}$ | $5.46767\times {10}^{1}$ | $1.08095\times {10}^{2}$ | $1.12273\times {10}^{2}$ | |

Med | $3.45849\times {10}^{3}$ | $4.00694\times {10}^{3}$ | $3.60060\times {10}^{3}$ | $3.16126\times {10}^{3}$ | $3.43925\times {10}^{3}$ | $3.13390\times {10}^{3}$ | $3.23554\times {10}^{3}$ | $3.32527\times {10}^{3}$ | |

F24 | Avg | $3.27506\times {10}^{3}$ | $1.23863\times {10}^{4}$ | $3.28556\times {10}^{3}$ | $3.03779\times {10}^{3}$ | $3.06590\times {10}^{3}$ | $3.04667\times {10}^{3}$ | $3.06144\times {10}^{3}$ | $\mathbf{3.03338}\times {10}^{3}$ |

Std | $7.20968\times {10}^{1}$ | $2.31843\times {10}^{3}$ | $9.67271\times {10}^{1}$ | $2.58595\times {10}^{1}$ | $2.70330\times {10}^{1}$ | $2.74866\times {10}^{1}$ | $3.40843\times {10}^{1}$ | $3.05895\times {10}^{1}$ | |

Med | $3.27224\times {10}^{3}$ | $1.23542\times {10}^{4}$ | $3.26943\times {10}^{3}$ | $3.03091\times {10}^{3}$ | $3.07165\times {10}^{3}$ | $3.04372\times {10}^{3}$ | $3.06031\times {10}^{3}$ | $3.03091\times {10}^{3}$ | |

F25 | Avg | $4.74285\times {10}^{3}$ | $1.50522\times {10}^{4}$ | $1.02495\times {10}^{4}$ | $\mathbf{4.37560}\times {10}^{3}$ | $6.24899\times {10}^{3}$ | $5.52341\times {10}^{3}$ | $6.53827\times {10}^{3}$ | $5.46227\times {10}^{3}$ |

Std | $1.28907\times {10}^{3}$ | $1.05431\times {10}^{3}$ | $2.50030\times {10}^{3}$ | $2.04274\times {10}^{3}$ | $3.92201\times {10}^{3}$ | $1.86055\times {10}^{3}$ | $4.03151\times {10}^{3}$ | $2.66427\times {10}^{3}$ | |

Med | $4.31756\times {10}^{3}$ | $1.52262\times {10}^{4}$ | $1.13049\times {10}^{4}$ | $2.90000\times {10}^{3}$ | $$ |