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Table 9: Experimental Configuration for First Comparison as in [111] The mean and standard deviation results of the are shown in Table 10 and Table 11 respectively. The first and second comparisons over 30 experimental runs best results are highlighted in the bold font. For the first comparison, it can be seen that the proposed method is able to achieve the best results for Sphere, Bukin, Bohachevsky, Zakharov, Booth, and Michalewicz fu nctions. Also, for the uni-modal function with no local minima such as “Sphere” function outcome clarify that SSAG4-tuner algorithm has the best result. On the other hand, the Emperor Penguins Colony (EPC) a gorithm achieved the best results for Rastrigin, Ackley. and Griewank functions, with multi-local minima. Furthermore, SSAGA_tuner obtains the best results for Michalewicz function which is complex and a multi-modal type. Based on the conducted experiments, the overall results confirm that the proposed SSAG4-tuner algorithm is appropriate for optimization, whether the optimization problems subject has uni-modal or multi-modal search space nature. For the standard deviation results in the same table, it is notable that the proposed SSAG@4-tuner algorithm performance is stable.

Table 9 Experimental Configuration for First Comparison as in [111] The mean and standard deviation results of the are shown in Table 10 and Table 11 respectively. The first and second comparisons over 30 experimental runs best results are highlighted in the bold font. For the first comparison, it can be seen that the proposed method is able to achieve the best results for Sphere, Bukin, Bohachevsky, Zakharov, Booth, and Michalewicz fu nctions. Also, for the uni-modal function with no local minima such as “Sphere” function outcome clarify that SSAG4-tuner algorithm has the best result. On the other hand, the Emperor Penguins Colony (EPC) a gorithm achieved the best results for Rastrigin, Ackley. and Griewank functions, with multi-local minima. Furthermore, SSAGA_tuner obtains the best results for Michalewicz function which is complex and a multi-modal type. Based on the conducted experiments, the overall results confirm that the proposed SSAG4-tuner algorithm is appropriate for optimization, whether the optimization problems subject has uni-modal or multi-modal search space nature. For the standard deviation results in the same table, it is notable that the proposed SSAG@4-tuner algorithm performance is stable.

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Table 1: Research Studies on Initial Population Diversity All the mentioned methods focus on increasing the initial population diversity in order to increases the robustness of the proposed algorithm toward premature convergence [77, 88, 89], not trapped in local optima [90], and achieve balance among exploitation and exploration [91].
Table 1: Research Studies on Initial Population Diversity All the mentioned methods focus on increasing the initial population diversity in order to increases the robustness of the proposed algorithm toward premature convergence [77, 88, 89], not trapped in local optima [90], and achieve balance among exploitation and exploration [91].
Figure 1: Global Taxonomy of Parameter Setting in EAs [94] efficiency by striking the right balance among wide-area exploration and local-nearby exploitation during the search.
Figure 1: Global Taxonomy of Parameter Setting in EAs [94] efficiency by striking the right balance among wide-area exploration and local-nearby exploitation during the search.
Table 2: Research Studies on Parameter Control
Table 2: Research Studies on Parameter Control
Figure 2: (a) Single salp, (b) Salps chain (salps swarm) [104]
Figure 2: (a) Single salp, (b) Salps chain (salps swarm) [104]
Figure 3: Standard SSA Algorithm Population Representation
Figure 3: Standard SSA Algorithm Population Representation
Algorithm 1 Standard Salp Swarm Algorithm Pseudo Code Figure 5: Standard GA Algorithm Population Representation
Algorithm 1 Standard Salp Swarm Algorithm Pseudo Code Figure 5: Standard GA Algorithm Population Representation
Figure 6: GA Algorithm Crossover Technique
Figure 6: GA Algorithm Crossover Technique
Figure 7: GA Algorithm Mutation Technique
Figure 7: GA Algorithm Mutation Technique
Figure 8: Multiple Random Populations Structure Algorithm 3 Generating a Diversified Initial Population
Figure 8: Multiple Random Populations Structure Algorithm 3 Generating a Diversified Initial Population
Figure 9: Pie-chart of proportional selection scheme example. Note that the sk aes y; is unity. For example, Figure 9 pie-charts the probability of five indi- vidual GApop = (#1, #2, %3, 4,25) where the fitness vector is (f(#1) = 0.54, f(a2) = 1.5, f(a3) = 2.66, f(a4) = 3.22, f(a@5) = 4.13). The selection probability of the each individual is represented as a portion in the pie-chart. In a nutshell, the larger portion means higher chance of selecting that individual.
Figure 9: Pie-chart of proportional selection scheme example. Note that the sk aes y; is unity. For example, Figure 9 pie-charts the probability of five indi- vidual GApop = (#1, #2, %3, 4,25) where the fitness vector is (f(#1) = 0.54, f(a2) = 1.5, f(a3) = 2.66, f(a4) = 3.22, f(a@5) = 4.13). The selection probability of the each individual is represented as a portion in the pie-chart. In a nutshell, the larger portion means higher chance of selecting that individual.
GA Termination Criteria The selection, encoding, crossover, mutation, decoding and evaluation with elitism operators are repeated until the maximum number of generations (GAjarGen) is reached. After GAnazGen is met, the best individual is selected to be the optimized parameter for SSA.
GA Termination Criteria The selection, encoding, crossover, mutation, decoding and evaluation with elitism operators are repeated until the maximum number of generations (GAjarGen) is reached. After GAnazGen is met, the best individual is selected to be the optimized parameter for SSA.
Table 3: Parameters Settings Table 4: Benchmark Functions Configurations
Table 3: Parameters Settings Table 4: Benchmark Functions Configurations
Table 5: Mathematical Definition of the Employed Benchmark Functions
Table 5: Mathematical Definition of the Employed Benchmark Functions
* best results in bold Table 6: Mean (avg) and Standard Deviation (std) of best obtained results between standard SSA, SSA.,zq, and SSAGA_tuner algorithms
* best results in bold Table 6: Mean (avg) and Standard Deviation (std) of best obtained results between standard SSA, SSA.,zq, and SSAGA_tuner algorithms
Figure 10: Proposed Self-Adaptive Salp Swarm Algorithm Flowchart
Figure 10: Proposed Self-Adaptive Salp Swarm Algorithm Flowchart
* best results in bold Table 7: p-values of Wilcoxon test for Standard SSA, SSA,;qg and SSAGa,_tuner Algorithms: best obtained results for employed benchmark functions
* best results in bold Table 7: p-values of Wilcoxon test for Standard SSA, SSA,;qg and SSAGa,_tuner Algorithms: best obtained results for employed benchmark functions
Table 8: Computational Time
Table 8: Computational Time
* best results in bold [able 10: Mean (avg) and Standard Deviation (std) of best obtained results for employed benchmark functions
* best results in bold [able 10: Mean (avg) and Standard Deviation (std) of best obtained results for employed benchmark functions
* best results in bold [able 11: Mean (avg) and Standard Deviation (std) of best obtained results for employed benchmark function
* best results in bold [able 11: Mean (avg) and Standard Deviation (std) of best obtained results for employed benchmark function
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Cognitive ScienceApplied MathematicsComputer ScienceMathematical Optimization
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