IA-DTPSO: A Multi-Strategy Integrated Particle Swarm Optimization for Predicting the Total Urban Water Resources in China
Abstract
:1. Introduction
- It is an approximate method that is not specific to a particular problem.
- It is a process of continuously learning towards the optimal solution through trial and error.
- Demonstrates significant multi-functionality and robustness.
- It is an optimization logic used to determine approximate solutions to complex global optimization problems.
- (i)
- Swarm-behavior inspired: Swarm-behavior-inspired algorithms are techniques that mimic collaborative behavior in biological social systems to solve problems. They organize a large number of simple individual units (such as ants, bees, bird swarm agents) together, allowing them to interact and learn in complex environments, and jointly search for optimal solutions. In recent years, newly proposed population-based algorithms include: Whale Optimization Algorithm (WOA) [18], Northern Goshawk Optimization (NGO) [19], Bottlenose Dolphin Optimizer (BDO) [20], Nutcracker Optimization Algorithm (NOA) [21], Mantis Search Algorithm (MSA) [22], Genghis Khan Shark Optimizer (GKSO) [23], Black-winged kite algorithm (BKA) [24], Secretary Bird Optimization Algorithm (SBOA) [25], and Horned Lizard Optimization Algorithm (HLOA) [26].
- (ii)
- Human-behavior inspired: Human-behavior-inspired algorithms typically draw inspiration from human creativity, artistic thinking, and problem-solving approaches, simulating the process of humans making a series of decisions through team collaboration. In recent years, this type of algorithm includes: Enterprise Development Optimizer (EDO) [27], Hiking Optimization Algorithm (HOA) [28], Great Wall Construction Algorithm (GWCA) [29], Football Team Training Algorithm (FTTA) [30], Alpine Skiing Optimization (ASO) [31], Information Acquisition Optimizer (IAO) [32], Adolescent Identity Search Algorithm (AISA) [33], and Information Decision Search Algorithm (IDSE) [34].
- (iii)
- Evolution-phenomena inspired: Evolution-phenomena-inspired algorithms are mainly a type of computational technology that draw inspiration from biological evolution theory. These mainly include Genetic Algorithm (GA) [35], Genetic Programming (GP) [36], Evolutionary Programming (EP) [37], Evolutionary Strategy (ES) [38], Differential Evolution (DE) algorithm [39], Biogeography-based optimization (BBO) [40], Clonal Selection Algorithm (CSA) [41], and Alpha Evolution (AE) [42].
- (iv)
- Nature-science-phenomena inspired: Nature-science-phenomena-inspired algorithms based on natural science phenomena mainly come from observations of natural phenomena and scientific laws in various fields. The latest achievements in this research direction mainly include: Tangent Search Algorithm (TSA) [43], Kepler Optimization Algorithm (KOA) [44], Exponential- Trigonometric Optimization (ETO) algorithm [45], Artemisinin Optimization (AO) algorithm [46], Weighted Average Algorithm (WAA) [5], Newton-Raphson-based Optimizer (NRBO) [47], Polar Lights Optimization (PLO) [48], and FATA morgana algorithm (FATA) [49].
- Difficulty in achieving the optimal balance of ENE, resulting in MAs to local optimum.
- Multiple operators are typically used to approximate the optimum, complicating the search scenario.
- Performance degradation in high-dimensional search space.
- (i)
- A multi-strategy PSO with information acquisition, referred to as IA-DTPSO, is proposed and the entire optimization process is modeled.
- (ii)
- The good ENE ability of IA-DTPSO is validated on CEC2022.
- (iii)
- IA-DTPSO is compared with 11 other algorithms on different dimensions of CEC2022, verifying the superiority of IA-DTPSO.
- (iv)
- IA-DTPSO and seven other algorithms are employed to optimize parameters of TDGM (1,1,r,ξ,Csz) and applied to predict TUWRs in China. In addition, the IA-DTPSO optimized model is compared with three existing models, and the results indicate that the model optimized by IA-DTPSO achieves the minimum error among the four error evaluation metrics in both comparisons.
2. The Classic PSO
3. The Proposed IA-DTPSO
3.1. Sobol Sequence Initialization
3.2. Information Acquisition Strategy
3.2.1. Information Gathering
3.2.2. Information Filtering and Evaluation
3.2.3. Information Analysis and Organization
3.3. SCC Method
3.4. Tangent Flight Strategy
3.5. Dimension Learning Strategy
Algorithm 1: IA-DTPSO’s pseudo-code |
Start IA-DTPSO Input: Particles’ number (N) and iterations (T) Output: The optimum 1: Use Equation (3) for Sobol sequence initialization and store the current optimum |
2: While (it < T) Do 3: For i = 1 to N Do 4: Use Equation (4) to form the initial information system 5: End For 6: Update the parameter a using Equation (15) 7: Calculate the Spearman’s correlation coefficient Sc using Equations (12) and (14) 8: For i = 1 to N Do 9: For j = 1 to D Do 10: If Sc <= 0 11: For 12: Use Equation (13) to determine the dimension that requires reverse solution position update 13: End For 14: End If 15: End For 16: End For 17: For i = 1 to N Do 18: Calculate the movement size step using Equation (15) 19: Use Equation (16) for the tangent flight or PSO update scheme to randomly update particles’ position 20: End For 21: For i = 1 to N Do 22: Exploration 23: Update relevant parameters using Equations (6)–(9) 24: Use Equation (5) for information filtering and evaluation process 25: End 26: Exploitation 27: Update parameter using Equation (11) 28: Use Equation (10) for information analysis and organization 29: End 30: End For 31: For i = 1 to N Do 32: Update radius using Equation (18) 33: Construct the neighborhood using Equation (19) 34: For j = 1 to D Do 35: Update a randomly selected neighbor particle on the neighborhood using Equation (20) 36: End For 37: End For 38: Compute fitness values and store the current optimum 39: it = it + 1 40: End While 41: Output the optimum |
End IA-DTPSO |
3.6. Time Complexity Analysis of IA-DTPSO
4. Experimental Results and Discussion
4.1. Experimental Design and Parameter Setting
- (1)
- (2)
- PSO [17] and its various improved versions: Elite Archives-driven PSO (EAPSO) [60], Gaussian Quantum-behaved PSO (G-QPSO) [61], Hybrid algorithm based on Jellyfish Search PSO (HJSPSO) [62], single-objective variant PSO (PSO-sono) [63], and Multi-strategy PSO incorporating Snow Ablation Optimizer (SAO-MPSO) [64].
4.2. ENE Behavior Analysis
4.3. Experimental Results and Analysis
5. Simulation and Prediction of TUWRs in China Based on IA-DTPSO and TDGM(1,1,r,ξ,Csz)
5.1. TDGM(1,1,r,ξ,Csz)
5.2. Investigation Data Analysis
5.3. Model Evaluation Criteria
5.4. IA-DTPSO and Other Algorithms for Parameter Optimization and Prediction of TDGM (1,1,r,ξ,Csz)
5.5. Four Models for Simulating and Predicting TUWRs in China
6. Conclusions and Future Prospects
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Algorithms | Proposed Year | Parameter | Value |
---|---|---|---|
PSO | 1995 | ω, c1, c2 | 0.8, 2, 2 |
RUN | 2021 | a, b | 20, 12 |
NGO | 2021 | - | - |
NOA | 2023 | Prp, Pa2, N, | 0.2, 0.4, 25, 0.05 |
GKSO | 2023 | m | 1.5 |
IVYA | 2024 | - | - |
EAPSO | 2023 | - | - |
G-QPSO | 2010 | ω1, ω2, c1, c2 | 0.6, 0.8, 2, 2 |
HJSPSO | 2023 | cmin, cmax, ωmin, ωmax, β, γ, c0 | 0.5, 2.5, 0.4, 0.9, 0.1, 0.1, 0.5 |
PSO-sono | 2022 | ωmin, ωmax, iw, r | 0.6, 0.8, [0.4, 0.9], 0.5 |
SAO-MPSO | 2024 | m, fads, Jump | 1.5, 2, [0, 1] |
IA-DTPSO | 2025 | θ, a, ω, c1, c2 | [−1, 1], [0, 2], 0.8, 2, 2 |
Settings | Specifications |
---|---|
OS | Windows 11 Version 23H2 22631.4317 |
CPU | 11th Gen Intel (R) Core (TM) i7-11700 @ 2.50 GHz |
RAM | 8 GB |
Language (version) | Matlab (R2024a) |
F | Index | Algorithms | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | RUN | NGO | NOA | GKSO | IVYA | EAPSO | G-QPSO | HJSPSO | PSO-Sono | SAO-MPSO | IA-DTPSO | ||
F1 | Best | 3.001 × 102 | TO | TO | 2.628 × 103 | TO | TO | TO | 1.891 × 103 | TO | 3.875 × 103 | TO | TO |
Worst | 3.009 × 102 | TO | TO | 1.997 × 104 | TO | 3.075 × 102 | TO | 3.548 × 103 | TO | 2.374 × 104 | TO | TO | |
Mean | 3.004 × 102 | TO | TO | 8.435 × 103 | TO | 3.011 × 102 | TO | 2.679 × 103 | TO | 1.147 × 104 | TO | TO | |
WRST | 8.007 × 10−9/- | 8.007 × 10−9/- | 7.992 × 10−9/- | 8.007 × 10−9/- | 6.054 × 10−9/- | 8.007 × 10−9/- | 3.338 × 10−4/- | 8.007 × 10−9/- | 8.007 × 10−9/- | 8.007 × 10−9/- | 1.427 × 10−6/- | - | |
FT | 8.800 | 7.100 | 5.300 | 11.300 | 3.675 | 8.100 | 2.275 | 10.000 | 5.700 | 11.700 | 2.675 | 1.375 | |
Rank | 8 | 7 | 5 | 11 | 4 | 9 | 3 | 10 | 6 | 12 | 2 | 1 | |
F2 | Best | TO | TO | TO | 4.562 × 102 | TO | TO | TO | 5.000 × 102 | TO | 4.576 × 102 | TO | TO |
Worst | 4.073 × 102 | 4.089 × 102 | 4.071 × 102 | 6.144 × 102 | 4.089 × 102 | 4.742 × 102 | 4.089 × 102 | 6.265 × 102 | 4.041 × 102 | 6.218 × 102 | 4.089 × 102 | 4.001 × 102 | |
Mean | 4.025 × 102 | 4.036 × 102 | 4.024 × 102 | 5.194 × 102 | 4.055 × 102 | 4.101 × 102 | 4.050 × 102 | 5.678 × 102 | 4.007 × 102 | 5.004 × 102 | 4.049 × 102 | TO | |
WRST | 4.388 × 10−2/- | 6.949 × 10−1/= | 5.310 × 10−2/= | △/- | 1.604 × 10−4/- | 6.220 × 10−4/- | 1.135 × 10−2/- | △/- | 1.264 × 10−1/= | △/- | 5.842 × 10−7/- | - | |
FT | 5.300 | 4.400 | 4.750 | 10.900 | 5.750 | 6.350 | 5.475 | 11.800 | 3.850 | 10.250 | 6.125 | 3.050 | |
Rank | 4 | 5 | 3 | 11 | 8 | 9 | 7 | 12 | 2 | 10 | 6 | 1 | |
F3 | Best | 6.001 × 102 | 6.002 × 102 | TO | 6.111 × 102 | TO | TO | TO | 6.246 × 102 | TO | 6.184 × 102 | TO | TO |
Worst | 6.103 × 102 | 6.209 × 102 | TO | 6.414 × 102 | 6.100 × 102 | 6.005 × 102 | TO | 6.437 × 102 | TO | 6.387 × 102 | 6.004 × 102 | 6.002 × 102 | |
Mean | 6.034 × 102 | 6.097 × 102 | TO | 6.278 × 102 | 6.018 × 102 | TO | TO | 6.365 × 102 | TO | 6.260 × 102 | TO | TO | |
WRST | 1.065 × 10−7/- | △/- | 2.946 × 10−8/+ | △/- | 2.062 × 10−6/- | 4.355 × 10−7/- | 2.439 × 10−8/+ | △/- | 6.810 × 10−7/+ | △/- | 6.092 × 10−7/- | - | |
FT | 8.000 | 8.700 | 3.200 | 10.800 | 7.250 | 1.475 | 2.825 | 11.800 | 4.625 | 10.350 | 3.075 | 5.900 | |
Rank | 8 | 9 | 2 | 11 | 7 | 6 | 1 | 12 | 3 | 10 | 5 | 4 | |
F4 | Best | 8.080 × 102 | 8.109 × 102 | 8.030 × 102 | 8.369 × 102 | 8.090 × 102 | 8.090 × 102 | 8.040 × 102 | 8.304 × 102 | 8.030 × 102 | 8.397 × 102 | 8.060 × 102 | 8.025 × 102 |
Worst | 8.448 × 102 | 8.338 × 102 | 8.107 × 102 | 8.640 × 102 | 8.328 × 102 | 8.348 × 102 | 8.318 × 102 | 8.432 × 102 | 8.090 × 102 | 8.691 × 102 | 8.259 × 102 | 8.149 × 102 | |
Mean | 8.194 × 102 | 8.205 × 102 | 8.069 × 102 | 8.512 × 102 | 8.176 × 102 | 8.186 × 102 | 8.174 × 102 | 8.374 × 102 | 8.064 × 102 | 8.540 × 102 | 8.133 × 102 | 8.083 × 102 | |
WRST | 3.293 × 10−5/- | 1.431 × 10−7/- | 4.388 × 10−2/+ | △/- | 1.198 × 10−6/- | 1.200 × 10−6/- | 1.103 × 10−5/- | △/- | 7.114 × 10−3/+ | △/- | 5.111 × 10−3/- | - | |
FT | 6.700 | 7.400 | 2.100 | 11.350 | 6.250 | 6.900 | 6.350 | 10.000 | 1.950 | 11.500 | 4.550 | 2.950 | |
Rank | 8 | 9 | 2 | 11 | 6 | 7 | 5 | 10 | 1 | 12 | 4 | 3 | |
F5 | Best | TO | 9.023 × 102 | TO | 9.975 × 102 | TO | 1.007 × 103 | TO | 1.079 × 103 | TO | 1.001 × 103 | TO | TO |
Worst | 9.001 × 102 | 1.021 × 103 | 9.001 × 102 | 1.381 × 103 | 9.017 × 102 | 1.710 × 103 | 9.005 × 102 | 1.182 × 103 | 9.005 × 102 | 1.366 × 103 | 9.005 × 102 | 9.006 × 102 | |
Mean | TO | 9.714 × 102 | TO | 1.199 × 103 | 9.003 × 102 | 1.243 × 103 | TO | 1.110 × 103 | TO | 1.161 × 103 | 9.001 × 102 | TO | |
WRST | 2.745 × 10−4/+ | △/- | 9.996 × 10−7/+ | △/- | 4.088 × 10−1/= | △/- | 6.326 × 10−6/- | △/- | 4.703 × 10−3/+ | △/- | 2.033 × 10−2/- | - | |
FT | 5.650 | 8.000 | 2.875 | 11.000 | 4.900 | 10.900 | 1.600 | 9.750 | 4.550 | 10.350 | 3.375 | 5.050 | |
Rank | 2 | 8 | 1 | 11 | 7 | 12 | 5 | 9 | 3 | 10 | 6 | 4 | |
F6 | Best | 1.866 × 103 | 1.903 × 103 | 1.828 × 103 | 8.824 × 105 | 1.826 × 103 | 1.857 × 103 | 1.942 × 103 | 3.479 × 105 | 1.843 × 103 | 4.901 × 105 | 1.902 × 103 | TO |
Worst | 6.960 × 103 | 4.950 × 103 | 1.943 × 103 | 3.144 × 107 | 5.528 × 103 | 8.090 × 103 | 7.181 × 103 | 4.242 × 106 | 3.069 × 103 | 2.214 × 107 | 7.657 × 103 | 1.803 × 103 | |
Mean | 3.069 × 103 | 3.096 × 103 | 1.882 × 103 | 8.279 × 106 | 2.236 × 103 | 4.031 × 103 | 4.335 × 103 | 2.007 × 106 | 2.109 × 103 | 6.362 × 106 | 4.436 × 103 | 1.801 × 103 | |
WRST | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | - | |
FT | 5.700 | 6.450 | 2.750 | 11.350 | 3.950 | 6.850 | 7.150 | 10.500 | 4.150 | 11.150 | 7.000 | 1.000 | |
Rank | 5 | 6 | 2 | 12 | 4 | 7 | 8 | 10 | 3 | 11 | 9 | 1 | |
F7 | Best | 2.002 × 103 | 2.017 × 103 | 2.001 × 103 | 2.046 × 103 | 2.002 × 103 | 2.001 × 103 | TO | 2.070 × 103 | 2.001 × 103 | 2.051 × 103 | 2.001 × 103 | 2.001 × 103 |
Worst | 2.045 × 103 | 2.058 × 103 | 2.011 × 103 | 2.096 × 103 | 2.026 × 103 | 2.084 × 103 | 2.054 × 103 | 2.105 × 103 | 2.025 × 103 | 2.121 × 103 | 2.025 × 103 | 2.022 × 103 | |
Mean | 2.028 × 103 | 2.036 × 103 | 2.004 × 103 | 2.072 × 103 | 2.020 × 103 | 2.021 × 103 | 2.017 × 103 | 2.088 × 103 | 2.010 × 103 | 2.085 × 103 | 2.012 × 103 | 2.009 × 103 | |
WRST | 2.062 × 10−6/- | 1.431 × 10−7/- | 1.782 × 10−3/+ | △/- | 1.610 × 10−4/- | 1.143 × 10−2/- | 1.404 × 10−1/= | △/- | 8.392 × 10−1/= | △/- | 8.392 × 10−1/= | - | |
FT | 7.500 | 8.000 | 2.050 | 10.300 | 5.700 | 5.700 | 4.650 | 11.400 | 4.100 | 11.200 | 3.800 | 3.600 | |
Rank | 8 | 9 | 1 | 10 | 6 | 7 | 5 | 12 | 3 | 11 | 4 | 2 | |
F8 | Best | 2.202 × 103 | 2.204 × 103 | 2.208 × 103 | 2.228 × 103 | TO | 2.201 × 103 | TO | 2.224 × 103 | 2.210 × 103 | 2.221 × 103 | TO | 2.207 × 103 |
Worst | 2.228 × 103 | 2.226 × 103 | 2.223 × 103 | 2.245 × 103 | 2.221 × 103 | 2.224 × 103 | 2.222 × 103 | 2.235 × 103 | 2.227 × 103 | 2.312 × 103 | 2.221 × 103 | 2.215 × 103 | |
Mean | 2.223 × 103 | 2.222 × 103 | 2.218 × 103 | 2.237 × 103 | 2.216 × 103 | 2.219 × 103 | 2.220 × 103 | 2.232 × 103 | 2.223 × 103 | 2.246 × 103 | 2.216 × 103 | 2.210 × 103 | |
WRST | 1.201 × 10−6/- | 1.201 × 10−6/- | 3.705 × 10−5/- | △/- | 7.114 × 10−3/- | 1.807 × 10−5/- | 1.201 × 10−6/- | △/- | 4.539 × 10−7/- | △/- | 7.114 × 10−3/- | - | |
FT | 7.250 | 7.100 | 4.800 | 11.150 | 3.400 | 5.200 | 4.500 | 10.100 | 7.550 | 11.500 | 3.450 | 2.000 | |
Rank | 8 | 7 | 4 | 11 | 3 | 5 | 6 | 10 | 8 | 12 | 2 | 1 | |
F9 | Best | 2.486 × 103 | 2.529 × 103 | 2.529 × 103 | 2.570 × 103 | 2.529 × 103 | 2.529 × 103 | 2.529 × 103 | 2.643 × 103 | 2.529 × 103 | 2.586 × 103 | 2.529 × 103 | 2.486 × 103 |
Worst | 2.486 × 103 | 2.529 × 103 | 2.529 × 103 | 2.710 × 103 | 2.529 × 103 | 2.676 × 103 | 2.529 × 103 | 2.669 × 103 | 2.529 × 103 | 2.683 × 103 | 2.529 × 103 | 2.490 × 103 | |
Mean | 2.486 × 103 | 2.529 × 103 | 2.529 × 103 | 2.620 × 103 | 2.529 × 103 | 2.537 × 103 | 2.529 × 103 | 2.659 × 103 | 2.529 × 103 | 2.640 × 103 | 2.529 × 103 | 2.488 × 103 | |
WRST | △/+ | △/- | 1.127 × 10−8/- | △/- | 6.777 × 10−8/- | 5.366 × 10−8/- | 8.007 × 10−9/- | △/- | 6.644 × 10−8/- | △/- | 1.945 × 10−8/- | - | |
FT | 1.000 | 8.850 | 4.250 | 10.400 | 7.525 | 6.375 | 4.175 | 11.550 | 6.550 | 10.900 | 4.425 | 2.000 | |
Rank | 1 | 8 | 4 | 10 | 7 | 9 | 3 | 12 | 6 | 11 | 5 | 2 | |
F10 | Best | TO | TO | TO | 2.503 × 103 | TO | TO | TO | 2.508 × 103 | TO | 2.502 × 103 | TO | TO |
Worst | 2.633 × 103 | 2.619 × 103 | TO | 2.676 × 103 | TO | 2.638 × 103 | 2.618 × 103 | 2.651 × 103 | TO | 2.684 × 103 | TO | TO | |
Mean | 2.555 × 103 | 2.534 × 103 | TO | 2.533 × 103 | TO | 2.541 × 103 | 2.512 × 103 | 2.539 × 103 | TO | 2.547 × 103 | TO | TO | |
WRST | △/- | 6.674 × 10−6/- | 8.604 × 10−1/= | △/- | 6.868 × 10−4/- | 4.540 × 10−6/- | 1.105 × 10−5/- | △/- | 3.048 × 10−4/- | △/- | 6.750 × 10−1/= | - | |
FT | 6.750 | 8.100 | 4.000 | 9.950 | 3.550 | 7.950 | 6.550 | 10.400 | 5.650 | 9.600 | 3.650 | 1.850 | |
Rank | 12 | 8 | 5 | 7 | 2 | 10 | 6 | 9 | 3 | 11 | 4 | 1 | |
F11 | Best | 2.601 × 103 | TO | TO | 2.762 × 103 | TO | TO | TO | 2.822 × 103 | TO | 2.769 × 103 | TO | TO |
Worst | 3.001 × 103 | 3.184 × 103 | TO | 2.871 × 103 | 3.000 × 103 | 3.000 × 103 | 3.000 × 103 | 2.899 × 103 | TO | 3.429 × 103 | 3.184 × 103 | TO | |
Mean | 2.672 × 103 | 2.659 × 103 | TO | 2.815 × 103 | 2.640 × 103 | 2.768 × 103 | 2.673 × 103 | 2.865 × 103 | TO | 2.835 × 103 | 2.964 × 103 | TO | |
WRST | 3.473 × 10−8/- | 3.473 × 10−8/- | 2.512 × 10−1/= | 3.473 × 10−8/- | 1.889 × 10−4/- | 6.682 × 10−5/- | 5.164 × 10−2/= | 3.473 × 10−8/- | 1.512 × 10−5/- | 3.473 × 10−8/- | 8.221 × 10−6/- | - | |
FT | 7.750 | 6.750 | 2.400 | 8.900 | 4.675 | 7.100 | 4.075 | 10.050 | 5.200 | 8.900 | 9.900 | 2.300 | |
Rank | 6 | 5 | 2 | 9 | 4 | 8 | 7 | 11 | 3 | 10 | 12 | 1 | |
F12 | Best | 2.801 × 103 | 2.862 × 103 | 2.859 × 103 | 2.872 × 103 | 2.863 × 103 | 2.864 × 103 | 2.863 × 103 | 2.931 × 103 | 2.865 × 103 | 2.875 × 103 | 2.862 × 103 | 2.846 × 103 |
Worst | 2.926 × 103 | 2.867 × 103 | 2.864 × 103 | 2.967 × 103 | 2.868 × 103 | 2.920 × 103 | 2.866 × 103 | 2.966 × 103 | 2.871 × 103 | 3.000 × 103 | 2.866 × 103 | 2.849 × 103 | |
Mean | 2.857 × 103 | 2.864 × 103 | 2.862 × 103 | 2.891 × 103 | 2.865 × 103 | 2.871 × 103 | 2.864 × 103 | 2.948 × 103 | 2.866 × 103 | 2.898 × 103 | 2.864 × 103 | 2.847 × 103 | |
WRST | 1.803 × 10−6/- | △/- | △/- | △/- | 6.786 × 10−8/- | 6.757 × 10−8/- | 6.786 × 10−8/- | △/- | △/- | △/- | 6.786 × 10−8/- | - | |
FT | 2.550 | 5.300 | 3.300 | 10.450 | 5.900 | 8.600 | 5.150 | 11.850 | 7.600 | 10.400 | 5.800 | 1.100 | |
Rank | 2 | 6 | 3 | 10 | 7 | 9 | 5 | 12 | 8 | 11 | 4 | 1 | |
Mean Rank | 6.000 | 7.250 | 2.833 | 10.333 | 5.083 | 8.167 | 5.083 | 10.750 | 4.083 | 10.917 | 5.250 | 1.833 | |
Final Ranking | 7 | 8 | 2 | 10 | 4 | 9 | 4 | 11 | 3 | 12 | 6 | 1 | |
Mean FT | 6.079 | 7.179 | 3.481 | 10.654 | 5.210 | 6.792 | 4.565 | 10.767 | 5.123 | 10.650 | 4.819 | 2.681 | |
Final FT | 7 | 9 | 2 | 11 | 6 | 8 | 3 | 12 | 5 | 10 | 4 | 1 | |
+/=/− | 2/0/10 | 0/1/11 | 4/3/5 | 0/0/12 | 0/1/11 | 0/0/12 | 1/2/9 | 0/0/12 | 3/2/7 | 0/0/12 | 0/2/10 | -/-/- |
F | Index | Algorithms | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | RUN | NGO | NOA | GKSO | IVYA | EAPSO | G-QPSO | HJSPSO | PSO-Sono | SAO-MPSO | IA-DTPSO | ||
F1 | Std | 2.461 × 10−1 | 1.625 × 10−5 | 5.384 × 10−10 | 4.211 × 103 | 1.258 × 10−13 | 2.249 | 4.124 × 10−14 | 4.362 × 102 | 3.157 × 10−9 | 5.113 × 103 | 2.916 × 10−14 | 0.000 |
RMSE | 2.994 × 102 | 2.990 × 102 | 2.990 × 102 | 9.379 × 103 | 2.990 × 102 | 3.001 × 102 | 2.990 × 102 | 2.711 × 103 | 2.990 × 102 | 1.251 × 104 | 2.990 × 102 | 2.990 × 102 | |
δ | 2.991 × 102 | 2.990 × 102 | 2.990 × 102 | 2.627 × 103 | 2.990 × 102 | 2.990 × 102 | 2.990 × 102 | 1.890 × 103 | 2.990 × 102 | 3.874 × 103 | 2.990 × 102 | 2.990 × 102 | |
F2 | Std | 2.265 | 4.481 | 2.538 | 3.991 × 101 | 3.834 | 2.175 × 101 | 3.660 | 3.138 × 101 | 1.458 | 3.467 × 101 | 4.042 | 3.083 × 10−2 |
RMSE | 4.015 × 102 | 4.026 × 102 | 3.990 × 102 | 5.198 × 102 | 4.045 × 102 | 4.096 × 102 | 4.040 × 102 | 5.676 × 102 | 3.997 × 102 | 5.005 × 102 | 4.039 × 102 | 4.014 × 102 | |
δ | 3.990 × 102 | 3.990 × 102 | 3.990 × 102 | 4.552 × 102 | 3.990 × 102 | 3.990 × 102 | 3.990 × 102 | 4.990 × 102 | 3.990 × 102 | 4.566 × 102 | 3.990 × 102 | 3.990 × 102 | |
F3 | Std | 2.602 | 7.359 | 1.744 × 10−6 | 7.342 | 2.593 | 1.228 × 10−1 | 6.901 × 10−14 | 3.930 | 4.006 × 10−3 | 4.209 | 9.164 × 10−2 | 4.160 × 10−2 |
RMSE | 6.024 × 102 | 6.087 × 102 | 5.990 × 102 | 6.268 × 102 | 6.008 × 102 | 5.990 × 102 | 5.990 × 102 | 6.355 × 102 | 5.990 × 102 | 6.250 × 102 | 5.990 × 102 | 5.990 × 102 | |
δ | 5.991 × 102 | 5.992 × 102 | 5.990 × 102 | 6.101 × 102 | 5.990 × 102 | 5.990 × 102 | 5.990 × 102 | 6.236 × 102 | 5.990 × 102 | 6.174 × 102 | 5.990 × 102 | 5.990 × 102 | |
F4 | Std | 9.612 | 5.622 | 2.012 | 7.638 | 6.515 | 6.833 | 6.587 | 3.618 | 1.618 | 8.390 | 6.020 | 2.867 |
RMSE | 8.185 × 102 | 8.196 × 102 | 8.059 × 102 | 8.503 × 102 | 8.166 × 102 | 8.176 × 102 | 8.165 × 102 | 8.364 × 102 | 8.054 × 102 | 8.531 × 102 | 8.124 × 102 | 8.073 × 102 | |
δ | 8.070 × 102 | 8.099 × 102 | 8.020 × 102 | 8.359 × 102 | 8.080 × 102 | 8.080 × 102 | 8.030 × 102 | 8.294 × 102 | 8.020 × 102 | 8.387 × 102 | 8.050 × 102 | 8.015 × 102 | |
F5 | Std | 3.486 × 10−2 | 3.548 × 101 | 2.002 × 10−2 | 1.137 × 102 | 4.573 × 10−1 | 1.707 × 102 | 1.543 × 10−1 | 2.964 × 101 | 1.139 × 10−1 | 8.556 × 101 | 1.385 × 10−1 | 1.334 × 10−1 |
RMSE | 8.990 × 102 | 9.710 × 102 | 8.990 × 102 | 1.203 × 103 | 8.993 × 102 | 1.254 × 103 | 8.990 × 102 | 1.109 × 103 | 8.990 × 102 | 1.163 × 103 | 8.991 × 102 | 8.990 × 102 | |
δ | 8.990 × 102 | 9.013 × 102 | 8.990 × 102 | 9.965 × 102 | 8.990 × 102 | 1.006 × 103 | 8.990 × 102 | 1.078 × 103 | 8.990 × 102 | 9.998 × 102 | 8.990 × 102 | 8.990 × 102 | |
F6 | Std | 1.600 × 103 | 1.128 × 103 | 3.221 × 101 | 9.251 × 106 | 8.287 × 102 | 2.139 × 103 | 2.003 × 103 | 1.298 × 106 | 3.062 × 102 | 5.700 × 106 | 2.261 × 103 | 9.067 × 10−1 |
RMSE | 3.442 × 103 | 3.284 × 103 | 1.881 × 103 | 1.224 × 107 | 2.376 × 103 | 4.537 × 103 | 4.753 × 103 | 2.372 × 106 | 2.129 × 103 | 8.446 × 106 | 4.952 × 103 | TO | |
δ | 1.865 × 103 | 1.902 × 103 | 1.827 × 103 | 8.824 × 105 | 1.825 × 103 | 1.856 × 103 | 1.941 × 103 | 3.479 × 105 | 1.842 × 103 | 4.901 × 105 | 1.901 × 103 | 1.799 × 103 | |
F7 | Std | 9.656 | 1.171 × 101 | 3.449 | 1.378 × 101 | 6.571 | 1.823 × 101 | 1.383 × 101 | 9.648 | 9.078 | 1.718 × 101 | 9.943 | 5.864 |
RMSE | 2.027 × 103 | 2.035 × 103 | 2.003 × 103 | 2.071 × 103 | 2.019 × 103 | 2.020 × 103 | 2.016 × 103 | 2.087 × 103 | 2.009 × 103 | 2.084 × 103 | 2.011 × 103 | 2.008 × 103 | |
δ | 2.001 × 103 | 2.016 × 103 | TO | 2.045 × 103 | 2.001 × 103 | TO | 1.999 × 103 | 2.069 × 103 | TO | 2.050 × 103 | TO | TO | |
F8 | Std | 5.340 | 4.507 | 5.146 | 4.450 | 8.882 | 5.876 | 4.653 | 2.753 | 4.466 | 1.754 × 101 | 8.845 | 2.329 |
RMSE | 2.222 × 103 | 2.221 × 103 | 2.217 × 103 | 2.236 × 103 | 2.215 × 103 | 2.218 × 103 | 2.219 × 103 | 2.231 × 103 | 2.222 × 103 | 2.246 × 103 | 2.215 × 103 | 2.209 × 103 | |
δ | 2.201 × 103 | 2.203 × 103 | 2.207 × 103 | 2.227 × 103 | 2.199 × 103 | TO | 2.199 × 103 | 2.223 × 103 | 2.209 × 103 | 2.220 × 103 | 2.199 × 103 | 2.206 × 103 | |
F9 | Std | 1.141 × 10−3 | 3.325 × 10−5 | 1.043 × 10−13 | 3.961 × 101 | 4.092 × 10−9 | 3.286 × 101 | 0.000 | 8.315 | 5.291 × 10−12 | 2.874 × 101 | 1.807 × 10−13 | 1.108 |
RMSE | 2.485 × 103 | 2.528 × 103 | 2.528 × 103 | 2.619 × 103 | 2.528 × 103 | 2.536 × 103 | 2.528 × 103 | 2.659 × 103 | 2.528 × 103 | 2.639 × 103 | 2.528 × 103 | 2.487 × 103 | |
δ | 2.485 × 103 | 2.528 × 103 | 2.528 × 103 | 2.569 × 103 | 2.528 × 103 | 2.528 × 103 | 2.528 × 103 | 2.642 × 103 | 2.528 × 103 | 2.585 × 103 | 2.528 × 103 | 2.485 × 103 | |
F10 | Std | 6.277 × 101 | 5.267 × 101 | 8.037 × 10−2 | 5.130 × 101 | 5.454 × 10−2 | 5.760 × 101 | 3.488 × 101 | 4.883 × 101 | 7.003 × 10−2 | 7.598 × 101 | 7.548 × 10−2 | 5.131 × 10−2 |
RMSE | 2.555 × 103 | 2.534 × 103 | 2.499 × 103 | 2.532 × 103 | 2.499 × 103 | 2.541 × 103 | 2.511 × 103 | 2.538 × 103 | 2.499 × 103 | 2.547 × 103 | 2.499 × 103 | 2.499 × 103 | |
δ | 2.499 × 103 | 2.499 × 103 | 2.499 × 103 | 2.502 × 103 | 2.499 × 103 | 2.499 × 103 | 2.499 × 103 | 2.507 × 103 | 2.499 × 103 | 2.501 × 103 | 2.499 × 103 | 2.499 × 103 | |
F11 | Std | 1.455 × 102 | 1.378 × 102 | 6.211 × 10−10 | 3.421 × 101 | 1.231 × 102 | 1.808 × 102 | 1.352 × 102 | 2.235 × 101 | 2.612 × 10−9 | 1.603 × 102 | 1.852 × 102 | 3.460 × 10−13 |
RMSE | 2.674 × 103 | 2.662 × 103 | 2.599 × 103 | 2.815 × 103 | 2.642 × 103 | 2.772 × 103 | 2.675 × 103 | 2.864 × 103 | 2.599 × 103 | 2.839 × 103 | 2.969 × 103 | 2.599 × 103 | |
δ | TO | 2.599 × 103 | 2.599 × 103 | 2.761 × 103 | 2.599 × 103 | 2.599 × 103 | 2.599 × 103 | 2.821 × 103 | 2.599 × 103 | 2.768 × 103 | 2.599 × 103 | 2.599 × 103 | |
F12 | Std | 2.080 × 101 | 1.145 | 1.688 | 2.276 × 101 | 1.362 | 1.232 × 101 | 1.064 | 9.563 | 1.749 | 3.320 × 101 | 9.740 × 10−1 | 7.480 × 10−1 |
RMSE | 2.856 × 103 | 2.863 × 103 | 2.861 × 103 | 2.890 × 103 | 2.864 × 103 | 2.870 × 103 | 2.863 × 103 | 2.947 × 103 | 2.865 × 103 | 2.897 × 103 | 2.863 × 103 | 2.846 × 103 | |
δ | 2.800 × 103 | 2.861 × 103 | 2.858 × 103 | 2.871 × 103 | 2.862 × 103 | 2.863 × 103 | 2.862 × 103 | 2.930 × 103 | 2.864 × 103 | 2.874 × 103 | 2.861 × 103 | 2.845 × 103 |
F | Index | Algorithms | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | RUN | NGO | NOA | GKSO | IVYA | EAPSO | G-QPSO | HJSPSO | PSO-Sono | SAO-MPSO | IA-DTPSO | ||
F1 | Best | 3.153 × 102 | TO | 2.016 × 103 | 2.665 × 104 | TO | 5.133 × 103 | TO | 1.452 × 104 | 6.166 × 102 | 2.779 × 104 | TO | TO |
Worst | 3.434 × 102 | TO | 6.215 × 103 | 6.186 × 104 | TO | 1.751 × 104 | TO | 2.237 × 104 | 2.105 × 103 | 9.624 × 104 | TO | TO | |
Mean | 3.247 × 102 | TO | 4.014 × 103 | 3.917 × 104 | TO | 9.801 × 103 | TO | 1.873 × 104 | 1.314 × 103 | 5.183 × 104 | TO | TO | |
WRST | △/- | △/- | △/- | △/- | △/- | △/- | 5.075 × 10−1/= | △/- | △/- | △/- | 6.653 × 10−8/+ | - | |
FT | 6.000 | 4.000 | 8.000 | 11.200 | 5.000 | 9.000 | 2.750 | 10.000 | 7.000 | 11.800 | 1.000 | 2.250 | |
Rank | 6 | 4 | 8 | 11 | 5 | 9 | 3 | 10 | 7 | 12 | 1 | 2 | |
F2 | Best | 4.154 × 102 | TO | 4.002 × 102 | 8.056 × 102 | TO | 4.289 × 102 | TO | 9.092 × 102 | 4.449 × 102 | 7.176 × 102 | 4.026 × 102 | 4.105 × 102 |
Worst | 4.753 × 102 | 4.491 × 102 | 4.747 × 102 | 1.499 × 103 | 4.685 × 102 | 4.723 × 102 | 4.491 × 102 | 1.118 × 103 | 4.755 × 102 | 1.157 × 103 | 4.686 × 102 | 4.316 × 102 | |
Mean | 4.429 × 102 | 4.417 × 102 | 4.536 × 102 | 1.045 × 103 | 4.402 × 102 | 4.522 × 102 | 4.388 × 102 | 1.025 × 103 | 4.546 × 102 | 9.211 × 102 | 4.462 × 102 | 4.238 × 102 | |
WRST | 8.182 × 10−1/= | 1.610 × 10−4/- | 1.201 × 10−6/- | △/- | 1.481 × 10−3/- | 7.898 × 10−8/- | 1.217 × 10−3/- | △/- | △/- | △/- | 1.587 × 10−5/- | - | |
FT | 4.900 | 4.650 | 7.050 | 11.300 | 4.500 | 6.650 | 3.050 | 11.350 | 7.600 | 10.350 | 4.300 | 2.300 | |
Rank | 5 | 4 | 8 | 12 | 3 | 7 | 2 | 11 | 9 | 10 | 6 | 1 | |
F3 | Best | 6.154 × 102 | 6.164 × 102 | TO | 6.294 × 102 | 6.087 × 102 | TO | TO | 6.518 × 102 | TO | 6.291 × 102 | TO | 6.026 × 102 |
Worst | 6.459 × 102 | 6.431 × 102 | 6.002 × 102 | 6.817 × 102 | 6.324 × 102 | 6.223 × 102 | TO | 6.686 × 102 | 6.033 × 102 | 6.675 × 102 | 6.030 × 102 | 6.181 × 102 | |
Mean | 6.337 × 102 | 6.277 × 102 | TO | 6.585 × 102 | 6.184 × 102 | 6.020 × 102 | TO | 6.630 × 102 | 6.006 × 102 | 6.511 × 102 | 6.004 × 102 | 6.063 × 102 | |
WRST | 1.235 × 10−7/- | 2.218 × 10−7/- | △/+ | △/- | 2.690 × 10−6/- | 1.251 × 10−5/+ | △/+ | △/- | 7.898 × 10−8/+ | △/- | 7.898 × 10−8/+ | - | |
FT | 8.700 | 8.000 | 3.000 | 10.950 | 7.200 | 2.500 | 1.550 | 11.550 | 4.350 | 10.400 | 3.800 | 6.000 | |
Rank | 9 | 8 | 2 | 11 | 7 | 5 | 1 | 12 | 4 | 10 | 3 | 6 | |
F4 | Best | 8.399 × 102 | 8.438 × 102 | 8.247 × 102 | 9.495 × 102 | 8.328 × 102 | 8.428 × 102 | 8.199 × 102 | 9.244 × 102 | 8.195 × 102 | 9.414 × 102 | 8.139 × 102 | 8.319 × 102 |
Worst | 8.897 × 102 | 8.955 × 102 | 8.515 × 102 | 9.987 × 102 | 9.025 × 102 | 8.866 × 102 | 8.955 × 102 | 9.565 × 102 | 8.468 × 102 | 1.008 × 103 | 8.557 × 102 | 8.762 × 102 | |
Mean | 8.642 × 102 | 8.739 × 102 | 8.396 × 102 | 9.745 × 102 | 8.643 × 102 | 8.655 × 102 | 8.414 × 102 | 9.444 × 102 | 8.315 × 102 | 9.737 × 102 | 8.318 × 102 | 8.531 × 102 | |
WRST | 2.074 × 10−2/- | 4.680 × 10−5/- | 3.382 × 10−4/+ | △/- | 6.557 × 10−3/- | 4.320 × 10−3/- | 8.355 × 10−3/+ | △/- | 7.948 × 10−7/+ | △/- | 9.278 × 10−5/+ | - | |
FT | 6.650 | 7.950 | 3.400 | 11.300 | 6.800 | 6.950 | 3.550 | 10.150 | 2.000 | 11.550 | 2.500 | 5.200 | |
Rank | 6 | 9 | 3 | 12 | 7 | 8 | 4 | 10 | 1 | 11 | 2 | 5 | |
F5 | Best | 9.019 × 102 | 1.341 × 103 | 9.081 × 102 | 2.247 × 103 | 9.091 × 102 | 1.940 × 103 | TO | 2.579 × 103 | 9.001 × 102 | 2.379 × 103 | 9.002 × 102 | 9.006 × 102 |
Worst | 2.213 × 103 | 2.316 × 103 | 1.514 × 103 | 4.371 × 103 | 2.304 × 103 | 2.498 × 103 | 9.258 × 102 | 3.076 × 103 | 9.551 × 102 | 5.071 × 103 | 1.590 × 103 | 9.079 × 102 | |
Mean | 1.511 × 103 | 1.732 × 103 | 1.186 × 103 | 3.080 × 103 | 1.306 × 103 | 2.295 × 103 | 9.015 × 102 | 2.780 × 103 | 9.061 × 102 | 3.171 × 103 | 1.017 × 103 | 9.042 × 102 | |
WRST | 4.680 × 10−5/- | △/- | △/- | △/- | △/- | △/- | 1.306 × 10−6/+ | △/- | 1.404 × 10−1/= | △/- | 4.903 × 10−1/= | - | |
FT | 6.700 | 7.400 | 5.300 | 11.100 | 5.950 | 8.950 | 1.250 | 10.550 | 3.200 | 11.250 | 3.750 | 2.600 | |
Rank | 7 | 8 | 5 | 11 | 6 | 9 | 1 | 10 | 3 | 12 | 4 | 2 | |
F6 | Best | 5.703 × 103 | 1.923 × 103 | 2.288 × 103 | 7.281 × 107 | 1.864 × 103 | 1.926 × 103 | 1.930 × 103 | 3.348 × 107 | 1.842 × 103 | 9.198 × 107 | 1.947 × 103 | 1.815 × 103 |
Worst | 7.610 × 104 | 4.447 × 103 | 4.619 × 103 | 5.995 × 108 | 2.266 × 104 | 5.921 × 103 | 2.277 × 104 | 1.987 × 108 | 4.698 × 103 | 3.962 × 108 | 2.505 × 104 | 1.919 × 103 | |
Mean | 2.908 × 104 | 3.547 × 103 | 3.083 × 103 | 2.420 × 108 | 1.002 × 104 | 3.351 × 103 | 8.944 × 103 | 1.201 × 108 | 2.769 × 103 | 2.049 × 108 | 9.325 × 103 | 1.833 × 103 | |
WRST | △/- | △/- | △/- | △/- | 9.173 × 10−8/- | △/- | △/- | △/- | 1.431 × 10−7/- | △/- | △/- | - | |
FT | 8.750 | 5.000 | 4.400 | 11.400 | 6.250 | 4.300 | 5.900 | 10.350 | 3.400 | 11.250 | 5.900 | 1.100 | |
Rank | 9 | 5 | 3 | 12 | 8 | 4 | 6 | 10 | 2 | 11 | 7 | 1 | |
F7 | Best | 2.048 × 103 | 2.045 × 103 | 2.045 × 103 | 2.143 × 103 | 2.027 × 103 | 2.067 × 103 | 2.021 × 103 | 2.163 × 103 | 2.029 × 103 | 2.168 × 103 | 2.021 × 103 | 2.045 × 103 |
Worst | 2.167 × 103 | 2.142 × 103 | 2.085 × 103 | 2.318 × 103 | 2.142 × 103 | 2.155 × 103 | 2.172 × 103 | 2.195 × 103 | 2.059 × 103 | 2.352 × 103 | 2.181 × 103 | 2.072 × 103 | |
Mean | 2.099 × 103 | 2.109 × 103 | 2.064 × 103 | 2.209 × 103 | 2.070 × 103 | 2.112 × 103 | 2.062 × 103 | 2.182 × 103 | 2.045 × 103 | 2.244 × 103 | 2.068 × 103 | 2.056 × 103 | |
WRST | 1.600 × 10−5/- | 1.803 × 10−6/- | 4.679 × 10−2/- | △/- | 1.332 × 10−2/- | 1.235 × 10−7/- | 5.979 × 10−1/= | △/- | 1.481 × 10−3/+ | △/- | 9.892 × 10−1/= | - | |
FT | 6.550 | 7.650 | 4.500 | 10.950 | 5.100 | 7.850 | 3.750 | 10.300 | 2.200 | 11.600 | 3.850 | 3.700 | |
Rank | 7 | 8 | 4 | 11 | 6 | 9 | 3 | 10 | 1 | 12 | 5 | 2 | |
F8 | Best | 2.225 × 103 | 2.223 × 103 | 2.223 × 103 | 2.250 × 103 | 2.221 × 103 | 2.221 × 103 | 2.221 × 103 | 2.238 × 103 | 2.225 × 103 | 2.239 × 103 | 2.221 × 103 | 2.216 × 103 |
Worst | 2.363 × 103 | 2.243 × 103 | 2.229 × 103 | 2.424 × 103 | 2.341 × 103 | 2.576 × 103 | 2.358 × 103 | 2.263 × 103 | 2.236 × 103 | 2.532 × 103 | 2.240 × 103 | 2.231 × 103 | |
Mean | 2.243 × 103 | 2.227 × 103 | 2.227 × 103 | TO | 2.232 × 103 | 2.329 × 103 | 2.264 × 103 | 2.253 × 103 | 2.230 × 103 | 2.376 × 103 | 2.227 × 103 | 2.226 × 103 | |
WRST | 1.116 × 10−3/- | 5.250 × 10−1/= | 9.031 × 10−1/= | △/- | 6.787 × 10−2/= | 8.292 × 10−5/- | 5.979 × 10−1/= | △/- | 1.159 × 10−4/- | △/- | 1.636 × 10−1/= | - | |
FT | 6.550 | 4.350 | 4.500 | 10.300 | 3.550 | 9.200 | 5.500 | 8.950 | 6.150 | 11.250 | 4.300 | 3.400 | |
Rank | 7 | 3 | 2 | 10 | 6 | 11 | 9 | 8 | 5 | 12 | 4 | 1 | |
F9 | Best | 2.465 × 103 | 2.481 × 103 | 2.481 × 103 | 2.565 × 103 | 2.481 × 103 | 2.481 × 103 | 2.481 × 103 | 2.712 × 103 | 2.481 × 103 | 2.579 × 103 | 2.481 × 103 | 2.472 × 103 |
Worst | 2.465 × 103 | 2.481 × 103 | 2.481 × 103 | 2.775 × 103 | 2.481 × 103 | 2.482 × 103 | 2.481 × 103 | 2.916 × 103 | 2.481 × 103 | 2.816 × 103 | 2.481 × 103 | 2.481 × 103 | |
Mean | 2.465 × 103 | 2.481 × 103 | 2.481 × 103 | 2.650 × 103 | 2.481 × 103 | 2.481 × 103 | 2.481 × 103 | 2.809 × 103 | 2.481 × 103 | 2.703 × 103 | 2.481 × 103 | 2.476 × 103 | |
WRST | △/+ | △/- | △/- | △/- | △/- | △/- | 5.903 × 10−8/- | △/- | △/- | △/- | 6.541 × 10−8/- | - | |
FT | 1.000 | 7.550 | 5.300 | 10.200 | 5.600 | 9.000 | 3.200 | 11.850 | 7.450 | 10.950 | 3.900 | 2.000 | |
Rank | 1 | 8 | 4 | 10 | 6 | 9 | 3 | 12 | 7 | 11 | 5 | 2 | |
F10 | Best | TO | 2.501 × 103 | TO | 2.538 × 103 | TO | TO | 2.501 × 103 | 2.601 × 103 | 2.501 × 103 | 2.522 × 103 | TO | TO |
Worst | 4.867 × 103 | 2.627 × 103 | 2.625 × 103 | 6.769 × 103 | 2.711 × 103 | 5.023 × 103 | 3.985 × 103 | 2.674 × 103 | 2.637 × 103 | 7.760 × 103 | 4.510 × 103 | 2.501 × 103 | |
Mean | 3.639 × 103 | 2.507 × 103 | 2.507 × 103 | 3.024 × 103 | 2.511 × 103 | 3.197 × 103 | 2.886 × 103 | 2.634 × 103 | 2.508 × 103 | 4.594 × 103 | 3.056 × 103 | 2.501 × 103 | |
WRST | 1.227 × 10−3/- | 2.218 × 10−7/- | 7.205 × 10−2/= | △/- | 2.561 × 10−3/- | 1.929 × 10−2/- | 4.540 × 10−6/- | △/- | 1.794 × 10−4/- | △/- | 5.874 × 10−6/- | - | |
FT | 8.900 | 5.950 | 3.650 | 8.350 | 2.050 | 6.600 | 7.750 | 8.600 | 4.750 | 9.500 | 9.050 | 2.850 | |
Rank | 11 | 3 | 2 | 8 | 5 | 10 | 7 | 6 | 4 | 12 | 9 | 1 | |
F11 | Best | 2.651 × 103 | 2.900 × 103 | TO | 4.176 × 103 | 2.900 × 103 | 2.900 × 103 | 2.900 × 103 | 6.225 × 103 | TO | 3.676 × 103 | 2.900 × 103 | TO |
Worst | 3.008 × 103 | 3.000 × 103 | 3.000 × 103 | 7.276 × 103 | 3.360 × 103 | 3.000 × 103 | 3.000 × 103 | 7.128 × 103 | 3.000 × 103 | 5.998 × 103 | 2.900 × 103 | 3.038 × 103 | |
Mean | 2.950 × 103 | 2.910 × 103 | 2.888 × 103 | 5.612 × 103 | 2.963 × 103 | 2.930 × 103 | 2.945 × 103 | 6.742 × 103 | 2.885 × 103 | 4.959 × 103 | 2.900 × 103 | 2.922 × 103 | |
WRST | 3.852 × 10−2/- | 7.557 × 10−1/= | 3.382 × 10−4/+ | △/- | 8.103 × 10−2/= | 3.639 × 10−3/- | 5.231 × 10−2/= | △/- | 2.561 × 10−3/+ | △/- | 7.656 × 10−7/+ | - | |
FT | 7.050 | 6.250 | 4.500 | 10.850 | 5.500 | 4.400 | 4.350 | 11.950 | 5.150 | 10.200 | 1.350 | 6.450 | |
Rank | 8 | 4 | 2 | 11 | 9 | 6 | 7 | 12 | 1 | 10 | 3 | 5 | |
F12 | Best | 2.896 × 103 | 2.941 × 103 | 2.935 × 103 | 3.113 × 103 | 2.944 × 103 | 2.947 × 103 | 2.934 × 103 | 3.469 × 103 | 2.954 × 103 | 3.059 × 103 | 2.945 × 103 | 2.900 × 103 |
Worst | 3.394 × 103 | 2.984 × 103 | 2.947 × 103 | 3.371 × 103 | 2.981 × 103 | 3.060 × 103 | 2.999 × 103 | 3.668 × 103 | 2.998 × 103 | 3.596 × 103 | 3.016 × 103 | 2.900 × 103 | |
Mean | 3.198 × 103 | 2.954 × 103 | 2.939 × 103 | 3.215 × 103 | 2.957 × 103 | 2.971 × 103 | 2.953 × 103 | 3.574 × 103 | 2.972 × 103 | 3.191 × 103 | 2.970 × 103 | 2.900 × 103 | |
WRST | 1.201 × 10−6/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | △/- | - | |
FT | 9.550 | 4.750 | 2.250 | 10.300 | 4.800 | 5.900 | 4.400 | 11.950 | 6.800 | 9.700 | 6.550 | 1.050 | |
Rank | 10 | 4 | 2 | 11 | 5 | 7 | 3 | 12 | 8 | 9 | 6 | 1 | |
Mean Rank | 7.167 | 5.667 | 3.750 | 10.833 | 6.083 | 7.833 | 4.083 | 10.250 | 4.333 | 11.000 | 4.583 | 2.417 | |
Final Ranking | 8 | 6 | 2 | 11 | 7 | 9 | 3 | 10 | 4 | 12 | 5 | 1 | |
Mean FT | 6.775 | 6.125 | 4.654 | 10.683 | 5.192 | 6.775 | 3.917 | 10.629 | 5.004 | 10.817 | 4.188 | 3.242 | |
Final FT | 8 | 7 | 4 | 11 | 6 | 8 | 2 | 10 | 5 | 12 | 3 | 1 | |
+/=/− | 1/1/10 | 0/2/10 | 3/2/7 | 0/0/12 | 0/2/10 | 1/0/11 | 3/4/5 | 0/0/12 | 4/1/7 | 0/0/12 | 4/3/5 | -/-/- |
F | Index | Algorithms | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | RUN | NGO | NOA | GKSO | IVYA | EAPSO | G-QPSO | HJSPSO | PSO-Sono | SAO-MPSO | IA-DTPSO | ||
F1 | Std | 6.898 | 7.562 × 10−4 | 1.241 × 103 | 8.173 × 103 | 8.985 × 10−4 | 3.391 × 103 | 8.880 × 10−6 | 1.993 × 103 | 3.761 × 102 | 1.630 × 104 | 4.304 × 10−13 | 5.222 × 10−7 |
RMSE | 3.238 × 102 | 2.990 × 102 | 4.192 × 103 | 3.998 × 104 | 2.995 × 102 | 1.034 × 104 | 2.990 × 102 | 1.883 × 104 | 1.363 × 103 | 5.420 × 104 | 2.990 × 102 | 2.990 × 102 | |
δ | 3.143 × 102 | 2.990 × 102 | 2.015 × 103 | 2.665 × 104 | 2.990 × 102 | 5.132 × 103 | 2.990 × 102 | 1.452 × 104 | 6.156 × 102 | 2.779 × 104 | 2.990 × 102 | 2.990 × 102 | |
F2 | Std | 2.793 × 101 | 1.797 × 101 | 1.656 × 101 | 1.700 × 102 | 2.180 × 101 | 1.055 × 101 | 1.948 × 101 | 5.161 × 101 | 1.057 × 101 | 1.316 × 102 | 1.585 × 101 | 3.711 |
RMSE | 4.427 × 102 | 4.411 × 102 | 4.529 × 102 | 1.057 × 103 | 4.397 × 102 | 4.513 × 102 | 4.383 × 102 | 1.025 × 103 | 4.537 × 102 | 9.290 × 102 | 4.455 × 102 | 4.228 × 102 | |
δ | 4.144 × 102 | 3.990 × 102 | 3.992 × 102 | 8.046 × 102 | 3.990 × 102 | 4.279 × 102 | 3.990 × 102 | 9.082 × 102 | 4.439 × 102 | 7.166 × 102 | 4.016 × 102 | 4.095 × 102 | |
F3 | Std | 9.017 | 8.651 | 7.371 × 10−2 | 1.211 × 101 | 7.627 | 6.064 | 9.377 × 10−4 | 3.797 | 8.564 × 10−1 | 9.456 | 7.621 × 10−1 | 4.275 |
RMSE | 6.328 × 102 | 6.267 × 102 | 5.990 × 102 | 6.576 × 102 | 6.174 × 102 | 6.011 × 102 | 5.990 × 102 | 6.620 × 102 | 5.996 × 102 | 6.501 × 102 | 5.994 × 102 | 6.053 × 102 | |
δ | 6.144 × 102 | 6.154 × 102 | 5.990 × 102 | 6.284 × 102 | 6.077 × 102 | 5.990 × 102 | 5.990 × 102 | 6.508 × 102 | 5.990 × 102 | 6.281 × 102 | 5.990 × 102 | 6.016 × 102 | |
F4 | Std | 1.502 × 101 | 1.415 × 101 | 6.527 | 1.365 × 101 | 1.409 × 101 | 1.287 × 101 | 1.670 × 101 | 8.125 | 7.039 | 1.627 × 101 | 1.267 × 101 | 1.231 × 101 |
RMSE | 8.633 × 102 | 8.730 × 102 | 8.386 × 102 | 9.736 × 102 | 8.634 × 102 | 8.646 × 102 | 8.406 × 102 | 9.434 × 102 | 8.305 × 102 | 9.729 × 102 | 8.309 × 102 | 8.522 × 102 | |
δ | 8.389 × 102 | 8.428 × 102 | 8.237 × 102 | 9.485 × 102 | 8.318 × 102 | 8.418 × 102 | 8.189 × 102 | 9.234 × 102 | 8.185 × 102 | 9.404 × 102 | 8.129 × 102 | 8.309 × 102 | |
F5 | Std | 3.758 × 102 | 2.793 × 102 | 2.020 × 102 | 5.955 × 102 | 3.863 × 102 | 1.738 × 102 | 5.727 | 1.492 × 102 | 1.234 × 101 | 6.723 × 102 | 1.766 × 102 | 2.139 |
RMSE | 1.554 × 103 | 1.752 × 103 | 1.202 × 103 | 3.133 × 103 | 1.358 × 103 | 2.301 × 103 | 9.005 × 102 | 2.782 × 103 | 9.052 × 102 | 3.237 × 103 | 1.030 × 103 | 9.032 × 102 | |
δ | 9.009 × 102 | 1.340 × 103 | 9.071 × 102 | 2.246 × 103 | 9.081 × 102 | 1.939 × 103 | 8.990 × 102 | 2.578 × 103 | 8.991 × 102 | 2.378 × 103 | 8.992 × 102 | 8.996 × 102 | |
F6 | Std | 2.008 × 104 | 7.669 × 102 | 6.916 × 102 | 1.425 × 108 | 7.584 × 103 | 1.261 × 103 | 7.327 × 103 | 3.893 × 107 | 8.278 × 102 | 9.403 × 107 | 7.738 × 103 | 2.375 × 101 |
RMSE | 3.505 × 104 | 3.624 × 103 | 3.155 × 103 | 2.790 × 108 | 1.245 × 104 | 3.568 × 103 | 1.144 × 104 | 1.259 × 108 | 2.883 × 103 | 2.244 × 108 | 1.199 × 104 | 1.832 × 103 | |
δ | 5.702 × 103 | 1.922 × 103 | 2.287 × 103 | 7.281 × 107 | 1.863 × 103 | 1.925 × 103 | 1.929 × 103 | 3.348 × 107 | 1.841 × 103 | 9.198 × 107 | 1.946 × 103 | 1.814 × 103 | |
F7 | Std | 3.216 × 101 | 2.292 × 101 | 1.181 × 101 | 4.638 × 101 | 2.474 × 101 | 2.839 × 101 | 3.994 × 101 | 9.078 | 9.092 | 5.094 × 101 | 4.697 × 101 | 8.845 |
RMSE | 2.099 × 103 | 2.108 × 103 | 2.063 × 103 | 2.208 × 103 | 2.070 × 103 | 2.112 × 103 | 2.062 × 103 | 2.181 × 103 | 2.044 × 103 | 2.243 × 103 | 2.068 × 103 | 2.055 × 103 | |
δ | 2.047 × 103 | 2.044 × 103 | 2.044 × 103 | 2.142 × 103 | 2.026 × 103 | 2.066 × 103 | 2.020 × 103 | 2.162 × 103 | 2.028 × 103 | 2.167 × 103 | 2.020 × 103 | 2.044 × 103 | |
F8 | Std | 3.882 × 101 | 4.257 | 1.411 | 4.428 × 101 | 2.676 × 101 | 9.088 × 101 | 5.559 × 101 | 6.503 | 2.490 | 7.743 × 101 | 8.026 | 3.748 |
RMSE | 2.242 × 103 | 2.226 × 103 | 2.226 × 103 | 2.299 × 103 | 2.231 × 103 | 2.329 × 103 | 2.263 × 103 | 2.252 × 103 | 2.229 × 103 | 2.376 × 103 | 2.226 × 103 | 2.225 × 103 | |
δ | 2.224 × 103 | 2.222 × 103 | 2.222 × 103 | 2.249 × 103 | 2.220 × 103 | 2.220 × 103 | 2.220 × 103 | 2.237 × 103 | 2.224 × 103 | 2.238 × 103 | 2.220 × 103 | 2.215 × 103 | |
F9 | Std | 1.829 × 10−2 | 3.946 × 10−3 | 1.702 × 10−6 | 5.092 × 101 | 9.247 × 10−5 | 2.422 × 10−1 | 1.368 × 10−12 | 5.391 × 101 | 1.078 × 10−3 | 6.991 × 101 | 3.306 × 10−5 | 2.286 |
RMSE | 2.464 × 103 | 2.480 × 103 | 2.480 × 103 | 2.649 × 103 | 2.480 × 103 | 2.480 × 103 | 2.480 × 103 | 2.808 × 103 | 2.480 × 103 | 2.703 × 103 | 2.480 × 103 | 2.476 × 103 | |
δ | 2.464 × 103 | 2.480 × 103 | 2.480 × 103 | 2.564 × 103 | 2.480 × 103 | 2.480 × 103 | 2.480 × 103 | 2.711 × 103 | 2.480 × 103 | 2.578 × 103 | 2.480 × 103 | 2.471 × 103 | |
F10 | Std | 8.723 × 102 | 2.812 × 101 | 2.785 × 101 | 1.170 × 103 | 4.710 × 101 | 8.874 × 102 | 4.374 × 102 | 1.884 × 101 | 3.044 × 101 | 2.323 × 103 | 4.664 × 102 | 1.253 × 10−1 |
RMSE | 3.736 × 103 | 2.506 × 103 | 2.506 × 103 | 3.231 × 103 | 2.510 × 103 | 3.311 × 103 | 2.917 × 103 | 2.633 × 103 | 2.507 × 103 | 5.120 × 103 | 3.088 × 103 | TO | |
δ | 2.499 × 103 | TO | 2.499 × 103 | 2.537 × 103 | 2.499 × 103 | 2.499 × 103 | TO | TO | TO | 2.521 × 103 | 2.499 × 103 | 2.499 × 103 | |
F11 | Std | 7.486 × 101 | 3.072 × 101 | 9.754 × 101 | 8.589 × 102 | 1.058 × 102 | 4.702 × 101 | 5.104 × 101 | 2.046 × 102 | 1.187 × 102 | 6.222 × 102 | 7.807 × 10−13 | 9.178 × 101 |
RMSE | 2.950 × 103 | 2.909 × 103 | 2.888 × 103 | 5.673 × 103 | 2.964 × 103 | 2.929 × 103 | 2.944 × 103 | 6.744 × 103 | 2.886 × 103 | 4.995 × 103 | 2.899 × 103 | 2.923 × 103 | |
δ | 2.650 × 103 | 2.899 × 103 | 2.599 × 103 | 4.175 × 103 | 2.899 × 103 | 2.899 × 103 | 2.899 × 103 | 6.224 × 103 | 2.599 × 103 | 3.675 × 103 | 2.899 × 103 | 2.599 × 103 | |
F12 | Std | 1.481 × 102 | 1.042 × 101 | 3.139 | 7.512 × 101 | 1.007 × 101 | 2.848 × 101 | 1.459 × 101 | 5.104 × 101 | 1.208 × 101 | 1.195 × 102 | 1.768 × 101 | 1.037 × 10−4 |
RMSE | 3.200 × 103 | 2.953 × 103 | 2.938 × 103 | 3.215 × 103 | 2.956 × 103 | 2.970 × 103 | 2.952 × 103 | 3.573 × 103 | 2.971 × 103 | 3.192 × 103 | 2.969 × 103 | 2.899 × 103 | |
δ | 2.895 × 103 | 2.940 × 103 | 2.934 × 103 | 3.112 × 103 | 2.943 × 103 | 2.946 × 103 | 2.933 × 103 | 3.468 × 103 | 2.953 × 103 | 3.058 × 103 | 2.944 × 103 | 2.899 × 103 |
Years | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |
---|---|---|---|---|---|---|---|---|---|---|
TUWRs | 24,129.6 | 28,053.1 | 25,330.1 | 25,255.2 | 27,434.3 | 24,180.2 | 30,906.4 | 23,256.7 | 29,528.8 | 27,957.9 |
Years | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 |
TUWRs | 27,266.9 | 27,962.6 | 32,466.4 | 28,761.2 | 27,462.5 | 29,041.0 | 31,605.2 | 29,638.2 | 27,088.1 | 24,780.0 |
Years | Real Value | IA-DTPSO | PSO | GKSO | IVYA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | ||
2005 | 28,053.1 | 27,916.57 | −136.53 | 0.49 | 24,398.68 | −3654.42 | 13.03 | 26,529.37 | −1523.73 | 5.43 | 25,472.86 | −2580.23 | 9.19 |
2006 | 25,330.1 | 25,594.21 | 264.11 | 1.04 | 25,454.02 | 123.92 | 0.49 | 26,220.56 | 890.46 | 3.52 | 25,966.25 | 636.15 | 2.51 |
2007 | 25,255.2 | 25,617.06 | 361.86 | 1.43 | 26,417.97 | 1162.77 | 4.60 | 26,288.93 | 1033.73 | 4.09 | 26,595.10 | 1339.90 | 5.30 |
2008 | 27,434.3 | 26,010.91 | −1423.39 | 5.19 | 27,180.11 | −254.19 | 0.93 | 26,494.88 | −939.41 | 3.42 | 27,052.92 | −381.37 | 1.39 |
2009 | 24,180.2 | 26,496.10 | 2315.90 | 9.58 | 27,742.49 | 3562.29 | 14.73 | 26,770.27 | 2590.07 | 10.71 | 27,386.22 | 3206.02 | 13.25 |
2010 | 30,906.4 | 26,978.82 | −3927.58 | 12.71 | 28,130.40 | −2776.00 | 8.98 | 27,071.13 | −3835.27 | 12.41 | 27,628.87 | −3277.52 | 10.60 |
2011 | 23,256.7 | 27,423.85 | 4167.15 | 17.92 | 28,372.31 | 5115.61 | 22.00 | 27,373.44 | 4116.74 | 17.70 | 27,805.52 | 4548.82 | 19.55 |
2012 | 29,528.8 | 27,818.17 | −1710.63 | 5.79 | 28,494.53 | −1034.27 | 3.50 | 27,665.48 | −1863.32 | 6.31 | 27,934.13 | −1594.66 | 5.40 |
2013 | 27,957.9 | 28,158.21 | 200.31 | 0.72 | 28,519.84 | 561.94 | 2.01 | 27,942.35 | −15.55 | 0.06 | 28,027.75 | 69.85 | 0.24 |
2014 | 27,266.9 | 28,444.74 | 1177.84 | 4.32 | 28,467.42 | 1200.52 | 4.40 | 28,202.71 | 935.81 | 3.43 | 28,095.92 | 829.02 | 3.04 |
2015 | 27,962.6 | 28,680.48 | 717.88 | 2.57 | 28,353.20 | 390.60 | 1.40 | 28,446.89 | 484.29 | 1.73 | 28,145.54 | 182.94 | 0.65 |
2016 | 32,466.4 | 28,869.04 | −3597.36 | 11.08 | 28,190.29 | −4276.11 | 13.17 | 28,675.96 | −3790.44 | 11.67 | 28,181.67 | −4284.72 | 13.19 |
2017 | 28,761.2 | 29,014.29 | 253.09 | 0.88 | 27,989.42 | −771.78 | 2.68 | 28,891.27 | 130.07 | 0.45 | 28,207.97 | −553.22 | 1.92 |
2018 | 27,462.5 | 29,120.10 | 1657.60 | 6.04 | 27,759.33 | 296.83 | 1.08 | 29,094.15 | 1631.65 | 5.94 | 28,227.12 | 764.62 | 2.78 |
MAPEsimulation (%) | 5.6366 | 6.6432 | 6.2061 | 6.3627 | |||||||||
2019 | 29,041 | 29,106.99 | 65.99 | 0.23 | 28,640.37 | −400.63 | 1.3795 | 29,285.85 | 244.85 | 0.84 | 28,241.06 | −799.93 | 2.75 |
2020 | 31,605.2 | 29,112.08 | −2493.12 | 7.89 | 28,817.00 | −2788.20 | 8.8220 | 29,467.49 | −2137.70 | 6.76 | 28,251.21 | −3353.98 | 10.61 |
2021 | 29,638.2 | 29,086.75 | −551.45 | 1.86 | 29,009.75 | −628.45 | 2.1204 | 29,640.08 | 1.88 | 0.01 | 28,258.59 | −1379.60 | 4.65 |
2022 | 27,088.1 | 29,034.33 | 1946.23 | 7.18 | 29,216.74 | 2128.64 | 7.8582 | 29,804.48 | 2716.37 | 10.02 | 28,263.97 | 1175.87 | 4.34 |
2023 | 24,780 | 28,957.86 | 4177.86 | 16.86 | 29,436.13 | 4656.13 | 18.7899 | 29,961.43 | 5181.43 | 20.90 | 28,267.89 | 3487.89 | 14.07 |
MAPEprediction (%) | 6.8041 | 7.2254 | 7.7102 | 7.2876 | |||||||||
MAPE (%) | 5.9439 | 6.7964 | 6.6019 | 6.6061 | |||||||||
Years | Real Value | EAPSO | HJSPSO | PSO-sono | SAO-MPSO | ||||||||
SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | ||
2005 | 28,053.1 | 28,036.28 | −16.81 | 0.06 | 27,865.98 | −187.11 | 0.66 | 27,772.07 | −281.02 | 1.00 | 27,744.11 | −308.98 | 1.10 |
2006 | 25,330.1 | 24,823.89 | −506.20 | 1.99 | 26,510.91 | 1180.81 | 4.66 | 26,521.71 | 1191.61 | 4.70 | 25,728.56 | 398.46 | 1.57 |
2007 | 25,255.2 | 25,798.03 | 542.83 | 2.14 | 25,896.87 | 641.67 | 2.54 | 25,936.51 | 681.31 | 2.69 | 26,184.17 | 928.97 | 3.67 |
2008 | 27,434.3 | 26,288.65 | −1145.64 | 4.17 | 25,813.99 | −1620.30 | 5.90 | 25,854.32 | −1579.97 | 5.75 | 26,590.81 | −843.48 | 3.07 |
2009 | 24,180.2 | 26,745.13 | 2564.93 | 10.60 | 26,043.52 | 1863.32 | 7.70 | 26,074.90 | 1894.70 | 7.83 | 26,952.85 | 2772.65 | 11.46 |
2010 | 30,906.4 | 27,137.43 | −3768.96 | 12.19 | 26,433.89 | −4472.50 | 14.47 | 26,454.43 | −4451.96 | 14.40 | 27,270.65 | −3635.74 | 11.76 |
2011 | 23,256.7 | 27,484.06 | 4227.36 | 18.17 | 26,897.13 | 3640.43 | 15.65 | 26,907.61 | 3650.91 | 15.69 | 27,546.62 | 4289.92 | 18.44 |
2012 | 29,528.8 | 27,794.22 | −1734.57 | 5.87 | 27,385.82 | −2142.97 | 7.25 | 27,387.58 | −2141.21 | 7.25 | 27,784.27 | −1744.52 | 5.90 |
2013 | 27,957.9 | 28,075.01 | 117.11 | 0.41 | 27,875.64 | −82.25 | 0.29 | 27,869.90 | −87.99 | 0.31 | 27,987.46 | 29.56 | 0.10 |
2014 | 27,266.9 | 28,331.62 | 1064.72 | 3.90 | 28,354.76 | 1087.86 | 3.98 | 28,342.48 | 1075.58 | 3.94 | 28,159.99 | 893.09 | 3.27 |
2015 | 27,962.6 | 28,568.01 | 605.40 | 2.16 | 28,817.97 | 855.37 | 3.05 | 28,799.80 | 837.20 | 2.99 | 28,305.45 | 342.85 | 1.22 |
2016 | 32,466.4 | 28,787.22 | −3679.17 | 11.33 | 29,263.39 | −3203.00 | 9.86 | 29,239.83 | −3226.56 | 9.93 | 28,427.14 | −4039.25 | 12.44 |
2017 | 28,761.2 | 28,991.69 | 230.49 | 0.80 | 29,690.86 | 929.66 | 3.23 | 29,662.25 | 901.05 | 3.13 | 28,528.04 | −233.15 | 0.81 |
2018 | 27,462.5 | 29,183.33 | 1720.83 | 6.26 | 30,100.99 | 2638.49 | 9.60 | 30,067.59 | 2605.09 | 9.48 | 28,610.82 | 1148.32 | 4.18 |
MAPEsimulation (%) | 5.7233 | 6.3508 | 6.3688 | 5.6466 | |||||||||
2019 | 29,041 | 29,363.72 | 322.72 | 1.11 | 30,494.74 | 1453.74 | 5.00 | 30,456.75 | 1415.75 | 4.87 | 28,677.83 | −363.16 | 1.25 |
2020 | 31,605.2 | 29,534.15 | −2071.04 | 6.55 | 30,873.19 | −732.01 | 2.31 | 30,830.78 | −774.41 | 2.45 | 28,731.17 | −2874.02 | 9.09 |
2021 | 29,638.2 | 29,695.73 | 57.53 | 0.19 | 31,237.40 | 1599.20 | 5.39 | 31,190.71 | 1552.51 | 5.23 | 28,772.67 | −865.52 | 2.92 |
2022 | 27,088.1 | 29,849.35 | 2761.25 | 10.19 | 31,588.41 | 4500.31 | 16.61 | 31,537.54 | 4449.44 | 16.42 | 28,803.96 | 1715.86 | 6.33 |
2023 | 24,780 | 29,995.80 | 5215.80 | 21.04 | 31,927.15 | 7147.15 | 28.84 | 31,872.23 | 7092.23 | 28.62 | 28,826.43 | 4046.43 | 16.32 |
MAPEprediction (%) | 7.8201 | 11.6347 | 11.522 | 7.1856 | |||||||||
MAPE (%) | 6.2751 | 7.7413 | 7.7249 | 6.0516 |
Parameters | IA-DTPSO | PSO | GKSO | IVYA | EAPSO | HJSPSO | PSO-Sono | SAO-MPSO |
---|---|---|---|---|---|---|---|---|
Csz | 24,123.6 | 24,160.2 | 24,385.5 | 24,346.2 | 24,488.9 | 24,146.9 | 24,500 | 24,245.4 |
ξ | 0.080129 | 0.560555 | 0.377924 | 0.439050 | 0.198431 | 0.029187 | 0.345376 | 0.067554 |
r | 1.453199 | 0.360578 | 0.927702 | 0.899874 | 0.905127 | 0.937307 | 1 | 0.925674 |
a | 0.058716 | 0.17176 | 0.64349 | 0.27198 | 1.4176 | 0.64964 | 0.64406 | 0.12418 |
b | 6780.2789 | −39.7023 | 13,448.3342 | 7691.1691 | 30,532.6828 | 9443.9293 | 9426.1429 | 4152.6776 |
c | 23,519.5322 | 8199.7156 | 20,248.424 | 16,383.655 | 6180.5493 | 24,060.5466 | 24,153.8696 | 21,550.6303 |
Years | 2024 | 2025 | 2026 | 2027 | 2028 |
---|---|---|---|---|---|
TUWRs | 26,376.97 | 26,028.78 | 24,960.55 | 28,731.54 | 33,688.46 |
Years | Real Value | ID_T | GM(1,1) | DGM(1,1) | NGBM(1,1) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | SimD | ResE | APE (%) | ||
2005 | 28,053.1 | 27,916.57 | −136.53 | 0.49 | 25,987.99 | −2065.11 | 7.36 | 26,023.11 | −2029.99 | 7.24 | 25,987.99 | −2065.11 | 7.36 |
2006 | 25,330.1 | 25,594.21 | 264.11 | 1.04 | 26,221.03 | 890.93 | 3.52 | 26,251.27 | 921.17 | 3.64 | 26,221.03 | 890.93 | 3.52 |
2007 | 25,255.2 | 25,617.06 | 361.86 | 1.43 | 26,456.15 | 1200.95 | 4.76 | 26,481.43 | 1226.23 | 4.86 | 26,456.15 | 1200.95 | 4.76 |
2008 | 27,434.3 | 26,010.91 | −1423.39 | 5.19 | 26,693.38 | −740.92 | 2.70 | 26,713.60 | −720.70 | 2.63 | 26,693.38 | −740.92 | 2.70 |
2009 | 24,180.2 | 26,496.10 | 2315.90 | 9.58 | 26,932.74 | 2752.54 | 11.38 | 26,947.82 | 2767.62 | 11.45 | 26,932.74 | 2752.54 | 11.38 |
2010 | 30,906.4 | 26,978.82 | −3927.58 | 12.71 | 27,174.25 | −3732.15 | 12.08 | 27,184.08 | −3722.32 | 12.04 | 27,174.25 | −3732.15 | 12.08 |
2011 | 23,256.7 | 27,423.85 | 4167.15 | 17.92 | 27,417.92 | 4161.22 | 17.89 | 27,422.42 | 4165.72 | 17.91 | 27,417.92 | 4161.22 | 17.89 |
2012 | 29,528.8 | 27,818.17 | −1710.63 | 5.79 | 27,663.78 | −1865.02 | 6.32 | 27,662.85 | −1865.95 | 6.32 | 27,663.78 | −1865.02 | 6.32 |
2013 | 27,957.9 | 28,158.21 | 200.31 | 0.72 | 27,911.84 | −46.06 | 0.16 | 27,905.39 | −52.51 | 0.19 | 27,911.84 | −46.06 | 0.16 |
2014 | 27,266.9 | 28,444.74 | 1177.84 | 4.32 | 28,162.12 | 895.22 | 3.28 | 28,150.05 | 883.15 | 3.24 | 28,162.12 | 895.22 | 3.28 |
2015 | 27,962.6 | 28,680.48 | 717.88 | 2.57 | 28,414.65 | 452.05 | 1.62 | 28,396.85 | 434.25 | 1.55 | 28,414.65 | 452.05 | 1.62 |
2016 | 32,466.4 | 28,869.04 | −3597.36 | 11.08 | 28,669.45 | −3796.95 | 11.70 | 28,645.83 | −3820.57 | 11.77 | 28,669.45 | −3796.95 | 11.70 |
2017 | 28,761.2 | 29,014.29 | 253.09 | 0.88 | 28,926.52 | 165.32 | 0.57 | 28,896.98 | 135.78 | 0.47 | 28,926.52 | 165.32 | 0.57 |
2018 | 27,462.5 | 29,120.10 | 1657.60 | 6.04 | 29,185.91 | 1723.41 | 6.28 | 29,150.34 | 1687.84 | 6.15 | 29,185.91 | 1723.41 | 6.28 |
MAPEsimulation (%) | 5.6366 | 6.4009 | 6.3887 | 6.4005 | |||||||||
2019 | 29,041 | 29,106.99 | 65.99 | 0.23 | 29,447.62 | 406.62 | 1.40 | 29,405.91 | 364.91 | 1.26 | 29,447.62 | 406.62 | 1.40 |
2020 | 31,605.2 | 29,112.08 | −2493.12 | 7.89 | 29,711.67 | −1893.53 | 5.99 | 29,663.73 | −1941.47 | 6.14 | 29,711.67 | −1893.53 | 5.99 |
2021 | 29,638.2 | 29,086.75 | −551.45 | 1.86 | 29,978.10 | 339.90 | 1.15 | 29,923.81 | 285.61 | 0.96 | 29,978.10 | 339.90 | 1.15 |
2022 | 27,088.1 | 29,034.33 | 1946.23 | 7.18 | 30,246.91 | 3158.81 | 11.66 | 30,186.17 | 3098.07 | 11.44 | 30,246.91 | 3158.81 | 11.66 |
2023 | 24,780 | 28,957.86 | 4177.86 | 16.86 | 30,518.14 | 5738.14 | 23.16 | 30,450.83 | 5670.83 | 22.88 | 30,518.14 | 5738.14 | 23.16 |
MAPEprediction (%) | 6.8041 | 8.6711 | 8.5370 | 8.5839 | |||||||||
MAPE (%) | 5.9439 | 6.9983 | 6.9540 | 6.9751 |
Years | 2024 | 2025 | 2026 | 2027 | 2028 |
---|---|---|---|---|---|
ID_T | 26,376.97 | 26,028.78 | 24,960.55 | 28,731.54 | 33,688.46 |
GM(1,1) | 30,791.79 | 31,067.90 | 31,346.48 | 31,627.57 | 31,911.17 |
DGM(1,1) | 30,717.80 | 30,987.12 | 31,258.80 | 31,532.87 | 31,809.33 |
NGBM(1,1) | 29,691.42 | 29,811.48 | 29,928.85 | 30,043.79 | 30,156.50 |
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Zhu, Z.; Wang, J.; Yu, K. IA-DTPSO: A Multi-Strategy Integrated Particle Swarm Optimization for Predicting the Total Urban Water Resources in China. Biomimetics 2025, 10, 233. https://doi.org/10.3390/biomimetics10040233
Zhu Z, Wang J, Yu K. IA-DTPSO: A Multi-Strategy Integrated Particle Swarm Optimization for Predicting the Total Urban Water Resources in China. Biomimetics. 2025; 10(4):233. https://doi.org/10.3390/biomimetics10040233
Chicago/Turabian StyleZhu, Zheyu, Jiawei Wang, and Kanhua Yu. 2025. "IA-DTPSO: A Multi-Strategy Integrated Particle Swarm Optimization for Predicting the Total Urban Water Resources in China" Biomimetics 10, no. 4: 233. https://doi.org/10.3390/biomimetics10040233
APA StyleZhu, Z., Wang, J., & Yu, K. (2025). IA-DTPSO: A Multi-Strategy Integrated Particle Swarm Optimization for Predicting the Total Urban Water Resources in China. Biomimetics, 10(4), 233. https://doi.org/10.3390/biomimetics10040233