Organizations: Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan · Sino-German College of Applied Sciences, Tongji University, Shanghai 200092, China · School of Mechanical Engineering, Tongji University, Shanghai 200092, China · Chongqing Institute of Microelectronics Industry Technology, University of Electronic Science and Technology of China, Chongqing 401332, China · Artificial Intelligence and Big Data College, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, China · Department of Information Engineering, Yantai Vocational College, Yantai 264670, China
Bound-constrained single-objective numerical optimisation remains a key benchmark for assessing the robustness and efficiency of evolutionary algorithms. This report documents RDEx-SOP, an exploitation-biased success-history differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session). RDEx-SOP combines success-history parameter adaptation, an exploitation-biased hybrid branch, and lightweight local perturbations to balance fast convergence and final solution quality under a strict evaluation budget. We evaluate RDEx-SOP on the official CEC 2025 SOP benchmark with the U-score framework (Speed and Accuracy categories). Experimental results show that RDEx-SOP achieves strong overall performance and statistically competitive final outcomes across the 29 benchmark functions.
Figures & tables
Rank
Algorithm
Total Score
Avg Score/Prob.
Speed
Accuracy
1
RDEx
81229.5
2801.02
76490.5
4739.0
2
LSRTDE
73664.5
2540.16
68007.5
5657.0
3
RDE
69459.0
2395.14
58066.0
11393.0
4
jSOa
44653.0
1539.76
20984.0
23669.0
5
mLSHADE_LR
44106.5
1520.91
25274.5
18832.0
6
IEACOP
15312.5
528.02
5635.5
9677.0
TABLE I: CEC 2025 SOP evaluation (median target): overall scores over 29 problems and 25 runs for the selected algorithm set.
Competitor
Final
TTT
AUC
W/T/L
Holm
A12
W/T/L
Holm
A12
W/T/L
Holm
A12
LSRTDE
4/24/1
2/27/0
0.48
17/12/0
10/19/0
0.73
23/6/0
21/8/0
0.79
jSOa
21/5/3
21/5/3
0.92
23/3/3
23/3/3
0.98
27/2/0
27/2/0
1.00
IEACOP
27/1/1
27/1/1
1.00
25/3/1
25/3/1
1.00
23/0/6
23/0/6
1.00
mLSHADE-LR
21/4/4
21/4/4
0.91
23/3/3
23/3/3
0.98
23/2/4
23/2/4
1.00
RDE
17/6/6
17/6/6
0.83
18/2/9
18/2/9
0.93
19/2/8
19/2/8
1.00
TABLE II: Pairwise summary over the 29 CEC2025 SOP functions (25 runs). For each metric (Final, TTT, and AUC), we report uncorrected per-function Wilcoxon W/T/L at α=0.05 , Holm-corrected W/T/L across the 29 functions, and the median Vargha–Delaney A12 effect size (larger is better for minimization).
Algorithm
Final
TTT
AUC
RDEx-SOP
2.26
1.84
1.76
LSRTDE
2.29
2.69
2.72
jSOa
3.79
4.43
4.97
IEACOP
5.83
4.95
4.03
mLSHADE-LR
4.07
4.36
4.48
RDE
2.76
2.72
3.03
TABLE III: Friedman tests on per-function medians over the 29 CEC2025 SOP functions (25 runs). Final: χ2=77.67 , df=5 , p=2.57E−15 ; TTT: χ2=63.85 , df=5 , p=1.94E−12 ; AUC: χ2=60.07 , df=5 , p=1.17E−11 . Lower average rank indicates better performance for each metric.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Problem
RDEx-SOP
LSRTDE
jSOa
IEACOP
mLSHADE-LR
RDE
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
0.00E+00
0.00E+00
0.00E+00
0.00E+00
=
4.55E-15
6.63E-15
=
2.85E-06
8.17E-07
+
0.00E+00
0.00E+00
=
0.00E+00
0.00E+00
=
2
0.00E+00
0.00E+00
0.00E+00
0.00E+00
=
4.32E-14
2.43E-14
+
1.20E-06
1.68E-06
+
5.00E-14
2.45E-14
+
0.00E+00
0.00E+00
=
3
5.90E+01
1.51E+00
5.66E+01
1.08E+01
=
5.86E+01
7.11E-15
-
1.91E+00
1.99E+00
-
6.93E+00
1.49E+01
-
2.18E+01
1.22E+00
-
4
3.82E+00
1.90E+00
3.10E+00
1.39E+00
=
1.07E+01
2.17E+00
+
2.99E+01
7.31E+00
+
8.08E+00
3.07E+00
+
7.72E+00
1.57E+00
+
5
2.36E-07
5.47E-07
5.89E-08
1.70E-07
=
1.23E-13
3.08E-14
=
1.32E-01
2.05E-01
+
2.95E-03
1.03E-02
=
0.00E+00
0.00E+00
=
Appendix
TABLE IV: Experimental comparison results between RDEx-SOP and other competitors on the 29 benchmark functions in CEC2025 SOP.
Problem
RDEx-SOP
LSRTDE
jSOa
IEACOP
mLSHADE-LR
RDE
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
538.2
4.1
578.2
3.8
+
785.2
148.1
+
1001.0
0.0
+
805.5
70.6
+
477.0
5.6
-
2
485.9
5.5
514.0
5.0
+
920.7
143.0
+
1001.0
0.0
+
980.5
51.5
+
412.4
4.5
-
3
1001.0
0.0
975.8
123.7
=
1001.0
0.0
=
114.0
41.1
-
811.2
93.9
-
739.9
42.7
-
4
675.7
73.9
705.8
38.3
+
999.0
7.7
+
1001.0
0.0
+
971.5
38.5
+
981.8
21.2
+
5
846.8
136.9
814.3
116.5
=
811.7
65.2
=
1001.0
0.0
+
1001.0
0.0
+
607.2
4.6
-
Appendix
TABLE V: Time-to-target comparison on the 29 CEC2025 SOP functions. The time-to-target is the first checkpoint index (1–1000) where the run reaches the median target (smaller is better); runs that never reach the target are assigned 1001.
Problem
RDEx-SOP
LSRTDE
jSOa
IEACOP
mLSHADE-LR
RDE
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
2.09
0.05
2.34
0.03
+
2.54
0.02
+
0.51
0.02
-
1.98
0.12
-
1.75
0.03
-
2
0.78
0.01
0.82
0.02
+
1.17
0.02
+
1.47
0.29
+
0.71
0.17
=
0.73
0.02
-
3
1.36
0.04
1.32
0.13
=
1.36
0.01
=
0.24
0.08
-
1.35
0.16
=
1.07
0.06
-
4
1.45
0.09
1.53
0.08
+
1.87
0.03
+
1.53
0.12
+
1.98
0.04
+
1.83
0.03
+
5
0.29
0.01
0.30
0.01
+
0.33
0.00
+
0.35
0.12
+
0.14
0.01
-
0.19
0.00
-
Appendix
TABLE VI: Anytime convergence comparison using AUC over 1000 checkpoints on the 29 CEC2025 SOP functions. For each run, AUC is computed as the mean of log10(1+max(ft−TGT,0)) across checkpoints (smaller is better).
Differential Evolution is a population-based optimizer that uses scaled differences between candidate solutions to search difficult numerical problems.
Constrained single-objective numerical optimisation requires both feasibility maintenance and strong objective-value convergence under limited evaluation budgets. This report documents RDEx-CSOP, a constrained differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session). RDEx-CSOP combines success-history parameter adaptation with an exploitation-biased hybrid search and an ε-constraint handling mechanism with a time-varying threshold. We evaluate RDEx-CSOP on the official CEC 2025 CSOP benchmark using the U-score framework (Speed, Accuracy, and Constraint categories). The results show that RDEx-CSOP achieves the highest total score and the best average rank among all released comparison algorithms, mainly through strong speed and competitive constraint-handling performance across the 28 benchmark functions.
Sichen Tao, Yifei Yang, Ruihan Zhao +3
Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5
Multiobjective optimisation in the CEC 2025 MOP track is evaluated not only by final IGD values but also by how quickly an algorithm reaches the target region under a fixed evaluation budget. This report documents RDEx-MOP, the reconstructed differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session) bound-constrained multiobjective track. RDEx-MOP integrates indicator-based environmental selection, a niche-maintained Pareto-candidate set, and complementary differential evolution operators for exploration and exploitation. We evaluate RDEx-MOP on the official CEC 2025 MOP benchmark using the released checkpoint traces and the median-target U-score framework. Experimental results show that RDEx-MOP achieves the highest total score and the best average rank among all released comparison algorithms, including the earlier RDEx baseline.
Sichen Tao, Yifei Yang, Ruihan Zhao +3
Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5
Constrained multiobjective optimisation requires fast feasibility attainment together with stable convergence and diversity preservation under strict evaluation budgets. This report documents RDEx-CMOP, the differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session) constrained multiobjective track. RDEx-CMOP integrates an ε-level feasibility schedule, a SPEA2-style indicator-driven fitness assignment, and a fitness-oriented current-to-pbest/1 mutation operator. We evaluate RDEx-CMOP on the official CEC 2025 CMOP benchmark using the median-target U-score framework and the released trace data. Experimental results show that RDEx-CMOP achieves the highest total score and the best overall average rank among all released comparison algorithms, with strong target-attainment behaviour and near-zero final violation on most problems.
Sichen Tao, Yifei Yang, Ruihan Zhao +3
Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5