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
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.
Figures & tables
Rank
Algorithm
Total Score
Avg Score/Prob.
Speed
Accuracy
1
RDEx-MOP
36343.5
3634.35
36343.5
0.0
2
RDEx
35956.5
3595.65
35956.5
0.0
3
TFBCEIBEA
15439.0
1543.90
7196.5
8242.5
4
TEMOFNSGA3
13811.5
1381.15
3811.5
10000.0
5
TGFMMOEA
11690.5
1169.05
2633.0
9057.5
TABLE I: CEC 2025 MOP evaluation (median target): overall scores over 10 problems and 30 runs for all released comparison algorithms.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Rank
Algorithm
Total Rank
Avg Rank/Prob.
Avg Speed
Avg Accuracy
1
RDEx-MOP
14.0
1.40
1.40
4.50
2
RDEx
16.0
1.60
1.60
4.50
3
TFBCEIBEA
34.0
3.40
3.50
2.50
4
TEMOFNSGA3
42.0
4.20
4.15
1.50
5
TGFMMOEA
44.0
4.40
4.35
2.00
Appendix
TABLE II: CEC 2025 MOP evaluation (median target): average rankings over 10 problems (lower is better) for all released comparison algorithms.
Competitor
Final IGD
TTT
AUC
W/T/L
Holm
A12
W/T/L
Holm
A12
W/T/L
Holm
A12
RDEx
2/8/0
0/10/0
0.55
2/8/0
0/10/0
0.52
0/9/1
0/10/0
0.45
TEMOFNSGA3
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
TFBCEIBEA
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
TGFMMOEA
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
10/0/0
10/0/0
1.00
Appendix
TABLE III: Complementary pairwise summary over the 10 CEC2025 MOP functions (30 runs). For each metric (Final IGD, TTT, and AUC), we report uncorrected per-function Wilcoxon W/T/L at α=0.05 , Holm-corrected W/T/L across functions, and the median Vargha–Delaney A12 effect size (larger is better for minimization).
Algorithm
Final IGD
TTT
AUC
RDEx-MOP
1.40
1.50
1.80
RDEx
1.60
1.50
1.20
TEMOFNSGA3
4.00
4.00
4.20
TFBCEIBEA
3.80
4.00
3.70
TGFMMOEA
4.20
4.00
4.10
Appendix
TABLE IV: Complementary Friedman tests on per-function medians over the 10 CEC2025 MOP functions (30 runs). Final IGD: χ2=30.40 , df=4 , p=7.30E−06 ; TTT: χ2=30.00 , df=4 , p=8.63E−06 ; AUC: χ2=31.28 , df=4 , p=5.07E−06 . Lower average rank indicates better performance for each metric.
Problem
RDEx-MOP
RDEx
TEMOFNSGA3
TFBCEIBEA
TGFMMOEA
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
1.06E+01
1.34E-02
1.06E+01
1.37E-02
=
1.51E+01
1.42E+00
+
1.34E+01
9.01E-01
+
1.54E+01
1.70E+00
+
2
4.22E-02
1.95E-03
4.30E-02
2.47E-03
=
2.42E+00
1.56E+00
+
3.10E+00
3.15E+00
+
5.13E+01
3.09E+01
+
3
4.29E-01
3.12E-01
3.66E-01
2.81E-01
=
1.67E+01
1.13E+00
+
1.75E+01
9.05E-01
+
1.77E+01
1.15E+00
+
4
4.09E-01
3.44E-05
4.09E-01
3.48E-05
=
4.56E-01
1.32E-01
+
8.40E-01
4.97E-01
+
4.46E-01
9.71E-02
+
5
1.09E-01
3.17E-02
1.25E-01
3.84E-02
=
1.13E+00
7.09E-01
+
1.07E+00
6.98E-01
+
1.60E+00
7.10E-01
+
Appendix
TABLE V: Final IGD comparison on the 10 CEC2025 MOP functions. For each algorithm, the mean and SD over 30 runs are reported; W gives the Wilcoxon outcome of RDEx-MOP against the competitor.
Problem
RDEx-MOP
RDEx
TEMOFNSGA3
TFBCEIBEA
TGFMMOEA
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
4.4
0.9
4.3
1.3
=
490.9
42.0
+
406.2
149.1
+
489.5
44.1
+
2
5.0
1.1
5.1
1.1
=
457.1
98.1
+
405.7
172.2
+
472.0
108.9
+
3
2.3
0.4
2.6
0.7
+
411.5
137.0
+
474.7
100.6
+
461.2
101.1
+
4
2.5
0.5
2.7
0.5
=
469.3
62.1
+
483.0
59.2
+
474.8
70.1
+
5
3.5
0.5
3.3
0.5
=
454.2
97.5
+
399.6
161.8
+
490.4
43.6
+
Appendix
TABLE VI: Time-to-target comparison on the 10 CEC2025 MOP functions. TTT is the first checkpoint index (1–500) where the run reaches the median target (smaller is better); runs that never reach the target are assigned 501.
Problem
RDEx-MOP
RDEx
TEMOFNSGA3
TFBCEIBEA
TGFMMOEA
Mean
SD
Mean
SD
W
Mean
SD
W
Mean
SD
W
Mean
SD
W
1
0.00
0.00
0.00
0.00
=
0.60
0.17
+
0.31
0.17
+
0.61
0.16
+
2
0.00
0.00
0.00
0.00
=
0.51
0.23
+
0.45
0.34
+
1.37
0.31
+
3
0.00
0.00
0.00
0.00
=
0.34
0.14
+
0.40
0.16
+
0.48
0.13
+
4
0.00
0.00
0.00
0.00
=
0.09
0.05
+
0.16
0.09
+
0.08
0.06
+
5
0.00
0.00
0.00
0.00
=
0.28
0.11
+
0.25
0.13
+
0.39
0.08
+
Appendix
TABLE VII: Anytime convergence comparison using AUC over 500 checkpoints on the 10 CEC2025 MOP functions. For each run, AUC is computed as the mean of log10(1+max(ft−TGT,0)) across checkpoints (smaller is better).
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
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.
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 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