RDEx-CSOP: Feasibility-Aware Reconstructed Differential Evolution with Adaptive epsilon-Constraint Ranking

Sichen Tao; Yifei Yang; Ruihan Zhao; Kaiyu Wang; Sicheng Liu; Shangce Gao

cs.NEMar 28, 2026

RDEx-CSOP: Feasibility-Aware Reconstructed Differential Evolution with Adaptive epsilon-Constraint Ranking

Authors: Sichen Tao, Yifei Yang, Ruihan Zhao, Kaiyu Wang, Sicheng Liu, Shangce Gao

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

Abstract

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.

Figures & tables

Rank	Algorithm	Total Score	Avg Score/Prob.	Speed	Accuracy	Constraint
1	RDEx-CSOP	53680.5	1917.16	44437.0	3440.0	5803.5
2	RDEx	49155.0	1755.54	39695.5	3730.5	5729.0
3	UDEIII	30545.0	1090.89	22368.5	3093.0	5083.5
4	CL-SRDE	28805.5	1028.77	19673.0	3245.5	5887.0

TABLE I: CEC 2025 CSOP evaluation (median target): overall scores over 28 problems and 25 runs for all released comparison algorithms.

Competitor	Final Q			TTT
Competitor	W/T/L	Holm	$A_{12}$	W/T/L	Holm	$A_{12}$
RDEx	1/26/1	1/27/0	0.52	4/24/0	1/27/0	0.58
UDEIII	16/4/8	15/5/8	0.84	19/3/6	19/3/6	0.89
CL-SRDE	6/18/4	6/19/3	0.50	24/4/0	23/5/0	0.92

TABLE II: Primary pairwise summary over the 28 CEC2025 CSOP functions (25 runs). We report uncorrected per-function Wilcoxon W/T/L at

\alpha=0.05

, Holm-corrected W/T/L across functions, and the median Vargha–Delaney

A_{12}

effect size for feasibility-aware final quality and time-to-target (larger is better for minimization).

Algorithm	Final Q	TTT
RDEx-CSOP	2.29	1.61
RDEx	2.39	2.14
UDEIII	2.84	2.89
CL-SRDE	2.48	3.36

TABLE III: Primary Friedman tests on per-function medians over the 28 CEC2025 CSOP functions (25 runs). Final Q:

\chi^{2}=2.90

df=3

p=0.408

; TTT:

\chi^{2}=30.47

df=3

p=2.62E-06

. Lower average rank indicates better performance.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Rank	Algorithm	Total Rank	Avg Rank/Prob.	Avg Speed	Avg Accuracy	Avg Constraint
1	RDEx-CSOP	38.0	1.36	1.59	2.75	2.52
2	RDEx	63.0	2.25	2.20	2.30	2.52
3	UDEIII	83.0	2.96	2.89	2.48	2.41
4	CL-SRDE	96.0	3.43	3.32	2.46	2.55

Appendix

TABLE IV: CEC 2025 CSOP evaluation (median target): average rankings over 28 problems (lower is better) for all released comparison algorithms.

Problem	RDEx-CSOP		RDEx			UDEIII			CL-SRDE
Problem	Mean	SD	Mean	SD	W	Mean	SD	W	Mean	SD	W
1	3.27E-30	4.75E-30	5.92E-30	9.27E-30	=	1.57E-28	9.70E-29	+	1.26E-31	6.18E-31	=
2	3.74E-30	5.62E-30	3.04E-30	4.86E-30	=	1.31E-28	7.83E-29	+	7.24E-31	2.42E-30	=
3	2.56E+02	7.36E+01	3.39E+02	1.63E+02	=	9.22E+01	5.54E+01	-	5.37E+02	1.07E+02	+
4	1.54E+01	1.42E+00	1.57E+01	1.45E+00	=	6.51E+00	6.78E+00	-	4.84E+01	8.86E+00	+
5	0.00E+00	0.00E+00	0.00E+00	0.00E+00	=	1.17E-28	4.17E-28	=	0.00E+00	0.00E+00	=

Appendix

TABLE V: Feasibility-aware final-quality comparison on the 28 CEC2025 CSOP functions. For each run, the final-quality score equals the final objective/IGD value for feasible runs and

B_{p}+\mathrm{CV}

for infeasible runs, where

B_{p}

is the largest finite final objective/IGD value on problem

p

plus

1

(smaller is better).

Problem	RDEx-CSOP		RDEx			UDEIII			CL-SRDE
Problem	Mean	SD	Mean	SD	W	Mean	SD	W	Mean	SD	W
1	1332.6	546.2	1382.6	548.3	=	1979.6	105.0	+	1327.4	137.8	=
2	1251.2	514.8	1298.5	527.0	=	1960.7	138.2	+	1399.3	222.3	+
3	1575.3	541.4	1813.9	272.3	=	394.8	162.1	-	2001.0	0.0	+
4	1607.4	529.8	1569.9	496.5	=	837.6	50.4	-	2001.0	0.0	+
5	986.2	12.0	986.6	13.9	=	1476.4	466.1	+	1395.2	14.8	+

Appendix

TABLE VI: Time-to-target comparison on the 28 CEC2025 CSOP functions. TTT is the first checkpoint index where the run reaches the median target (smaller is better); runs that never reach the target are assigned 2001.

Competitor	Final Obj.			Final CV			AUC
Competitor	W/T/L	Holm	$A_{12}$	W/T/L	Holm	$A_{12}$	W/T/L	Holm	$A_{12}$
RDEx	1/27/0	1/27/0	0.54	1/26/1	0/28/0	0.50	1/27/0	1/27/0	0.55
UDEIII	14/7/7	14/7/7	0.73	22/5/1	21/6/1	1.00	15/4/9	14/6/8	0.73
CL-SRDE	10/16/2	10/17/1	0.51	2/22/4	2/22/4	0.50	28/0/0	28/0/0	1.00

Appendix

TABLE VII: Complementary pairwise summary over the 28 CEC2025 CSOP functions (25 runs). For each metric (Final Obj., Final CV, and AUC), we report uncorrected per-function Wilcoxon W/T/L at

\alpha=0.05

, Holm-corrected W/T/L across functions, and the median Vargha–Delaney

A_{12}

effect size (larger is better for minimization).

Algorithm	Final Obj.	Final CV	AUC
RDEx-CSOP	2.11	2.21	1.75
RDEx	2.46	2.20	1.96
UDEIII	2.66	3.62	2.57
CL-SRDE	2.77	1.96	3.71

Appendix

TABLE VIII: Complementary Friedman tests on per-function medians over the 28 CEC2025 CSOP functions (25 runs). Final Obj.:

\chi^{2}=4.25

df=3

p=0.234

; Final CV:

\chi^{2}=29.00

df=3

p=4.82E-06

; AUC:

\chi^{2}=39.13

df=3

p=7.74E-08

. Lower average rank indicates better performance for each metric.

Problem	RDEx-CSOP		RDEx			UDEIII			CL-SRDE
Problem	Mean	SD	Mean	SD	W	Mean	SD	W	Mean	SD	W
1	3.27E-30	4.75E-30	5.92E-30	9.27E-30	=	1.57E-28	9.70E-29	+	1.26E-31	6.18E-31	=
2	3.74E-30	5.62E-30	3.04E-30	4.86E-30	=	1.31E-28	7.83E-29	+	7.24E-31	2.42E-30	=
3	2.56E+02	7.36E+01	3.39E+02	1.63E+02	=	9.22E+01	5.54E+01	-	5.37E+02	1.07E+02	+
4	1.54E+01	1.42E+00	1.57E+01	1.45E+00	=	6.51E+00	6.78E+00	-	4.84E+01	8.86E+00	+
5	0.00E+00	0.00E+00	0.00E+00	0.00E+00	=	1.17E-28	4.17E-28	=	0.00E+00	0.00E+00	=

Appendix

TABLE IX: Final objective comparison on the 28 CEC2025 CSOP functions. For each algorithm, the mean and SD over 25 runs are reported;

W

gives the Wilcoxon outcome of RDEx-CSOP against the competitor.

Problem	RDEx-CSOP		RDEx			UDEIII			CL-SRDE
Problem	Mean	SD	Mean	SD	W	Mean	SD	W	Mean	SD	W
1	-2.70E+05	0.00E+00	-2.70E+05	0.00E+00	=	0.00E+00	0.00E+00	+	-2.70E+05	0.00E+00	=
2	-2.70E+05	0.00E+00	-2.70E+05	0.00E+00	=	0.00E+00	0.00E+00	+	-2.70E+05	0.00E+00	=
3	-1.99E+05	1.85E+04	-1.85E+05	1.90E+04	+	0.00E+00	0.00E+00	+	-1.52E+05	2.11E+04	+
4	-4.45E+00	3.34E+00	-5.01E+00	3.12E+00	=	0.00E+00	0.00E+00	+	-2.01E+01	3.74E+00	-
5	-2.14E+03	0.00E+00	-2.14E+03	0.00E+00	=	0.00E+00	0.00E+00	+	-2.14E+03	0.00E+00	=

Appendix

TABLE X: Final constraint-violation comparison on the 28 CEC2025 CSOP functions. For each algorithm, the mean and SD over 25 runs are reported;

W

gives the Wilcoxon outcome of RDEx-CSOP against the competitor.

Problem	RDEx-CSOP		RDEx			UDEIII			CL-SRDE
Problem	Mean	SD	Mean	SD	W	Mean	SD	W	Mean	SD	W
1	0.17	0.01	0.17	0.00	=	0.14	0.01	-	0.32	0.01	+
2	0.20	0.01	0.20	0.01	=	0.14	0.01	-	0.38	0.01	+
3	1.87	0.65	2.18	0.50	=	0.50	0.18	-	3.15	0.11	+
4	0.78	0.24	0.84	0.32	=	0.81	0.04	=	1.80	0.08	+
5	0.36	0.01	0.36	0.01	=	0.30	0.01	-	0.60	0.02	+

Appendix

TABLE XI: Anytime convergence comparison using AUC over 2000 checkpoints on the 28 CEC2025 CSOP functions. For each run, AUC is computed as the mean of

\log_{10}(1+\max(f_{t}-\mathrm{TGT},0))

across checkpoints (smaller is better).

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RDEx-SOP: Exploitation-Biased Reconstructed Differential Evolution for Fixed-Budget Bound-Constrained Single-Objective Optimization

Sichen Tao, Yifei Yang, Ruihan Zhao, Kaiyu Wang+2

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

Differential Evolution Constrained Optimization

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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.

Abstract

Constrained Optimization

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