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

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

cs.NEMar 28, 2026

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

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

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
Competitor	W/T/L	Holm	$A_{12}$	W/T/L	Holm	$A_{12}$	W/T/L	Holm	$A_{12}$
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

\alpha=0.05

, Holm-corrected W/T/L across the 29 functions, and the median Vargha–Delaney

A_{12}

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:

\chi^{2}=77.67

df=5

p=2.57E-15

; TTT:

\chi^{2}=63.85

df=5

p=1.94E-12

; AUC:

\chi^{2}=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

0.00E+00

4.55E-15

6.63E-15

2.85E-06

8.17E-07

0.00E+00

4.32E-14

2.43E-14

1.20E-06

1.68E-06

5.00E-14

2.45E-14

0.00E+00

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

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

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

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
Problem	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
Problem	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

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

across checkpoints (smaller is better).

Differential Evolution

Differential Evolution is a population-based optimizer that uses scaled differences between candidate solutions to search difficult numerical problems.

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RDEx-CMOP: Feasibility-Aware Indicator-Guided Differential Evolution for Fixed-Budget Constrained Multiobjective Optimization
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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

Mar 28, 2026J/K move · Enter open · S save

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

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

Constrained Optimization Differential Evolution

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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.

Abstract

Differential Evolution

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