REMBGO for Evaluation-Limited Optimization: CEC2022 Benchmarking and EAF-STATCOM Generalization

Vikram Chekuri; Narapareddy Ramarao; Prashanth N A

cs.NEOct 9, 2026

REMBGO for Evaluation-Limited Optimization: CEC2022 Benchmarking and EAF-STATCOM Generalization

Authors: Vikram Chekuri, Narapareddy Ramarao, Prashanth N A

Organizations: Department of Electrical and Electronics Engineering, BMS Institute of Technology and Management, Bengaluru, Karnataka, India · Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India

Abstract

Metaheuristic comparisons are often reported at evaluation budgets far larger than an expensive engineering simulation can afford. This paper presents REMBGO, an evaluation-budget-aware refinement of EMBGO. Its contribution is not any single operator: it is the integration of population preservation, scale-normalized exploration and recovery mechanisms whose parent-relative benefit is concentrated under restricted function-evaluation budgets. REMBGO is evaluated on CEC2022 at a primary, application-aligned budget of 1040 function evaluations, with a surrounding budget ladder reported descriptively to characterise budget dependence rather than as a family of controlled hypotheses. A component-removal study finds no individual mechanism whose removal survives multiplicity correction, consistent with an integrated rather than a single-operator contribution. The algorithm is then applied to EAF--STATCOM controller tuning, and the resulting frozen gain vectors are transferred without retuning to twenty pre-specified unseen stochastic arc realizations ( $210$ fixed-gain simulations, all feasible). The selected gain-vector main effect accounts for only $3.6$ -- $5.8\%$ of the crossed validation variation, against approximately $61.4\%$ for interaction plus residual, and the matched REMBGO--EMBGO paired differences are controller-dependent in sign and not statistically significant. REMBGO is therefore presented as a resource-aware refinement whose benefit must be stated together with the evaluation budget, not as a universally superior optimizer.

Figures & tables

Parameter	Symbol	Value
Elite count	$K_{e}$	3
Radius scale	$\delta$	$\mathcal{U}(0.8,1.2)$
Radius decay	$\rho(\tau)$	$1.5\rightarrow 0.8$
Step gain	$\lambda$	$0.02\rightarrow 0.003$
Lévy exponent	$\beta_{L}$	1.5
Opposition probability	$p_{o}$	0.10

Table 1: Default REMBGO control parameters. The Cauchy and triple-leader probabilities, elite count and restart fraction are varied only in the sensitivity analysis of Supplementary Material S2.

Figure 1: Friedman mean rank of the five optimizers against the evaluation budget, for

D{=}10

(left) and

D{=}20

(right); lower mean rank is better. The dashed vertical marker identifies the exact

1040

-evaluation application budget.

$D$	FEs	PSO	GWO	FP-SHADE	EMBGO	REMBGO	Best	Friedman $p$	W/T/L
10	200	1.917	1.917	4.083	4.417	2.667	PSO/GWO	1.93e-05	10/2/0
10	1040	2.750	2.833	4.000	3.167	2.250	REMBGO	0.0892	4/6/2
10	200000	2.542	4.917	1.625	2.625	3.292	FP-SHADE	1.07e-06	0/9/3
20	125	2.250	1.250	4.583	4.333	2.583	GWO	7.66e-08	10/2/0
20	1040	2.500	2.250	3.833	3.833	2.583	GWO	0.0224	9/1/2
20	1000000	2.542	4.917	1.542	2.875	3.125	FP-SHADE	3.82e-06	0/8/4

Table 2: Representative benchmark rungs across the three budget regimes; lower mean rank is better and Best names the optimizer with the lowest observed mean rank. W/T/L reports REMBGO better / no significant difference / EMBGO better over the twelve functions after within-budget Holm correction; the full ladder is in Supplementary Material S1.

Figure 2: Holm-corrected paired function-level comparison between REMBGO and EMBGO across evaluation budgets. Green, grey and red mark functions significantly favouring REMBGO, with no significant difference, and favouring EMBGO, respectively; correction is applied across the twelve functions at each budget.

Removed component	Rank $D{=}10$	Rank $D{=}20$	$\Delta\log_{10}$ $D{=}10$	$\Delta\log_{10}$ $D{=}20$	Holm $p$ $D{=}10$	Holm $p$ $D{=}20$
Elitism	3.583	4.833	$-0.0411$	$-0.0064$	0.617	1.000
Weighted centroid	5.167	5.083	$-0.0058$	$-0.0015$	1.000	1.000
Normalized/decaying radius	6.667	6.500	$+0.0043$	$+0.0053$	1.000	1.000
Opposition	3.917	2.583	$-0.0380$	$-0.0527$	0.617	0.098
Cauchy mutation	7.583	8.167	$+0.0181$	$+0.0520$	1.000	1.000
Triple leader	7.833	8.000	$+0.0092$	$+0.0423$	1.000	0.068

Table 3: Component-removal results at the exact

1040

-evaluation budget; the removed elements include both retained and refined parts of REMBGO. Positive median

\Delta\log_{10}

error indicates degradation after removal, negative a descriptive improvement. No removal is significant after the suite-level Holm correction across the ten planned contrasts.

Figure 3: Component-removal penalties for REMBGO at the exact

1040

-evaluation budget (

D{=}10

left,

D{=}20

right). Positive values indicate degradation after removal, negative a descriptive improvement; no removal is significant after the suite-level Holm correction across the ten planned contrasts.

Figure 4: Fixed-gain generalization across twenty unseen stochastic EAF arc realizations for the five selected gain vectors of each controller. The first two panels show the validation objective distributions for the DQ-PI and Lyapunov controllers over the twenty pre-specified corrected arc realizations; the final panel partitions the crossed variation into arc-realization, gain-vector and interaction-plus-residual components. The corrected base-

42

reference case is excluded. No re-optimization is performed and no optimizer ranking is implied.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

$D$	FEs	PSO	GWO	FP-SHADE	EMBGO	REMBGO	Best	Friedman $p$	W/T/L
10	200	1.917	1.917	4.083	4.417	2.667	PSO/GWO	1.93e-05	10/2/0
10	316	2.417	1.750	4.167	4.083	2.583	GWO	1.89e-04	8/4/0
10	502	2.583	2.083	4.000	3.917	2.417	GWO	4.06e-03	6/5/1
10	796	2.417	2.333	4.000	3.500	2.750	GWO	0.0393	3/7/2
10	840	2.583	2.500	4.083	3.417	2.417	REMBGO	0.0382	3/7/2
10	1040	2.750	2.833	4.000	3.167	2.250	REMBGO	0.0892	4/6/2

Appendix

Table S1 : Complete five-optimizer CEC2022 evaluation-budget ladder. Mean Friedman ranks, lowest-mean-rank optimizer, per-rung omnibus Friedman

p

, and Holm-corrected REMBGO-vs-EMBGO win/tie/loss over the twelve functions. Source: archived CEC2022 budget-ladder result set.

Parameter	Value	Rank $D{=}10$	$\Delta\log_{10}$ $D{=}10$	Rank $D{=}20$	$\Delta\log_{10}$ $D{=}20$
Cauchy probability	0.1	2.167	$-0.0348$	2.833	$+0.0139$
	$0.2^{\ast}$	2.833	$\phantom{+}0.0000$	3.000	$\phantom{+}0.0000$
	0.3	3.000	$-0.0009$	2.167	$-0.0329$
	0.4	2.000	$-0.0107$	2.000	$-0.0337$
Elite count	1	2.500	$-0.0309$	2.500	$-0.0130$
	2	2.667	$-0.0018$	1.667	$-0.0230$

Appendix

Table S2 : REMBGO sensitivity at the exact

1040

-evaluation budget. Within each swept factor the ranks are computed across that factor’s settings; the default value (marked ∗ ) defines the zero of

\Delta\log_{10}

. Source: archived

1040

-evaluation sensitivity result set.

Figure S1 : REMBGO one-factor-at-a-time sensitivity at the exact

1040

-evaluation budget for

D{=}10

and

D{=}20

. The selected default of each factor is marked; nearby settings are descriptively better or worse without a consistent improvement across both dimensions.

Table S3 : Selected minimum-

J_{\mathrm{tot}}

gain vectors replayed in the fixed-gain transfer study, one per optimizer and controller. For DQ-PI the reactive integral gain follows

K_{i,Q}=K_{p,Q}/T_{i,Q}

and is not listed separately. Values are the archived stochastic-tuning champions; each reproduces the tabulated

J_{\mathrm{train}}

of Table S4 on replay.

Controller	Optimizer	$J_{\mathrm{train}}$	Val. mean	Val. SD	Val. median	Mean shift	Corr. base-42
DQ-PI	PSO	0.406577	0.416711	0.023752	0.409602	$+0.010133$	0.402806
	GWO	0.402520	0.419252	0.025181	0.411996	$+0.016732$	0.419992
	FP-SHADE	0.413838	0.407128	0.021850	0.410386	$-0.006710$	0.388682
	EMBGO	0.412499	0.413542	0.017652	0.408077	$+0.001044$	0.426294
	REMBGO	0.411379	0.419498	0.030625	0.413860	$+0.008119$	0.399341
Lyapunov	PSO	0.310776	0.343695	0.016917	0.345919	$+0.032919$	0.353066

Appendix

Table S4 : Fixed-gain replay of the ten selected minimum-

J_{\mathrm{tot}}

vectors.

J_{\mathrm{train}}

is the tuning-arc score; validation columns summarise

J_{\mathrm{tot}}

over the twenty pre-registered corrected unseen arcs; mean shift is validation mean minus

J_{\mathrm{train}}

, where

J_{\mathrm{train}}

is the STO-SR tuning-arc score recorded during the original campaign. The final column is the corrected base-

42

realization, reported as a reference case only and excluded from every validation statistic; it is not a reproduction of the STO-SR tuning trajectory. Source: the corrected-generator campaign dataset, 200 unseen rows.

Controller	Mean	Median	$95\%$ CI	Signed-rank $p$	Signs
DQ-PI	$+0.005956$	$+0.001871$	$[-0.005184,+0.007000]$	0.4980	8/0/12
Lyapunov	$-0.008843$	$-0.006007$	$[-0.019601,+0.004355]$	0.1650	12/0/8

Appendix

Table S5 : Matched REMBGO

-

EMBGO fixed-gain paired difference across the twenty unseen arcs (positive means the REMBGO vector has the larger, worse

J_{\mathrm{tot}}

). CI is a

10{,}000

-resample percentile bootstrap;

p

is the two-sided exact signed-rank test; signs are REMBGO better / ties / REMBGO worse. Source: the corrected-generator campaign dataset.

Controller	Arc realization	Gain vector	Interaction $+$ residual	Fixed-vector Friedman $p$	Kendall $W$
DQ-PI	34.98%	3.64%	61.38%	0.641	0.031
Lyapunov	32.79%	5.75%	61.46%	0.585	0.036

Appendix

Table S6 : Crossed-variation decomposition of the fixed-gain validation objective over the twenty unseen arcs and five selected vectors. Percentages are shares of the total sum of squares; the fixed-vector Friedman test and Kendall’s

W

are descriptive checks over post-selected champions. Source: the corrected-generator campaign dataset.

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