COAUTHOR BRIEF · 10-SEED CHECKPOINT

What a permutation model learns depends on what we ask it to optimize.

The same makespan can hide radically different flow time. The question is not simply which EDA wins—but which representation preserves useful disagreement when objectives conflict.

Working thesis

COIN may converge more slowly on a scalar landscape, yet positive–negative structural learning can become an advantage on a Pareto surface.

Singlemixed→MOpromising

research tension

Equal makespan does not mean equal schedules.

A

Makespan

When does the final job leave the final machine?

≠

B

Total flow time

How long does every job remain inside the system?

Two permutations can tie on A while separating strongly on B. Multi-objective analysis exposes structure erased by a scalar score.

flow-shop objective

Makespan

M1

J1J2J3J4

M2

J1J2J3J4

M3

J1J2J3J4

time completion events

Cmax = C(n,m)

How soon does the complete production schedule finish?

What the objective measures

Makespan is the completion time of the last scheduled job on the final machine. It emphasizes the critical path and the end of the schedule rather than the experience of every job.

Representation hypothesis

Adjacency can preserve transitions that compress the critical path. Starting-node information may matter when early blocking propagates through many machines.

flow-shop objective

Total flow time

M1

J1J2J3J4

M2

J1J2J3J4

M3

J1J2J3J4

time completion events

TFT = Σᵢ₌₁ⁿ C(i,m)

How long do all jobs remain in the production system?

What the objective measures

Total flow time sums the final-machine completion time of every job. Moving several jobs earlier can improve TFT even when the final makespan remains unchanged.

Representation hypothesis

Absolute position carries direct signal because every early completion contributes repeatedly to the sum. Node-position models should therefore have a natural advantage.

flow-shop objective

Internal machine idle time

M1

J1J2J3J4

M2

J1J2J3J4

M3

J1J2J3J4

time completion events

Iinternal = Σₖ [C(n,k) − S(1,k) − Σᵢ p(i,k)]

Where does productive work stop between the first start and the last completion on each machine?

What the objective measures

The evaluator excludes idle time before a machine first starts and after it finishes its last job. It sums only internal gaps created by blocking and uneven transitions.

Representation hypothesis

Idle gaps depend on both where jobs appear and how their processing profiles relate to nearby jobs. ROSE can model absolute position together with signed pairwise displacement, giving it a plausible structural advantage.

objective pairs

Pair the objective conflict with its representation

Comparison	Structural tension	Edge representation	Node representation	Hybrid question
A × BMakespan ↔ Total flow time	Final completion horizon versus cumulative job residence.	Edges may compress machine-to-machine continuity.	Early positions may reduce many completion times.	Can adjacency and early placement be retained together?
A × CMakespan ↔ Machine idle time	Finish early versus keep machines continuously utilized.	Transitions may reduce local blocking and gaps.	Specific jobs at critical positions may control idle periods.	Which signal changes across early and late schedule contexts?
B × CTotal flow time ↔ Machine idle time	Move jobs through quickly versus reduce unused machine capacity.	Local continuity may lower idle time without optimizing every completion.	Front-loading certain jobs may dominate total flow time.	Does the useful representation switch across the front?
A × B × CThree objectives ↔ Pareto surface	Several incompatible schedule structures must coexist.	Captures reusable local building blocks.	Captures global placement regularities.	Can context select the representation without collapsing diversity?

Edge baseline

COIN

RepresentationDirected successor edges

current node → next unused node

Green edge · Orange position · Blue retained template

How it samples: Start anywhere; repeatedly sample the next unused node from the current node’s row.
What it learns: Rewards edges repeated by good solutions and punishes edges repeated by bad solutions.
Objective hypothesis: Strong when adjacency carries objective signal; slower scalar convergence may preserve alternatives for MO.

Edge + template

COIN/WT

RepresentationDirected edges with punched parent

2?4?1

retain

sample

retain

sample

retain

↓ edge-guided repair

Green edge · Orange position · Blue retained template

How it samples: Keep part of a selected permutation, then regenerate missing nodes from the edge matrix.
What it learns: Combines edge evidence with explicit memory from one existing solution.
Objective hypothesis: Exploitation rises; useful when good building blocks should survive regeneration.

Node baseline

NB-COIN

RepresentationPosition → node associations

random position → unused node

Green edge · Orange position · Blue retained template

How it samples: Visit positions in random order and sample an unused node for each position.
What it learns: Rewards and punishes job placements rather than adjacency.
Objective hypothesis: Matches objectives with absolute positional regularities; random position order reduces fixed-chain bias.

Node + template

NB-COIN/WT

RepresentationPosition model with punched parent

2?4?1

retain

sample

retain

sample

retain

↓ position-guided repair

Green edge · Orange position · Blue retained template

How it samples: Retain selected positions, then fill holes from the node-position model.
What it learns: Combines placement frequency with direct template inheritance.
Objective hypothesis: A stronger exploitative node learner; may converge quickly but lose MO diversity.

Ordered node

CNB-COIN

RepresentationPosition → node, fixed position chain

p1→p2→p3→p4→p5

fixed construction order

Green edge · Orange position · Blue retained template

How it samples: Generate positions from the first to the last instead of visiting positions randomly.
What it learns: The same node-position evidence as NB-COIN, exposed through an ordered construction path.
Objective hypothesis: Tests whether construction order—not representation alone—changes what the model can learn.

Start-aware edge

SNE-COIN

RepresentationStart node + directed successor edges

STARTπ₁

↓ chooses first node

Green edge · Orange position · Blue retained template

How it samples: Learn the first node explicitly, then continue through the edge model.
What it learns: Separates where a permutation begins from which nodes should be adjacent.
Objective hypothesis: Useful when early jobs have distinct objective effects that ordinary cyclic edge learning hides.

Hybrid node–edge

HNE-COIN

RepresentationNode and edge evidence through a template

NODE

context
selector

EDGE

template context decides which signal fills each hole

Green edge · Orange position · Blue retained template

How it samples: A partial parent determines context; missing values are regenerated using node and edge signals.
What it learns: Allows position and adjacency representations to compete within one constructive process.
Objective hypothesis: An early form of context-aware EDA: representation choice is already conditioned by retained structure.

Chained hybrid

CNE-COIN

RepresentationNode decision followed by edge continuation

1Node context

→

2Edge continuation

→

2 → 7 → 4 → 1

Green edge · Orange position · Blue retained template

How it samples: Use node evidence to establish context, then extend the permutation through edge relations.
What it learns: Connects absolute placement and local adjacency sequentially rather than blending them uniformly.
Objective hypothesis: Tests whether representation order creates a better bridge between scalar exploitation and MO diversity.

mechanism

Why negative learning may matter more in MO

Good population

shared edges

shared positions

reward
→
learn similarity

COIN model

punish
←
learn difference

Bad population

repeated failures

collapsed patterns

COIN learns what good solutions share and what bad solutions repeat—potentially retaining useful structural contrast across a Pareto set.

edge histogram EDA

EHBSA/WO and EHBSA/WT

2H(2,7)7H(7,4)4

H(a,b) ∝ ε + Σₓ∈S 𝟙[xₖ=a ∧ xₖ₊₁=b]

Representation

A directed adjacency matrix H(a,b) estimates how often job b follows job a in the selected population.

Learning and sampling

The model accumulates local successor evidence. WO samples a complete permutation from H. WT retains part of a selected parent and uses H to reconstruct the missing positions.

Structural bias

The representation preserves local linkage but does not directly encode the absolute position of a job.

node histogram EDA

NHBSA/WO and NHBSA/WT

H(i,j) ∝ ε + Σₓ∈S 𝟙[xᵢ=j]

Representation

A position-by-job matrix H(i,j) estimates the probability of assigning job j to position i.

Learning and sampling

WO samples unused jobs from successive position distributions. WT keeps selected positions from a parent and fills each remaining position from the learned matrix.

Structural bias

The model captures absolute placement directly but represents adjacency only through correlations that the matrix cannot retain.

multi-reference mean ROSE

ROSE/WO and ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

target(j) = meanᵣ∈C [pos(r)+μ(r,j)]

Representation

ROSE models absolute placement together with signed relational displacement between pairs of jobs.

Learning and sampling

For selected permutations, it records node-position probabilities and the count, mean, standard deviation, minimum and maximum of Δ(a,b)=pos(b)−pos(a). Multi-reference sampling averages the positions predicted by recent placed jobs. WT starts from a punched template while WO constructs from an empty permutation.

Structural bias

Several reference jobs jointly predict a target position. The compact estimators require O(n²) memory.

single-reference range ROSE

SR-ROSE/WO and SR-ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

d ~ TruncNormal(μᵣⱼ,σᵣⱼ; minᵣⱼ,maxᵣⱼ)

Representation

SR-ROSE uses the same node-position matrix and compact pair statistics as ROSE, but conditions each placement on one selected reference job.

Learning and sampling

The model selects one recent job, samples a signed distance from a truncated normal bounded by the observed minimum and maximum, and combines the relational score with node-position likelihood. WT adds punched-template inheritance.

Structural bias

A single reference preserves one explicit relational hypothesis rather than averaging several potentially conflicting predictions. Memory remains O(n²).

single-reference histogram ROSE

SH-ROSE/WO and SH-ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

R(r,j,d) = [c(r,j,d)+ε] / Σδ≠0[c(r,j,δ)+ε]

Representation

SH-ROSE replaces the compact distance approximation with an empirical signed-distance histogram for every ordered job pair.

Learning and sampling

After selecting one reference job, it scores each feasible position from the learned probability of its exact signed offset. WT retains part of a parent and reconstructs the holes.

Structural bias

The histogram retains multimodal distance distributions that mean and range statistics may blur. The additional detail increases estimator memory from O(n²) to O(n³).

generalized Mallows EDA

GM-EDA

consensus2741controlled inversion distance

P(π|σ,θ) ∝ exp[−Σᵢ θᵢ Vᵢ(πσ⁻¹)]

Representation

A consensus permutation defines the central ranking. Stagewise inversion variables describe dispersion around that ranking.

Learning and sampling

The implementation obtains the consensus by mean Borda position and estimates a truncated geometric distribution for each Kendall inversion coordinate.

Structural bias

The model favors permutations close to one central ordering, making global rank consensus explicit.

random-key EDA

RK-EDA

2.12

7.31

4.58

1.86

zⱼ ~ Normal(μⱼ,σ²ⱼ), π = argsort(z)

Representation

Each job has an independent Gaussian random key. Sorting the sampled keys decodes a permutation.

Learning and sampling

The selected population updates one mean and variance for each job key. Sampling occurs in continuous space before the sort operation enforces a valid permutation.

Structural bias

The smooth latent coordinates learn global ordering efficiently, although independent keys do not explicitly store pairwise linkage.

Plackett–Luce EDA

PL-EDA

242%

731%

419%

18%

P(π)=Πᵢ wπᵢ / Σₖ₌ᵢⁿ wπₖ

Representation

One positive worth parameter represents the global preference for selecting each job.

Learning and sampling

At each position, the algorithm samples one unused job in proportion to its worth, removes it, and repeats until the permutation is complete.

Structural bias

The compact model learns global precedence preference but uses the same worth parameter at every position.

single objective · measured

Ten seeds confirm three different winners

AMakespanclick to zoom

RK-EDANHBSA/WTNB-COIN/WTROSE/WTNB-COIN

#	Algorithm	RPD ↓	wins
1	RK-EDA	0.44%	98
2	NHBSA/WT	0.58%	82
3	NB-COIN/WT	0.66%	53
4	ROSE/WT	1.17%	39
5	NB-COIN	1.26%	22
6	CNB-COIN	1.66%	19
7	HNE-COIN	1.75%	10
8	EHBSA/WT	1.77%	13

#	Algorithm	RPD ↓	wins
9	COIN/WT	1.98%	14
10	GM-EDA	2.18%	3
11	CNE-COIN	2.30%	10
12	SNE-COIN	2.56%	11
13	NHBSA/WO	3.02%	7
14	COIN	3.91%	3
15	EHBSA/WO	4.74%	0
16	PL-EDA	5.59%	1

BTotal flow timeclick to zoom

NB-COIN/WTNHBSA/WTRK-EDAEHBSA/WTCNB-COIN

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	0.48%	70
2	NHBSA/WT	0.53%	67
3	RK-EDA	0.86%	26
4	EHBSA/WT	0.97%	22
5	CNB-COIN	1.51%	4
6	ROSE/WT	1.54%	3
7	COIN/WT	1.60%	6
8	NB-COIN	1.72%	2

#	Algorithm	RPD ↓	wins
9	HNE-COIN	1.79%	1
10	CNE-COIN	2.04%	0
11	SNE-COIN	2.18%	2
12	GM-EDA	2.54%	0
13	NHBSA/WO	2.70%	2
14	COIN	5.30%	0
15	EHBSA/WO	6.83%	0
16	PL-EDA	7.58%	0

CMachine idle timeclick to zoom

ROSE/WTNHBSA/WTNB-COIN/WTEHBSA/WTNB-COIN

#	Algorithm	RPD ↓	wins
1	ROSE/WT	29.15%	62
2	NHBSA/WT	62.54%	121
3	NB-COIN/WT	69.79%	96
4	EHBSA/WT	79.92%	21
5	NB-COIN	94.15%	36
6	COIN/WT	94.65%	15
7	HNE-COIN	200.74%	23
8	CNE-COIN	229.87%	8

#	Algorithm	RPD ↓	wins
9	SNE-COIN	234.65%	8
10	CNB-COIN	239.01%	27
11	RK-EDA	277.23%	18
12	COIN	363.10%	0
13	NHBSA/WO	376.82%	10
14	GM-EDA	384.59%	0
15	EHBSA/WO	489.14%	0
16	PL-EDA	685.40%	0

All 16 algorithms are ranked across 200 paired blocks. Curves show only the five best final methods so individual trajectories remain readable. RPD is paired by TA instance × seed.

pareto frontier · measured

Union frontier of each algorithm—not the whole population

A × BMakespan × flow time · TA020 · 10 seedsclick to zoom

RK-EDAHNE-COINSNE-COINNB-COINCNB-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	1.026	0.072
2	HNE-COIN	0.969	0.136
3	SNE-COIN	0.960	0.151
4	NB-COIN	0.958	0.131
5	CNB-COIN	0.951	0.148
6	CNE-COIN	0.939	0.166
7	NHBSA/WO	0.889	0.181
8	NHBSA/WT	0.875	0.217

#	Algorithm	HV ↑	IGD+ ↓
9	GM-EDA	0.862	0.179
10	ROSE/WT	0.800	0.263
11	EHBSA/WT	0.785	0.280
12	COIN	0.743	0.302
13	NB-COIN/WT	0.685	0.343
14	EHBSA/WO	0.638	0.388
15	COIN/WT	0.596	0.417
16	PL-EDA	0.555	0.459

A × CMakespan × idle time · TA020 · 10 seedsclick to zoom

RK-EDANB-COINCNB-COINHNE-COINNHBSA/WT

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	0.997	0.065
2	NB-COIN	0.979	0.080
3	CNB-COIN	0.944	0.102
4	HNE-COIN	0.937	0.107
5	NHBSA/WT	0.904	0.138
6	CNE-COIN	0.893	0.133
7	GM-EDA	0.878	0.134
8	ROSE/WT	0.869	0.162

#	Algorithm	HV ↑	IGD+ ↓
9	SNE-COIN	0.861	0.153
10	EHBSA/WT	0.849	0.174
11	NHBSA/WO	0.839	0.161
12	COIN	0.834	0.181
13	EHBSA/WO	0.772	0.226
14	NB-COIN/WT	0.745	0.237
15	COIN/WT	0.695	0.272
16	PL-EDA	0.673	0.296

B × CFlow time × idle time · TA020 · 10 seedsclick to zoom

HNE-COINNB-COINCNB-COINRK-EDASNE-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	HNE-COIN	0.999	0.080
2	NB-COIN	0.998	0.076
3	CNB-COIN	0.995	0.083
4	RK-EDA	0.992	0.065
5	SNE-COIN	0.988	0.086
6	CNE-COIN	0.984	0.090
7	NHBSA/WT	0.957	0.118
8	NHBSA/WO	0.954	0.100

#	Algorithm	HV ↑	IGD+ ↓
9	COIN	0.945	0.113
10	EHBSA/WT	0.934	0.128
11	GM-EDA	0.924	0.104
12	ROSE/WT	0.915	0.139
13	EHBSA/WO	0.886	0.152
14	NB-COIN/WT	0.836	0.192
15	COIN/WT	0.805	0.204
16	PL-EDA	0.790	0.215

A × B × CThree objectives · TA020 · 10 seedsclick to zoom

RK-EDANB-COINHNE-COINCNB-COINSNE-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	1.011	0.066
2	NB-COIN	0.971	0.098
3	HNE-COIN	0.964	0.103
4	CNB-COIN	0.951	0.114
5	SNE-COIN	0.938	0.116
6	CNE-COIN	0.938	0.121
7	NHBSA/WO	0.906	0.125
8	GM-EDA	0.897	0.114

#	Algorithm	HV ↑	IGD+ ↓
9	NHBSA/WT	0.878	0.155
10	COIN	0.853	0.161
11	EHBSA/WT	0.839	0.172
12	ROSE/WT	0.829	0.178
13	EHBSA/WO	0.785	0.200
14	NB-COIN/WT	0.675	0.264
15	PL-EDA	0.662	0.274
16	COIN/WT	0.638	0.282

Tables rank all 16 algorithms across 200 instance-seed blocks. Axes retain objective names after per-instance normalization. The 3-objective panel projects makespan and flow time, with idle time encoded by point size and opacity.

TA022 case study · measured

Makespan and total flow time on TA022

SNE-COINCNE-COINNHBSA/WOHNE-COINNB-COIN

Five-seed union frontier
Each algorithm contributes its own nondominated frontier after unioning seeds 2026–2030.

#	Algorithm	HV ↑	IGD+ ↓
1	SNE-COIN	1.159	0.008
2	CNE-COIN	1.110	0.044
3	NHBSA/WO	1.089	0.042
4	HNE-COIN	1.082	0.049
5	NB-COIN	1.080	0.039
6	CNB-COIN	1.001	0.097
7	NHBSA/WT	0.994	0.117
8	COIN	0.879	0.186

#	Algorithm	HV ↑	IGD+ ↓
9	EHBSA/WT	0.878	0.167
10	NB-COIN/WT	0.769	0.261
11	EHBSA/WO	0.763	0.281
12	COIN/WT	0.675	0.305

12 algorithms from the completed confirmatory MO experiment. ROSE and ranking EDAs were not part of this legacy TA022 batch.

decision

What do we publish after the checkpoint?

Path 1

Journal: representation × objective

Full Single/MO analysis, three objectives, COIN variants, histogram and ranking EDAs, convergence and Pareto quality.

Choose if the 5–10 seed pattern is stable.

Path 2

ISAI-NLP: focused cut

One sharp claim: positive–negative structural learning preserves useful disagreement in multi-objective permutation search.

Choose a small, defensible subset.

Decision ruleDoes COIN’s MO advantage survive seed aggregation and more representations?5 seeds → pitch10 seeds → direction lock

research sequence

The ROSE Map

NOW · REPRESENTATION STUDYCOIN variants

ROSE appears as an exploratory comparator. This paper asks which structural representation fits each objective.

Evidence first, without a formal ROSE claim

NEXT · ROSE DEBUTROSE family

A dedicated study introduces multi-reference ROSE, SR-ROSE and SH-ROSE, with WO/WT reconstruction, parameter tuning and controlled ablation.

Compact statistics versus empirical distance histograms

THEN · CARE DEBUTCARE-EDA

Population context controls the mixture of edge, node and relational generators. Representation becomes an adaptive decision.

Context-aware representation ensemble

Research arcThis study identifies the representation problem. The ROSE family expands the representation. CARE learns when each representation should generate solutions.

CARE-EDA

Let the population decide which representation should generate next

CONTEXT-AWARE REPRESENTATION ENSEMBLE

One objective does not imply one useful representation.

Edge, position and relative-order models expose different structure. Their value can also change during the run. CARE treats offspring allocation as a learned decision.

Research question

Can population feedback select the right generative representation without permanently discarding the others?

observerank utility→allocateoffspring

CARE context

Static representation choice creates a blind spot

EHBSA

Local succession

Useful when adjacent jobs explain machine transitions, but it does not directly encode absolute placement.

P(xₖ₊₁=b | xₖ=a)

NHBSA

Absolute placement

Often converges quickly when early or late positions dominate, but independent columns lose pair context.

P(xᵢ=j)

ROSE

Relational distance

Captures precedence and separation across nonadjacent jobs, although its evidence can mature more slowly.

P(pos(b)-pos(a)=d)

CARE keeps all three generators alive, observes the quality of their offspring, and reallocates the next generation while retaining a minimum exploration share.

CARE concept

Three relations cover different permutation structure

EHBSA

Edge relation

A directed histogram records which unused job follows the current job.

P(xₖ₊₁=b | xₖ=a)

NHBSA

Position relation

Independent job distributions describe each absolute position.

P(xᵢ=j)

ROSE

Relative order

Signed displacement records precedence and distance between job pairs.

P(pos(b)-pos(a)=d)

Objective and instance structure determine which relation becomes useful. CARE allocates offspring across all three.

CARE architecture

Adaptive allocation preserves minority representations

EHBSAdirected edge relationP(job b | job a)

NHBSAindependent position relationP(job j | position i)

ROSErelative order relationP(pos(b)-pos(a))

CARE controllerrank utility updates the offspring allocationwE + wN + wR = 1

100 offspringeach expert retains at least 10%

Current prototype: every expert learns from its own offspring. The shared version remains a planned ablation.

controller mathematics

Fast average improvement currently receives the most credit

1 · rank offspringrᵢ = rank(fᵢ) / (N-1)

Lower objective values receive better normalized ranks.

2 · score each expertuₖ = 1 - mean(rᵢ | expert k)

Consistent offspring quality matters more than a rare best solution.

3 · smooth creditcₖ,t = 0.8cₖ,t-1 + 0.2uₖ,t

Memory reduces rapid allocation changes.

4 · retain explorationwₖ = 0.10 + 0.70 softmax(cₖ / 0.25)

Every relation keeps at least ten offspring.

WO and WT

Template inheritance changes both quality and allocation

CARE/WO

Every expert constructs a complete permutation from its learned distribution.

Mean expert allocationNHBSA about 65%More freedom, slower relational sampling

selected parentretain positionspunched templatemodel fills holespaired replacement

CARE/WT

Each expert retains part of a parent, then reconstructs the missing positions.

Mean expert allocationNHBSA 54–61%, ROSE 22–27%Stronger inheritance, more balanced mixture

pilot protocol

The demonstration isolates behavior before confirmatory testing

5Taillard instances
TA001–TA005

3single objectives
MS, TFT, idle

4methods
CARE and experts

40kevaluations
per method

Population	100	Generations	400
Seed	42	Selection	HBSA 50%, ROSE 10%
Template	50% punched positions	Rank policy	Final rank with ties; convergence reported separately

This pilot supports mechanism discovery. It does not support population-level significance claims.

makespan · internal experts

CARE ranks first against its three component experts

Instance	CARE/WT	EHBSA/WT	NHBSA/WT	ROSE/WT
TA001	1,297	1,297	1,297	1,297
TA002	1,366	1,370	1,377	1,365
TA003	1,113	1,127	1,098	1,098
TA004	1,313	1,315	1,313	1,323
TA005	1,244	1,254	1,250	1,248

1.40CARE mean rank

3/5top or tied top

0.288%mean gap

This is a mechanism comparison, not the full-field ranking. ROSE/WT has the lowest mean gap.

TA004 convergence · CARE/WT

Minority experts help CARE move beyond the dominant model

CARE/WT: 1313EHBSA/WT: 1315NHBSA/WT: 1313ROSE/WT: 1323

Early search

NHBSA gains the largest allocation because its offspring rank improves fastest.

Middle search

CARE keeps EHBSA and ROSE active instead of collapsing into NHBSA.

Late search

CARE reaches 1313 and matches NHBSA while maintaining a lower trajectory for much of the run.

flow time and idle time · CARE/WT

Rank reveals robustness that win count misses

Total flow time

Instance	CARE/WT	EHBSA/WT	NHBSA/WT	ROSE/WT
TA001	14,357	14,109	14,285	14,295
TA002	15,411	15,493	15,574	15,448
TA003	13,765	13,668	13,629	13,804
TA004	15,647	15,824	15,691	15,870
TA005	13,653	13,667	13,690	13,676

CARE rank 2.003 winsmean gap 0.551%

Internal idle time

Instance	CARE/WT	EHBSA/WT	NHBSA/WT	ROSE/WT
TA001	134	134	134	134
TA002	0	7	7	0
TA003	142	142	166	142
TA004	12	18	19	12
TA005	200	200	200	200

CARE rank 1.00top or tied top 5/5same final values as ROSE/WT

CARE evidence and next tests

The pilot exposes the controller question

What the pilot shows

Adaptive mixtures can match or exceed a strong standalone expert

CARE/WT has the best makespan mean rank and remains tied for every idle-time optimum found by ROSE/WT.

What remains unknown

One seed cannot establish stability.
Mean-rank credit favors early NHBSA convergence.
CARE/WO needs a matched rerun after quota optimization.
Shared learning and fixed-weight controls remain untested.

Planned ablations

Isolatedexperts learn from their own offspring

Sharedexperts learn from one elite cohort

Frozenweights fixed at the learned final ratio

Creditrank, best improvement, novelty and hybrid

Current paper: representation question. Next paper: formal ROSE debut. Later paper: CARE controller and co-adaptation.

full EDA field · makespan

CARE is third by mean rank; RK-EDA leads the scalar field

#	Algorithm	Rank↓	Top	Gap↓
1	RK-EDA	1.80	3	0.140%
2	ROSE/WT	4.30	2	0.730%
3	CARE/WT	4.80	0	0.800%
4	NB-COIN/WT	6.30	1	1.040%
5	NB-COIN	6.50	0	1.140%
6	NHBSA/WT	7.20	1	0.790%
7	GM-EDA	7.50	0	1.300%
8	HC-COIN	7.90	0	1.030%
9	HNE-COIN	8.10	0	1.140%

#	Algorithm	Rank↓	Gap↓
10	CNB-COIN	8.40	1.410%
11	EHBSA/WT	9.10	1.310%
12	COIN/WT	9.30	1.970%
13	SNE-COIN	12.40	2.380%
14	NHBSA/WO	14.00	2.690%
15	COIN	14.20	3.690%
16	EHBSA/WO	15.20	3.920%
17	PL-EDA	16.00	4.620%

Interpretation: CARE beats its component experts on rank, but does not beat the independent RK-EDA baseline. Its value is robustness across representations—not universal scalar dominance.

full EDA field · total flow time

CARE remains competitive, behind NB-COIN/WT and RK-EDA

#	Algorithm	Rank↓	Top	Gap↓
1	NB-COIN/WT	3.10	1	0.460%
2	RK-EDA	3.40	2	0.430%
3	CARE/WT	3.80	2	0.840%
4	EHBSA/WT	5.00	0	0.700%
5	NHBSA/WT	5.20	0	0.860%
6	NB-COIN	6.40	0	1.260%
7	ROSE/WT	7.40	0	1.180%
8	HNE-COIN	7.40	0	1.390%
9	CNB-COIN	8.20	0	1.470%

#	Algorithm	Rank↓	Gap↓
10	HC-COIN	10.30	1.910%
11	COIN/WT	10.40	1.990%
12	SNE-COIN	10.40	2.010%
13	GM-EDA	11.00	2.020%
14	NHBSA/WO	13.00	2.870%
15	COIN	15.60	4.930%
16	EHBSA/WO	16.00	6.290%
17	PL-EDA	16.40	6.460%

Interpretation: CARE ranks third and obtains two top values. The result supports adaptive coverage, while positional NB-COIN/WT still fits this objective best.

full EDA field · internal idle time

CARE and ROSE/WT jointly lead every tested instance

#	Algorithm	Rank↓	Top	Gap↓
1	CARE/WT	3.40	5	0.000
2	ROSE/WT	3.40	5	0.000
3	NB-COIN/WT	3.70	4	0.600
4	NB-COIN	3.90	4	1.000
5	EHBSA/WT	5.30	3	11.400
6	CNB-COIN	6.20	3	4.780
7	NHBSA/WT	7.10	2	16.450
8	COIN/WT	7.60	1	21.760
9	HNE-COIN	8.40	1	20.080

#	Algorithm	Rank↓	Top	Gap↓
10	CNE-COIN	10.50	0	33.720
11	NHBSA/WO	10.90	1	46.920
12	RK-EDA	11.20	0	42.840
13	SNE-COIN	11.90	0	51.310
14	GM-EDA	13.70	0	106.500
15	COIN	14.40	0	92.050
16	EHBSA/WO	15.60	0	112.590
17	PL-EDA	15.80	0	150.790

Strongest pilot result: CARE/WT and ROSE/WT tie at mean rank 3.40 and reach the best value on all five instances. More seeds must test whether adaptation adds stability beyond ROSE alone.

NB-COIN-E

Give scalar specialists a controlled share of Pareto search

EXTENDED NODE-BASED COIN

Pareto pressure searches inward. Specialists probe the extremes.

NB-COIN-E combines two scalar node-based learners with one multi-objective learner. A fixed quota controls how much generation budget follows each view of the same population.

Research question

Can objective specialists add useful frontier points without weakening the Pareto learner that drives convergence?

MS + TFTspecialists+MOlearner

NB-COIN-E context

The allocation ratio decides whether specialization helps

Scalar specialists

Search the ends of the frontier

Makespan and flow-time learners receive sharper scalar ranks. They can discover extreme schedules that Pareto selection may visit less often.

Benefit: broader structural hypotheses

Multi-objective learner

Pull the population toward the frontier

Pareto depth and crowding reward nondominated progress across both objectives. This learner supplies most of the convergence pressure.

Benefit: deeper, balanced trade-offs

Central trade-offScalar offspring become expensive when their discoveries do not survive in the pooled nondominated archive.10:10:8020:20:6033:33:34 with /WT

EX-COIN concept · fixed allocation

Three COIN models learn two extremes and the Pareto surface

34 offspringNB-COIN · makespanrank by f₁

33 offspringNB-COIN · flow timerank by f₂

33 offspringMO NB-COINPareto depth + crowding

shared mixed population → all three models update → pooled nondominated archive

EX-NB-COIN v1: the ratio remains 34:33:33. Unlike CARE, no controller reallocates offspring from observed utility.

dual SNE concept · temporal allocation

Two scalar SNE models alternate who generates each generation

Odd generationSNE-MS generates 100both models observe the population

⇄

Even generationSNE-TFT generates 100each model learns its own objective

G1 · MS G2 · TFT G3 · MS G4 · TFT … shared Pareto archive

Clean ablation: fixed 50:50 exposure without mixing offspring inside a generation. The risk is distribution whiplash—each generator receives no direct Pareto selection pressure.

EX-COIN pilot · measured

Scalar specialists did not improve the Pareto learner

Algorithm	Convergence↓	Spread↓	Pooled ND ratio↑	Archive	Time · 5 runs
MO NB-COIN	0.010	0.810	0.900	6.0	77.2 s
MO SNE-COIN	0.160	0.790	0.200	6.2	61.6 s
EX-NB-COIN · 34:33:33	0.178	0.747	0.089	5.8	99.8 s
Dual-SNE · alternating	0.318	0.653	0.183	7.6	81.1 s

Why EX-NB loses

Two-thirds of generation capacity follows scalar ranks. Extreme specialists do not receive credit for frontier contribution.

Next defensible version

Keep fixed quotas, but update specialists only from offspring that enter the pooled archive; compare 20:20:60 and 10:10:80.

Pilot only: TA001–TA005, makespan × total flow time, seed 42, population 100, 400 generations. Metrics use the pooled observed frontier; “convergence” is normalized set-to-reference distance, not IGD+.

EX-COIN Pareto frontier · measured

TA001 · Makespan versus total flow time

EX-NBDual-SNEMO-NBMO-SNE

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EX-COIN Pareto frontier · measured

TA002 · Makespan versus total flow time

EX-NBDual-SNEMO-NBMO-SNE

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EX-COIN Pareto frontier · measured

TA003 · Makespan versus total flow time

EX-NBDual-SNEMO-NBMO-SNE

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EX-COIN Pareto frontier · measured

TA004 · Makespan versus total flow time

EX-NBDual-SNEMO-NBMO-SNE

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EX-COIN Pareto frontier · measured

TA005 · Makespan versus total flow time

EX-NBDual-SNEMO-NBMO-SNE

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generation budget · common reference

Twice the budget moves EX-COIN inward—but MO NB moves faster

Algorithm	Convergence 400	Convergence 800	Improvement	ND ratio 400	ND ratio 800
EX-NB-COIN	0.220	0.150	↓ 31.5%	0.022	0.087
Dual-SNE	0.324	0.252	↓ 22.3%	0.090	0.205
MO NB-COIN	0.054	0.007	↓ 86.3%	0.378	0.872
MO SNE-COIN	0.166	0.158	↓ 5.0%	0.100	0.237

EX-NB uses the extra time

Its convergence distance falls by almost one-third and its pooled-front survival rises nearly fourfold.

Dual-SNE remains diverse

Convergence improves, while spread is essentially unchanged: 0.647 → 0.649.

The gap is selection pressure

MO NB exploits the same extra evaluations more effectively because every update is Pareto-directed.

Common-reference comparison: both budgets were normalized against the pooled observed frontier across all 400- and 800-generation archives.

EX-NB ratio · 800 generations

A small scalar allocation becomes useful; one-third is too expensive

Algorithm	MS:TFT:MO	Convergence↓	Spread↓	Pooled ND ratio↑	Archive
MO NB-COIN	0:0:100	0.045	0.785	0.444	5.8
EX-NB-COIN	10:10:80	0.075	0.824	0.589	4.8
EX-NB-COIN	20:20:60	0.171	0.771	0.080	7.2
EX-NB-COIN	34:33:33	0.218	0.775	0.067	5.4

10:10:80 is the candidate

It stays near MO NB while contributing the largest share of points to the pooled observed frontier.

20:20:60 keeps breadth

Archive size rises to 7.2, but most added points remain dominated.

Specialists are exploration bets

Twenty percent total scalar allocation is enough to probe extremes without replacing Pareto pressure.

One-seed mechanism result: TA001–TA005, makespan × total flow time, population 100, seed 42. Confirm with paired seeds before selecting the ratio.

EX-NHBSA/WO · 800 generations

EX rescues NHBSA’s Pareto search—but NB-COIN remains stronger

Algorithm	MS:TFT:MO	Convergence↓	Spread↓	Pooled ND ratio↑	Archive
MO NB-COIN	0:0:100	0.053	0.786	0.294	5.8
EX-NB-COIN	10:10:80	0.079	0.830	0.589	4.8
EX-NHBSA/WO	10:10:80	0.163	0.738	0.247	6.4
MO NHBSA/WO	0:0:100	0.227	0.724	0.014	7.8
EX-NHBSA/WO	20:20:60	0.236	0.747	0.133	7.0

10:10:80 improves depth

Convergence distance is 28.3% lower than standalone MO NHBSA/WO.

Frontier survival jumps

ND contribution rises from 0.014 to 0.247 on the pooled observed frontier.

Representation still matters

The same EX policy is stronger with NB-COIN’s positive–negative position learning than with NHBSA.

Pilot: TA001–TA005, makespan × total flow time, population 100, 800 generations, seed 42. All algorithms share one pooled observed reference.

EX-NHBSA/WT · 800 generations

With templates, EX buys spread rather than deeper convergence

Algorithm	MS:TFT:MO	Convergence↓	Spread↓	Pooled ND ratio↑	Archive
MO NHBSA/WT	0:0:100	0.091	0.765	0.640	9.2
EX-NHBSA/WT	20:20:60	0.147	0.696	0.427	7.0
EX-NHBSA/WT	10:10:80	0.166	0.692	0.233	6.2

Template already exploits

Paired parent–offspring replacement stabilizes good positional structure without scalar assistance.

20:20:60 is the WT candidate

More scalar injection improves convergence and ND survival relative to 10:10:80.

EX changes role

For /WO it rescues convergence; for /WT it mainly expands coverage and regularizes spacing.

WT implementation detail: paired replacement occurs inside each specialist quota before the three survivor blocks enter the pooled archive. This differs from the shared-observation /WO pilot and requires an explicit ablation.

EX-NB-COIN/WT · 800 generations

Balanced specialists drive the deepest EX-NB/WT frontier

Algorithm	MS:TFT:MO	Convergence↓	Spread↓	Pooled ND ratio↑	Archive
EX-NB-COIN/WT	33:33:34	0.044	0.627	0.774	6.4
EX-NB-COIN/WT	20:20:60	0.130	0.566	0.236	8.0
EX-NB-COIN/WT	10:10:80	0.190	0.676	0.040	4.6
MO NB-COIN/WT	0:0:100	0.354	0.691	0.050	5.2

33:33:34 goes deepest

Balanced scalar specialists contribute 77.4% of their archive to the pooled observed frontier.

20:20:60 covers smoothly

It keeps the largest archive and the lowest spacing error, but does not reach as far inward.

Template retains extremes

Unlike /WO, paired survival preserves specialist discoveries; the optimal allocation therefore shifts toward scalar search.

Mechanism pilot only: TA001–TA005, makespan × total flow time, population 100, 800 generations, seed 42. Metrics were recomputed against the new four-method pooled observed reference; confirm with paired seeds and a replacement-policy ablation.

CARE/WT · full matched scalar field

CARE is the most robust learner across all three objectives

#	Algorithm	Makespan rank↓	Flow-time rank↓	Idle-time rank↓	Mean rank↓
1	CARE/WT	4.80	3.80	3.40	4.00
2	NB-COIN/WT	6.3	3.1	3.7	4.37
3	ROSE/WT	4.3	7.4	3.4	5.03
4	RK-EDA	1.8	3.4	11.2	5.47
5	NB-COIN	6.5	6.4	3.9	5.60
6	EHBSA/WT	9.1	5.0	5.3	6.47
7	NHBSA/WT	7.2	5.2	7.1	6.50
8	CNB-COIN	8.4	8.2	6.2	7.60
9	HNE-COIN	8.1	7.4	8.4	7.97
10	COIN/WT	9.3	10.4	7.6	9.10
11	GM-EDA	7.5	11.0	13.7	10.73
12	SNE-COIN	12.4	10.4	11.9	11.57
13	NHBSA/WO	14.0	13.0	10.9	12.63
14	COIN	14.2	15.6	14.4	14.73
15	EHBSA/WO	15.2	16.0	15.6	15.60
16	PL-EDA	16.0	16.4	15.8	16.07

CARE/WT · 4.00best cross-objective mean rank

No universal standalone winnerRK leads makespan; NB/WT leads flow time; CARE and ROSE lead idle time

Controller value = robustnessCARE never needs to guess one representation before seeing objective feedback

Matched scope: TA001–TA005, seed 42, population 100, 400 generations, single-objective runs. CNE-COIN has an idle-only result and is excluded from the three-objective aggregate. This is a mechanism pilot—not statistical evidence across seeds. MO CARE has not yet been run.

ROSE

Learn where jobs belong relative to one another

RELATIONAL ORDER SAMPLING EDA

Position alone cannot describe every useful permutation pattern.

ROSE learns signed distance between job pairs. A candidate position can therefore depend on jobs already placed, including relationships that extend beyond immediate adjacency.

Research question

Can a relational model preserve precedence, separation and multimodal placement patterns that edge and node histograms blur?

reference jobrelative distance→target jobposition

representation context

ROSE occupies the space between adjacency and absolute position

EHBSA

Immediate edge

Records which job follows another, but longer-range separation disappears.

P(xₖ₊₁=b | xₖ=a)

NHBSA

Absolute position

Records where each job appears, but the placement of two jobs remains independent.

P(xᵢ=j)

ROSE

Signed displacement

Records whether one job occurs before or after another and how far apart they tend to appear.

Δ(a,b)=pos(b)-pos(a)

The representation adds relational context without committing to a single fixed adjacency chain.

multi-reference mean ROSE

ROSE/WO and ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

target(j) = meanᵣ∈C [pos(r)+μ(r,j)]

Representation

ROSE models absolute placement together with signed relational displacement between pairs of jobs.

Learning and sampling

For selected permutations, it records node-position probabilities and the count, mean, standard deviation, minimum and maximum of Δ(a,b)=pos(b)−pos(a). Multi-reference sampling averages the positions predicted by recent placed jobs. WT starts from a punched template while WO constructs from an empty permutation.

Structural bias

Several reference jobs jointly predict a target position. The compact estimators require O(n²) memory.

single-reference range ROSE

SR-ROSE/WO and SR-ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

d ~ TruncNormal(μᵣⱼ,σᵣⱼ; minᵣⱼ,maxᵣⱼ)

Representation

SR-ROSE uses the same node-position matrix and compact pair statistics as ROSE, but conditions each placement on one selected reference job.

Learning and sampling

The model selects one recent job, samples a signed distance from a truncated normal bounded by the observed minimum and maximum, and combines the relational score with node-position likelihood. WT adds punched-template inheritance.

Structural bias

A single reference preserves one explicit relational hypothesis rather than averaging several potentially conflicting predictions. Memory remains O(n²).

single-reference histogram ROSE

SH-ROSE/WO and SH-ROSE/WT

retained jobs
2 · ? · 7 · ? · 4

position likelihood×signed distance to context

candidate score for each hole

R(r,j,d) = [c(r,j,d)+ε] / Σδ≠0[c(r,j,δ)+ε]

Representation

SH-ROSE replaces the compact distance approximation with an empirical signed-distance histogram for every ordered job pair.

Learning and sampling

After selecting one reference job, it scores each feasible position from the learned probability of its exact signed offset. WT retains part of a parent and reconstructs the holes.

Structural bias

The histogram retains multimodal distance distributions that mean and range statistics may blur. The additional detail increases estimator memory from O(n²) to O(n³).

stratified RPD · matched five seeds

Problem scale changes what ROSE/WT can learn

Instance stratum	Makespan			Total flow time			Machine idle time
Instance stratum	RPD	rank	wins	RPD	rank	wins	RPD	rank	wins
TA001–01050 matched blocks	0.575%	3	18	1.499%	6	0	25.191%	1	34
TA011–02050 matched blocks	1.814%	5	0	1.475%	7	1	19.011%	6	1
TA021–03050 matched blocks	1.668%	6	0	1.268%	7	0	14.878%	11	0
TA001–030150 matched blocks	1.353%	5	18	1.414%	7	1	19.693%	2	35

TA001–010ROSE wins idle time

Rank 1 · 34/50 wins or ties. Relative order is strongly aligned with the small-instance idle landscape.

TA011–020The advantage breaks

Idle-time RPD rank falls to 6; NHBSA/WT becomes the block leader.

TA021–030Learning budget bites

Idle-time rank falls to 11 at 400 generations, while makespan remains sixth.

TA001–030Still second overall

ROSE/WT retains idle-time RPD rank 2, but the aggregate hides strong scale dependence.

Protocol: seeds 42 and 2026–2029, 16 common EDAs, population 100, 400 generations. RPD is computed against the best observed value inside each instance × seed block; rank and wins/ties are reported alongside it.

complete scalar ranking · matched five seeds

TA001–010: all 16 algorithms

Makespanclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	RK-EDA	0.268%	2.54	31
2	NHBSA/WT	0.518%	3.10	25
3	ROSE/WT	0.575%	2.94	18
4	NB-COIN/WT	0.592%	3.12	19
5	NB-COIN	0.804%	4.28	11
6	EHBSA/WT	1.018%	5.60	6
7	CNB-COIN	1.130%	5.60	10
8	HNE-COIN	1.251%	6.20	5
9	COIN/WT	1.460%	6.60	6
10	CNE-COIN	1.637%	7.52	5
11	GM-EDA	1.869%	9.06	1
12	SNE-COIN	2.390%	9.76	5
13	NHBSA/WO	2.684%	11.02	2
14	COIN	3.310%	12.04	1
15	EHBSA/WO	3.744%	13.54	0
16	PL-EDA	4.316%	14.64	1

Total flow timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NB-COIN/WT	0.431%	2.76	22
2	NHBSA/WT	0.534%	3.02	12
3	RK-EDA	0.848%	4.34	7
4	EHBSA/WT	1.144%	4.90	6
5	CNB-COIN	1.471%	6.20	1
6	ROSE/WT	1.499%	6.82	0
7	COIN/WT	1.677%	7.06	2
8	NB-COIN	1.730%	7.34	1
9	HNE-COIN	1.892%	7.80	0
10	CNE-COIN	2.301%	9.24	0
11	GM-EDA	2.721%	10.52	0
12	SNE-COIN	2.800%	10.10	0
13	NHBSA/WO	2.906%	10.76	0
14	COIN	5.874%	14.12	0
15	EHBSA/WO	7.183%	15.08	0
16	PL-EDA	8.030%	15.70	0

Machine idle timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	ROSE/WT	25.191%	2.12	34
2	NB-COIN/WT	47.407%	2.04	35
3	NHBSA/WT	73.332%	2.68	32
4	EHBSA/WT	156.599%	5.16	10
5	NB-COIN	158.771%	3.28	18
6	COIN/WT	169.475%	5.56	6
7	HNE-COIN	347.885%	5.10	12
8	CNE-COIN	405.378%	7.64	4
9	SNE-COIN	465.148%	8.92	1
10	CNB-COIN	467.562%	5.28	15
11	RK-EDA	570.654%	8.44	3
12	COIN	745.180%	12.56	0
13	GM-EDA	786.605%	13.28	0
14	NHBSA/WO	793.356%	9.10	7
15	EHBSA/WO	973.825%	13.80	0
16	PL-EDA	1391.549%	15.16	0

complete scalar ranking · matched five seeds

TA011–020: all 16 algorithms

Makespanclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	RK-EDA	0.565%	2.26	19
2	NHBSA/WT	0.577%	2.34	17
3	NB-COIN/WT	0.712%	2.80	10
4	NB-COIN	1.704%	5.64	3
5	ROSE/WT	1.814%	6.24	0
6	CNB-COIN	2.155%	7.60	0
7	HNE-COIN	2.194%	7.90	0
8	EHBSA/WT	2.341%	8.52	0
9	GM-EDA	2.427%	8.60	0
10	COIN/WT	2.450%	8.76	1
11	SNE-COIN	2.664%	9.58	1
12	CNE-COIN	2.895%	10.34	0
13	NHBSA/WO	3.264%	10.46	0
14	COIN	4.555%	13.16	0
15	EHBSA/WO	5.729%	14.70	0
16	PL-EDA	6.833%	15.68	0

Total flow timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NB-COIN/WT	0.384%	2.42	20
2	NHBSA/WT	0.568%	3.34	14
3	EHBSA/WT	0.760%	3.80	6
4	RK-EDA	0.975%	5.18	6
5	COIN/WT	1.316%	6.82	3
6	CNB-COIN	1.359%	6.94	1
7	ROSE/WT	1.475%	7.52	1
8	HNE-COIN	1.547%	7.86	0
9	SNE-COIN	1.606%	7.90	0
10	NB-COIN	1.668%	8.58	0
11	CNE-COIN	1.679%	8.42	0
12	GM-EDA	2.385%	10.56	0
13	NHBSA/WO	2.760%	11.64	0
14	COIN	4.894%	14.10	0
15	EHBSA/WO	6.364%	15.06	0
16	PL-EDA	7.106%	15.72	0

Machine idle timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NHBSA/WT	2.995%	1.90	28
2	NB-COIN/WT	5.583%	2.46	17
3	RK-EDA	18.416%	7.00	2
4	NB-COIN	18.462%	6.42	0
5	SNE-COIN	18.938%	6.52	1
6	ROSE/WT	19.011%	6.62	1
7	EHBSA/WT	19.073%	7.12	0
8	HNE-COIN	20.653%	7.60	0
9	COIN/WT	21.800%	7.56	0
10	CNB-COIN	23.391%	8.46	0
11	NHBSA/WO	23.538%	8.76	1
12	CNE-COIN	24.125%	9.24	0
13	GM-EDA	37.359%	12.34	0
14	COIN	38.934%	13.34	0
15	EHBSA/WO	50.638%	14.52	0
16	PL-EDA	66.161%	15.82	0

complete scalar ranking · matched five seeds

TA021–030: all 16 algorithms

Makespanclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NHBSA/WT	0.298%	2.14	18
2	NB-COIN/WT	0.508%	2.48	16
3	RK-EDA	0.709%	3.44	15
4	NB-COIN	1.294%	5.04	0
5	CNB-COIN	1.589%	6.66	1
6	ROSE/WT	1.668%	7.16	0
7	HNE-COIN	1.793%	7.62	0
8	SNE-COIN	1.876%	7.84	0
9	EHBSA/WT	2.052%	8.34	0
10	CNE-COIN	2.225%	9.36	1
11	COIN/WT	2.252%	9.56	1
12	NHBSA/WO	2.783%	10.78	0
13	GM-EDA	2.975%	11.24	1
14	COIN	3.839%	13.30	0
15	EHBSA/WO	4.562%	14.32	0
16	PL-EDA	5.676%	15.86	0

Total flow timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NB-COIN/WT	0.314%	2.30	20
2	NHBSA/WT	0.320%	2.34	23
3	EHBSA/WT	0.869%	5.24	2
4	RK-EDA	0.958%	5.22	4
5	NB-COIN	1.210%	7.36	0
6	COIN/WT	1.239%	7.44	1
7	ROSE/WT	1.268%	7.72	0
8	HNE-COIN	1.282%	7.86	0
9	CNB-COIN	1.302%	7.54	0
10	SNE-COIN	1.440%	7.88	0
11	CNE-COIN	1.502%	9.34	0
12	NHBSA/WO	2.019%	10.38	0
13	GM-EDA	2.110%	10.58	0
14	COIN	3.629%	13.98	0
15	EHBSA/WO	4.657%	15.04	0
16	PL-EDA	5.128%	15.74	0

Machine idle timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NHBSA/WT	2.126%	1.86	21
2	NB-COIN/WT	3.922%	2.42	16
3	SNE-COIN	6.603%	3.82	8
4	EHBSA/WT	10.871%	6.50	1
5	COIN/WT	11.798%	7.58	1
6	CNE-COIN	11.821%	7.18	0
7	HNE-COIN	11.948%	7.46	0
8	RK-EDA	12.231%	7.38	2
9	CNB-COIN	13.030%	8.04	0
10	NB-COIN	13.617%	8.48	0
11	ROSE/WT	14.878%	9.92	0
12	NHBSA/WO	15.699%	9.78	1
13	GM-EDA	21.158%	12.10	0
14	COIN	22.881%	12.94	0
15	EHBSA/WO	29.611%	14.56	0
16	PL-EDA	38.079%	15.88	0

complete scalar ranking · matched five seeds

TA001–030: all 16 algorithms

Makespanclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NHBSA/WT	0.464%	2.53	60
2	RK-EDA	0.514%	2.75	65
3	NB-COIN/WT	0.604%	2.80	45
4	NB-COIN	1.267%	4.99	14
5	ROSE/WT	1.353%	5.45	18
6	CNB-COIN	1.625%	6.62	11
7	HNE-COIN	1.746%	7.24	5
8	EHBSA/WT	1.804%	7.49	6
9	COIN/WT	2.054%	8.31	8
10	CNE-COIN	2.253%	9.07	6
11	SNE-COIN	2.310%	9.06	6
12	GM-EDA	2.424%	9.63	2
13	NHBSA/WO	2.910%	10.75	2
14	COIN	3.901%	12.83	1
15	EHBSA/WO	4.679%	14.19	0
16	PL-EDA	5.608%	15.39	1

Total flow timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NB-COIN/WT	0.376%	2.49	62
2	NHBSA/WT	0.474%	2.90	49
3	EHBSA/WT	0.924%	4.65	14
4	RK-EDA	0.927%	4.91	17
5	CNB-COIN	1.377%	6.89	2
6	COIN/WT	1.411%	7.11	6
7	ROSE/WT	1.414%	7.35	1
8	NB-COIN	1.536%	7.76	1
9	HNE-COIN	1.574%	7.84	0
10	CNE-COIN	1.827%	9.00	0
11	SNE-COIN	1.948%	8.63	0
12	GM-EDA	2.405%	10.55	0
13	NHBSA/WO	2.561%	10.93	0
14	COIN	4.799%	14.07	0
15	EHBSA/WO	6.068%	15.06	0
16	PL-EDA	6.755%	15.72	0

Machine idle timeclick to zoom

#	Algorithm	RPD↓	rank↓	wins
1	NB-COIN/WT	18.971%	2.31	68
2	ROSE/WT	19.693%	6.22	35
3	NHBSA/WT	26.151%	2.15	81
4	EHBSA/WT	62.181%	6.26	11
5	NB-COIN	63.617%	6.06	18
6	COIN/WT	67.691%	6.90	7
7	HNE-COIN	126.829%	6.72	12
8	CNE-COIN	147.108%	8.02	4
9	SNE-COIN	163.563%	6.42	10
10	CNB-COIN	167.994%	7.26	15
11	RK-EDA	200.434%	7.61	7
12	COIN	268.998%	12.95	0
13	NHBSA/WO	277.531%	9.21	9
14	GM-EDA	281.707%	12.57	0
15	EHBSA/WO	351.358%	14.29	0
16	PL-EDA	498.596%	15.62	0

stratified convergence · matched five seeds

TA001–010: convergence changes with problem scale

AMakespanclick to zoom

RK-EDANHBSA/WTROSE/WTNB-COIN/WTNB-COIN

#	Algorithm	RPD ↓	wins
1	RK-EDA	0.27%	31
2	NHBSA/WT	0.52%	25
3	ROSE/WT	0.58%	18
4	NB-COIN/WT	0.59%	19
5	NB-COIN	0.80%	11
6	EHBSA/WT	1.02%	6
7	CNB-COIN	1.13%	10
8	HNE-COIN	1.25%	5

#	Algorithm	RPD ↓	wins
9	COIN/WT	1.46%	6
10	CNE-COIN	1.64%	5
11	GM-EDA	1.87%	1
12	SNE-COIN	2.39%	5
13	NHBSA/WO	2.68%	2
14	COIN	3.31%	1
15	EHBSA/WO	3.74%	0
16	PL-EDA	4.32%	1

BTotal flow timeclick to zoom

NB-COIN/WTNHBSA/WTRK-EDAEHBSA/WTCNB-COIN

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	0.43%	22
2	NHBSA/WT	0.53%	12
3	RK-EDA	0.85%	7
4	EHBSA/WT	1.14%	6
5	CNB-COIN	1.47%	1
6	ROSE/WT	1.50%	0
7	COIN/WT	1.68%	2
8	NB-COIN	1.73%	1

#	Algorithm	RPD ↓
9	HNE-COIN	1.89%
10	CNE-COIN	2.30%
11	GM-EDA	2.72%
12	SNE-COIN	2.80%
13	NHBSA/WO	2.91%
14	COIN	5.87%
15	EHBSA/WO	7.18%
16	PL-EDA	8.03%

CMachine idle timeclick to zoom

ROSE/WTNB-COIN/WTNHBSA/WTEHBSA/WTNB-COIN

#	Algorithm	RPD ↓	wins
1	ROSE/WT	25.19%	34
2	NB-COIN/WT	47.41%	35
3	NHBSA/WT	73.33%	32
4	EHBSA/WT	156.60%	10
5	NB-COIN	158.77%	18
6	COIN/WT	169.48%	6
7	HNE-COIN	347.89%	12
8	CNE-COIN	405.38%	4

#	Algorithm	RPD ↓	wins
9	SNE-COIN	465.15%	1
10	CNB-COIN	467.56%	15
11	RK-EDA	570.65%	3
12	COIN	745.18%	0
13	GM-EDA	786.61%	0
14	NHBSA/WO	793.36%	7
15	EHBSA/WO	973.82%	0
16	PL-EDA	1391.55%	0

TA001–010 × 5 matched seeds. Best-so-far curves are expressed as mean RPD from the final winner inside each instance × seed block. Curves show the five best final methods; tables retain all 16.

stratified convergence · matched five seeds

TA011–020: convergence changes with problem scale

AMakespanclick to zoom

RK-EDANHBSA/WTNB-COIN/WTNB-COINROSE/WT

#	Algorithm	RPD ↓	wins
1	RK-EDA	0.57%	19
2	NHBSA/WT	0.58%	17
3	NB-COIN/WT	0.71%	10
4	NB-COIN	1.70%	3
5	ROSE/WT	1.81%	0
6	CNB-COIN	2.16%	0
7	HNE-COIN	2.19%	0
8	EHBSA/WT	2.34%	0

#	Algorithm	RPD ↓	wins
9	GM-EDA	2.43%	0
10	COIN/WT	2.45%	1
11	SNE-COIN	2.66%	1
12	CNE-COIN	2.90%	0
13	NHBSA/WO	3.26%	0
14	COIN	4.55%	0
15	EHBSA/WO	5.73%	0
16	PL-EDA	6.83%	0

BTotal flow timeclick to zoom

NB-COIN/WTNHBSA/WTEHBSA/WTRK-EDACOIN/WT

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	0.38%	20
2	NHBSA/WT	0.57%	14
3	EHBSA/WT	0.76%	6
4	RK-EDA	0.98%	6
5	COIN/WT	1.32%	3
6	CNB-COIN	1.36%	1
7	ROSE/WT	1.47%	1
8	HNE-COIN	1.55%	0

#	Algorithm	RPD ↓
9	SNE-COIN	1.61%
10	NB-COIN	1.67%
11	CNE-COIN	1.68%
12	GM-EDA	2.38%
13	NHBSA/WO	2.76%
14	COIN	4.89%
15	EHBSA/WO	6.36%
16	PL-EDA	7.11%

CMachine idle timeclick to zoom

NHBSA/WTNB-COIN/WTRK-EDANB-COINSNE-COIN

#	Algorithm	RPD ↓	wins
1	NHBSA/WT	3.00%	28
2	NB-COIN/WT	5.58%	17
3	RK-EDA	18.42%	2
4	NB-COIN	18.46%	0
5	SNE-COIN	18.94%	1
6	ROSE/WT	19.01%	1
7	EHBSA/WT	19.07%	0
8	HNE-COIN	20.65%	0

#	Algorithm	RPD ↓	wins
9	COIN/WT	21.80%	0
10	CNB-COIN	23.39%	0
11	NHBSA/WO	23.54%	1
12	CNE-COIN	24.12%	0
13	GM-EDA	37.36%	0
14	COIN	38.93%	0
15	EHBSA/WO	50.64%	0
16	PL-EDA	66.16%	0

TA011–020 × 5 matched seeds. Best-so-far curves are expressed as mean RPD from the final winner inside each instance × seed block. Curves show the five best final methods; tables retain all 16.

stratified convergence · matched five seeds

TA021–030: convergence changes with problem scale

AMakespanclick to zoom

NHBSA/WTNB-COIN/WTRK-EDANB-COINCNB-COIN

#	Algorithm	RPD ↓	wins
1	NHBSA/WT	0.30%	18
2	NB-COIN/WT	0.51%	16
3	RK-EDA	0.71%	15
4	NB-COIN	1.29%	0
5	CNB-COIN	1.59%	1
6	ROSE/WT	1.67%	0
7	HNE-COIN	1.79%	0
8	SNE-COIN	1.88%	0

#	Algorithm	RPD ↓	wins
9	EHBSA/WT	2.05%	0
10	CNE-COIN	2.23%	1
11	COIN/WT	2.25%	1
12	NHBSA/WO	2.78%	0
13	GM-EDA	2.97%	1
14	COIN	3.84%	0
15	EHBSA/WO	4.56%	0
16	PL-EDA	5.68%	0

BTotal flow timeclick to zoom

NB-COIN/WTNHBSA/WTEHBSA/WTRK-EDANB-COIN

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	0.31%	20
2	NHBSA/WT	0.32%	23
3	EHBSA/WT	0.87%	2
4	RK-EDA	0.96%	4
5	NB-COIN	1.21%	0
6	COIN/WT	1.24%	1
7	ROSE/WT	1.27%	0
8	HNE-COIN	1.28%	0

#	Algorithm	RPD ↓
9	CNB-COIN	1.30%
10	SNE-COIN	1.44%
11	CNE-COIN	1.50%
12	NHBSA/WO	2.02%
13	GM-EDA	2.11%
14	COIN	3.63%
15	EHBSA/WO	4.66%
16	PL-EDA	5.13%

CMachine idle timeclick to zoom

NHBSA/WTNB-COIN/WTSNE-COINEHBSA/WTCOIN/WT

#	Algorithm	RPD ↓	wins
1	NHBSA/WT	2.13%	21
2	NB-COIN/WT	3.92%	16
3	SNE-COIN	6.60%	8
4	EHBSA/WT	10.87%	1
5	COIN/WT	11.80%	1
6	CNE-COIN	11.82%	0
7	HNE-COIN	11.95%	0
8	RK-EDA	12.23%	2

#	Algorithm	RPD ↓	wins
9	CNB-COIN	13.03%	0
10	NB-COIN	13.62%	0
11	ROSE/WT	14.88%	0
12	NHBSA/WO	15.70%	1
13	GM-EDA	21.16%	0
14	COIN	22.88%	0
15	EHBSA/WO	29.61%	0
16	PL-EDA	38.08%	0

TA021–030 × 5 matched seeds. Best-so-far curves are expressed as mean RPD from the final winner inside each instance × seed block. Curves show the five best final methods; tables retain all 16.

stratified convergence · matched five seeds

TA001–030: convergence changes with problem scale

AMakespanclick to zoom

NHBSA/WTRK-EDANB-COIN/WTNB-COINROSE/WT

#	Algorithm	RPD ↓	wins
1	NHBSA/WT	0.46%	60
2	RK-EDA	0.51%	65
3	NB-COIN/WT	0.60%	45
4	NB-COIN	1.27%	14
5	ROSE/WT	1.35%	18
6	CNB-COIN	1.62%	11
7	HNE-COIN	1.75%	5
8	EHBSA/WT	1.80%	6

#	Algorithm	RPD ↓	wins
9	COIN/WT	2.05%	8
10	CNE-COIN	2.25%	6
11	SNE-COIN	2.31%	6
12	GM-EDA	2.42%	2
13	NHBSA/WO	2.91%	2
14	COIN	3.90%	1
15	EHBSA/WO	4.68%	0
16	PL-EDA	5.61%	1

BTotal flow timeclick to zoom

NB-COIN/WTNHBSA/WTEHBSA/WTRK-EDACNB-COIN

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	0.38%	62
2	NHBSA/WT	0.47%	49
3	EHBSA/WT	0.92%	14
4	RK-EDA	0.93%	17
5	CNB-COIN	1.38%	2
6	COIN/WT	1.41%	6
7	ROSE/WT	1.41%	1
8	NB-COIN	1.54%	1

#	Algorithm	RPD ↓
9	HNE-COIN	1.57%
10	CNE-COIN	1.83%
11	SNE-COIN	1.95%
12	GM-EDA	2.41%
13	NHBSA/WO	2.56%
14	COIN	4.80%
15	EHBSA/WO	6.07%
16	PL-EDA	6.75%

CMachine idle timeclick to zoom

NB-COIN/WTROSE/WTNHBSA/WTEHBSA/WTNB-COIN

#	Algorithm	RPD ↓	wins
1	NB-COIN/WT	18.97%	68
2	ROSE/WT	19.69%	35
3	NHBSA/WT	26.15%	81
4	EHBSA/WT	62.18%	11
5	NB-COIN	63.62%	18
6	COIN/WT	67.69%	7
7	HNE-COIN	126.83%	12
8	CNE-COIN	147.11%	4

#	Algorithm	RPD ↓	wins
9	SNE-COIN	163.56%	10
10	CNB-COIN	167.99%	15
11	RK-EDA	200.43%	7
12	COIN	269.00%	0
13	NHBSA/WO	277.53%	9
14	GM-EDA	281.71%	0
15	EHBSA/WO	351.36%	0
16	PL-EDA	498.60%	0

TA001–030 × 5 matched seeds. Best-so-far curves are expressed as mean RPD from the final winner inside each instance × seed block. Curves show the five best final methods; tables retain all 16.

complete convergence · all algorithms

Makespan: all 16 trajectories

#1RK-EDA0.440%#2NHBSA/WT0.580%#3NB-COIN/WT0.663%#4ROSE/WT1.169%#5NB-COIN1.264%#6CNB-COIN1.655%#7HNE-COIN1.749%#8EHBSA/WT1.768%#9COIN/WT1.975%#10GM-EDA2.185%#11CNE-COIN2.300%#12SNE-COIN2.560%#13NHBSA/WO3.025%#14COIN3.907%#15EHBSA/WO4.736%#16PL-EDA5.590%

Reading: every curve uses the same instance × seed normalization and evaluation budget. The thick purple trajectory is ROSE/WT; legend order follows final mean RPD, not visual crossing order.

complete convergence · all algorithms

Total flow time: all 16 trajectories

#1NB-COIN/WT0.477%#2NHBSA/WT0.529%#3RK-EDA0.858%#4EHBSA/WT0.968%#5CNB-COIN1.512%#6ROSE/WT1.545%#7COIN/WT1.600%#8NB-COIN1.723%#9HNE-COIN1.791%#10CNE-COIN2.037%#11SNE-COIN2.176%#12GM-EDA2.542%#13NHBSA/WO2.698%#14COIN5.296%#15EHBSA/WO6.827%#16PL-EDA7.578%

Reading: every curve uses the same instance × seed normalization and evaluation budget. The thick purple trajectory is ROSE/WT; legend order follows final mean RPD, not visual crossing order.

complete convergence · all algorithms

Machine idle time: all 16 trajectories

#1ROSE/WT29.154%#2NHBSA/WT62.539%#3NB-COIN/WT69.794%#4EHBSA/WT79.917%#5NB-COIN94.147%#6COIN/WT94.646%#7HNE-COIN200.744%#8CNE-COIN229.873%#9SNE-COIN234.650%#10CNB-COIN239.007%#11RK-EDA277.234%#12COIN363.099%#13NHBSA/WO376.819%#14GM-EDA384.586%#15EHBSA/WO489.144%#16PL-EDA685.396%

Reading: every curve uses the same instance × seed normalization and evaluation budget. The thick purple trajectory is ROSE/WT; legend order follows final mean RPD, not visual crossing order.

Pareto evidence · measured

ROSE must be judged by frontier depth and spread—not one scalar rank

A × BMakespan × flow time · TA020 · 10 seedsclick to zoom

RK-EDAHNE-COINSNE-COINNB-COINCNB-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	1.026	0.072
2	HNE-COIN	0.969	0.136
3	SNE-COIN	0.960	0.151
4	NB-COIN	0.958	0.131
5	CNB-COIN	0.951	0.148
6	CNE-COIN	0.939	0.166
7	NHBSA/WO	0.889	0.181
8	NHBSA/WT	0.875	0.217

#	Algorithm	HV ↑	IGD+ ↓
9	GM-EDA	0.862	0.179
10	ROSE/WT	0.800	0.263
11	EHBSA/WT	0.785	0.280
12	COIN	0.743	0.302
13	NB-COIN/WT	0.685	0.343
14	EHBSA/WO	0.638	0.388
15	COIN/WT	0.596	0.417
16	PL-EDA	0.555	0.459

A × CMakespan × idle time · TA020 · 10 seedsclick to zoom

RK-EDANB-COINCNB-COINHNE-COINNHBSA/WT

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	0.997	0.065
2	NB-COIN	0.979	0.080
3	CNB-COIN	0.944	0.102
4	HNE-COIN	0.937	0.107
5	NHBSA/WT	0.904	0.138
6	CNE-COIN	0.893	0.133
7	GM-EDA	0.878	0.134
8	ROSE/WT	0.869	0.162

#	Algorithm	HV ↑	IGD+ ↓
9	SNE-COIN	0.861	0.153
10	EHBSA/WT	0.849	0.174
11	NHBSA/WO	0.839	0.161
12	COIN	0.834	0.181
13	EHBSA/WO	0.772	0.226
14	NB-COIN/WT	0.745	0.237
15	COIN/WT	0.695	0.272
16	PL-EDA	0.673	0.296

B × CFlow time × idle time · TA020 · 10 seedsclick to zoom

HNE-COINNB-COINCNB-COINRK-EDASNE-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	HNE-COIN	0.999	0.080
2	NB-COIN	0.998	0.076
3	CNB-COIN	0.995	0.083
4	RK-EDA	0.992	0.065
5	SNE-COIN	0.988	0.086
6	CNE-COIN	0.984	0.090
7	NHBSA/WT	0.957	0.118
8	NHBSA/WO	0.954	0.100

#	Algorithm	HV ↑	IGD+ ↓
9	COIN	0.945	0.113
10	EHBSA/WT	0.934	0.128
11	GM-EDA	0.924	0.104
12	ROSE/WT	0.915	0.139
13	EHBSA/WO	0.886	0.152
14	NB-COIN/WT	0.836	0.192
15	COIN/WT	0.805	0.204
16	PL-EDA	0.790	0.215

A × B × CThree objectives · TA020 · 10 seedsclick to zoom

RK-EDANB-COINHNE-COINCNB-COINSNE-COIN

#	Algorithm	HV ↑	IGD+ ↓
1	RK-EDA	1.011	0.066
2	NB-COIN	0.971	0.098
3	HNE-COIN	0.964	0.103
4	CNB-COIN	0.951	0.114
5	SNE-COIN	0.938	0.116
6	CNE-COIN	0.938	0.121
7	NHBSA/WO	0.906	0.125
8	GM-EDA	0.897	0.114

#	Algorithm	HV ↑	IGD+ ↓
9	NHBSA/WT	0.878	0.155
10	COIN	0.853	0.161
11	EHBSA/WT	0.839	0.172
12	ROSE/WT	0.829	0.178
13	EHBSA/WO	0.785	0.200
14	NB-COIN/WT	0.675	0.264
15	PL-EDA	0.662	0.274
16	COIN/WT	0.638	0.282

Each line is the union frontier contributed by one algorithm. Tables include all 16 methods. TA021–TA030 will use its own common normalized reference front and must not be pooled before normalization.

single objective · all variants

Template inheritance matters more than the SR or SH refinement

Objective	ROSE/WT	SR-ROSE/WT	SH-ROSE/WT	ROSE/WO	SR-ROSE/WO	SH-ROSE/WO
Makespan	#6	#12	#15	#18	#19	#21
Total flow time	#8	#13	#15	#17	#19	#21
Machine idle time	#11	#13	#15	#18	#19	#20

WT EFFECTLarge and consistent

The punched parent supplies a stable scaffold while the relational model fills only missing positions.

SR EFFECTOne hypothesis is not enough

Single-reference compact sampling ranks below multi-reference ROSE/WT on every objective.

SH EFFECTMore expressive ≠ faster

The distance histogram retains multimodality, but 400 generations may not provide enough evidence to estimate it reliably.

Interpretation: current evidence supports “template-assisted relational reconstruction,” not a claim that additional relational complexity automatically improves performance.

multi-objective · preliminary full field

ROSE preserves its family ordering, but does not yet lead the Pareto search

Objective set	Full-field leader	ROSE/WT	SR-ROSE/WT	SH-ROSE/WT
Makespan × flow time	RK-EDA	#11distance 0.2581	#13distance 0.2830	#14
Makespan × idle time	RK-EDA	#12	#13	#14
Flow time × idle time	SNE-COIN	#13distance 0.1465	#14distance 0.1520	#15distance 0.1607
Three objectives	RK-EDA	#13distance 0.1856	#14distance 0.1946	#15distance 0.2043

What remains stableROSE/WT > SR-ROSE/WT > SH-ROSE/WT across all four MO settings.

What changesRK-EDA leads three comparisons; SNE-COIN leads flow time × idle time.

What we cannot claim yetThe displayed distance is a normalized set-distance proxy, not confirmatory IGD+.

Before publication: rebuild one common reference front, normalize objectives once, then recompute HV and formal IGD+ with the same bounds for all 21 methods.

representation verdict

ROSE is not the winner yet—but the experiment explains what it needs

SUPPORTED

Relational learning is viable

Multi-reference ROSE/WT reaches the upper half of the scalar field, including sixth place on makespan.

NOT SUPPORTED

More detailed relations always help

SR and SH trail the base multi-reference model; the empirical histogram may be data-hungry at selection rate 10%.

INSTANCE EFFECT

Idle-time strength is conditional

ROSE jointly leads the TA001–TA005 one-seed pilot, yet ranks eleventh over TA021–TA030 × five seeds.

NEXT CONTROLLED TEST

Separate budget from representation

Run 10–50% selection, convergence beyond generation 400, WT-retention ablation, and matched HV/IGD+.

Paper-safe statementROSE reveals a promising relational representation whose benefit depends on template support, objective structure, and learning budget.

ROSE research program

A formal debut needs tuning and controlled ablation

Current signal

ROSE/WT is strongest on internal machine idle time

The present comparison suggests that relative order carries objective-specific information that edge-only models miss.

Required evidence

Compare WO and WT under matched seeds.
Tune selection rates from 10% to 50%.
Separate compact statistics from empirical histograms.
Measure convergence beyond 400 generations.

Variant ablation

ROSEmulti-reference mean prediction

SR-ROSEsingle-reference compact distance

SH-ROSEsingle-reference distance histogram

WTtemplate-guided reconstruction

ROSE remains in the representation study as a comparator. This replicated deck prepares its independent algorithm paper.