---
kind: concept
slug: metaheuristic-optimization
title: Metaheuristic optimization
summary: >-
  Population-based search for hard, black-box objectives, simulator failures and feature subsets. Eight cards: a swarm method, a membrane optimizer, surrogate-based GA and NSGA-II, two simulator test generators, two feature-selection studies, and a learned router that uses a metaheuristic as its baseline. Trade-offs: tuning effort, no guarantees, author-reported evidence.
tags: [optimization, swarm-intelligence, metaheuristic, evolutionary-algorithm, simulation-testing, feature-selection]
papers: ["1904.05226", "2609.12756", "2609.16066", "2410.19277", "2412.13802", "2608.14156", "2008.04103", "2012.05999"]
related: [bayesian-optimization, hyperparameter-optimization, particle-swarm-optimization, neural-operator, image-thresholding, neuroevolution, fuzz-testing, surrogate-modeling, sim-to-real-transfer, neural-combinatorial-optimization, feature-selection]
status: draft
updated_at: 2026-11-01
---

## Overview

A metaheuristic is a general search procedure that does not need the gradient
of the objective and makes few assumptions about its shape. The paper that
motivates this page describes nature-inspired metaheuristics as a way to
escape local optima, and notes that they offer few guarantees on hard
multimodal problems [arxiv:1904.05226 §I].

The invariant shared by the variants is a population of candidate solutions
that is updated until a fixed budget runs out: a fixed number of rounds in the
swarm and surrogate GA cards, a cap of 100,000 fitness evaluations in the
membrane card [arxiv:2609.12756 §4.1], a budget of 220 simulator runs in the
MARTENS card [arxiv:2410.19277 §3.1], and six hours of fuzzing in the
SimADFuzz card [arxiv:2412.13802 §5.2.2]. In the feature-selection cards the
candidate is a subset of features, and in the review's wrapper methods each
subset is scored by a classifier [arxiv:2008.04103 §2.2]. In the swarm variant, each round
every candidate proposes a new position from its current position and from
information about the best candidate so far, and keeps the proposal if it
scores better [arxiv:1904.05226 §IV]. The GA variant names a genetic algorithm
with population 20 and 100 generations, but its selection, recombination and
mutation steps are not stated in the paper [arxiv:2609.16066 §4.3].

The paper also argues that no single metaheuristic is best on every problem,
so a new method is worth proposing when it helps on some problems
[arxiv:1904.05226 §I]. Treat that as the reason the design space is wide, not as
a ranking.

The second card changes where the cost sits. Its search does not run the
simulator for each candidate. It queries a trained neural surrogate, which is
cheap, and runs the simulator only on the designs the search returns
[arxiv:2609.16066 §4.3]. The two testing cards do the opposite: each candidate
is run in the simulator, and the search cost is the simulator's cost
[arxiv:2410.19277 §3.1] [arxiv:2412.13802 §5.1].

The routing card is not a population method. It trains a neural network that
builds routing solutions one stop at a time, with several routes grown in
parallel rather than a population of candidates that is improved
[arxiv:2608.14156 §3]. It is listed here because its comparison baseline is a
metaheuristic: Google OR-Tools, including its metaheuristic search, which the
card uses as the reference at each size [arxiv:2608.14156 §5.2] [arxiv:2608.14156 §5.3].
Read its results as a trade-off against a metaheuristic, not as a
metaheuristic variant.

## Variants

### Fitness Dependent Optimizer (swarm, weighted step)

Each agent (a "scout") takes a step whose length and direction depend on the
ratio of the best candidate's fitness to its own, minus one weight factor wf,
plus a random factor drawn from [-1, 1] [arxiv:1904.05226 §IV] [arxiv:1904.05226
eq. 2]. The paper also reuses the last step that improved an agent and tries it
again when the new step fails [arxiv:1904.05226 fig. 3]. Card:
[Fitness Dependent Optimizer: Inspired by the Bee Swarming Reproductive Process](/papers/1904.05226).

Reported results are author-reported. On 19 classical functions (10-D, 30
agents, 500 iterations, 30 runs) the authors say the method generally does
better on the first six functions and on several composite ones, and worse on
some others such as TF7 [arxiv:1904.05226 §V.1] [arxiv:1904.05226 tab. 2]. On
10 CEC-2019 functions the text says it outperforms the compared methods except
on CEC06 [arxiv:1904.05226 §V.2] [arxiv:1904.05226 tab. 3].

### Membrane-split artificial protozoa optimizer (population splitting, roulette guide)

The base is the artificial protozoa optimizer (APO). It moves each candidate
with one of four operators: foraging toward a guide, heterotrophic foraging,
dormancy and reproduction [arxiv:2609.12756 §2.1]. The membrane variant adds
two changes. First, each iteration it measures a volume-based diversity value.
When that value falls below a threshold ε, the whole population is one group;
otherwise it is split at random into m groups, each updated separately and then
merged again [arxiv:2609.12756 §3.1] [arxiv:2609.12756 alg. 1]. The number m is
drawn every iteration with m_max = 4 [arxiv:2609.12756 eq. 18]. Second, the
guide for autotrophic foraging is picked by a roulette wheel over a score that
mixes fitness and distance to the best solution [arxiv:2609.12756 §3.2]
[arxiv:2609.12756 eq. 19] [arxiv:2609.12756 eq. 21]. Card:
[MAAPO: an innovative membrane algorithm based on artificial protozoa optimizer for multilevel threshold image segmentation](/papers/2609.12756).

Reported results are author-reported. On 30 CEC2017 functions at 10-D, with 51
runs and 13 algorithms, the method has the best average Friedman rank (3.35),
ahead of MAQUATRE (3.37) and APO (3.55) [arxiv:2609.12756 §4.5]. Against plain
APO it wins 8 functions and loses none [arxiv:2609.12756 tab. 5]. On
multilevel thresholding of three RGB images it has the best average rank for
Kapur entropy on all three metrics, and for Otsu only on SSIM; for Otsu PSNR
PSO ranks better, and for Otsu FSIM DE does [arxiv:2609.12756 tab. 11]
[arxiv:2609.12756 tab. 12]. Its average runtime is 1.38 s against 0.81 s for APO
on the authors' laptop [arxiv:2609.12756 tab. 7].

### Particle swarm optimization (baseline)

The FDO paper uses PSO as the base for its update style and as a comparison
method [arxiv:1904.05226 §I] [arxiv:1904.05226 §V.1]. FDO replaces PSO's
velocity term with a fitness-derived step [arxiv:1904.05226 §I]. The PSO page
is [Particle swarm optimization](/concepts/particle-swarm-optimization). The
PSO comparison numbers in the FDO paper are taken from another study rather
than re-run by the authors [arxiv:1904.05226 §V.1]. In the feature-selection
review, PSO is also the strongest wrapper on average for SVM and AdaBoost, but
not for Naive Bayes [arxiv:2008.04103 §4.4].

### Genetic algorithm and NSGA-II over a neural surrogate

The compressor-design card runs a genetic algorithm (GA) for single-objective
tasks and NSGA-II for multi-objective tasks. Both search a trained neural
operator instead of the CFD solver. The GA uses a population of 20 over 100
generations, and NSGA-II a population of 30 over 100 generations
[arxiv:2609.16066 §4.3]. Card:
[Neural-operator surrogate for compressor-cascade flow fields](/papers/2609.16066).

The paper reports five single-objective tasks, one per performance parameter.
For efficiency, the surrogate predicts 0.871 at the optimum against a reference
of 0.854, and CFD gives 0.871 at the same design [arxiv:2609.16066 tab. 9].
Three multi-objective tasks are reported with the highest-efficiency point of
each solution set [arxiv:2609.16066 §4.3] [arxiv:2609.16066 tab. 10]. Every
optimal design was checked with CFD [arxiv:2609.16066 §4.3].

The authors state that the surrogate-based optimisation took 121 s, where
earlier work needed 1000 CFD runs [arxiv:2609.16066 §4.3]. One CFD run takes
about 800 s on the authors' CPU [arxiv:2609.16066 §2.2]. These are author-reported
timings; the paper does not state the hardware for the surrogate's prediction time.

### Genetic search for failing simulator scenarios (testing)

Here the search looks for inputs that make a system fail, not for the best
design. Both cards run every candidate in a simulator and record which ones
fail, so the search is bounded by simulator cost rather than by a surrogate.

MARTENS searches a pick-and-place scene in Isaac Sim for failures of a
detector [arxiv:2410.19277 §2.2]. A test is a chromosome with an (x, y, r)
triple per movable box and a lighting level [arxiv:2410.19277 §2.2]. The
fitness is a weighted sum of the largest position error and the largest
rotation error across the boxes, with both weights 0.5 [arxiv:2410.19277 eq. 1]
[arxiv:2410.19277 §3.1]. The search is a single-objective GA with one-point
crossover, two mutation operators and a cosine-distance duplicate filter
[arxiv:2410.19277 §2.2]. The failing tests then fine-tune the detector
[arxiv:2410.19277 §2.5]. Card:
[In-Simulation Testing of Deep Learning Vision Models in Autonomous Robotic Manipulators](/papers/2410.19277).

Author-reported results, against random search with the same budget of 220
evaluations and five runs each: the GA finds about 50% more failing tests in
use case 1 and 26% more in use case 2 [arxiv:2410.19277 tab. 2]
[arxiv:2410.19277 tab. 3]. Its failures are more spread out in features, with a
large effect in use case 1 and a medium one in use case 2, but the severity
spread does not differ significantly [arxiv:2410.19277 tab. 4]. Fine-tuning on
the failing images makes more than 99% of the failing tests pass when re-run
[arxiv:2410.19277 tab. 5] [arxiv:2410.19277 tab. 6]. A detector fine-tuned this
way reaches mAP 0.948 and 0.892 on the real test splits, against 0.806 and
0.755 for a detector trained on real images only [arxiv:2410.19277 tab. 8].
Those real sets have about 100 images per use case, and no variance across
seeds is reported for the real-data models [arxiv:2410.19277 §3.2.3].

SimADFuzz fuzzes a self-driving stack in CARLA [arxiv:2412.13802 §4.1]. A
chromosome holds the ego route, the NPC routes, the pedestrian routes and the
weather [arxiv:2412.13802 §4.2]. NSGA-II selects offspring on four objectives:
a Transformer score over the simulation trace, a classifier over static road
features, the minimum ego distance, and the number of unique violations
[arxiv:2412.13802 §4.2.1]. The Transformer is a learned score, not a stand-in
for the simulator; each offspring is still simulated [arxiv:2412.13802 §4.1]
[arxiv:2412.13802 §5.1]. Mutation removes NPCs that stay still or move away
from the ego vehicle, and places new ones [arxiv:2412.13802 §4.2.3]
[arxiv:2412.13802 alg. 1]. Card:
[SimADFuzz: Simulation-Feedback Fuzz Testing for Autonomous Driving Systems](/papers/2412.13802).

Author-reported results on InterFuser, Town03, with one shared seed set: 35
unique violations in six hours, against 26 for TM-Fuzzer, 18 for DriveFuzz and 3
for AV-Fuzzer [arxiv:2412.13802 §5.2.2] [arxiv:2412.13802 fig. 8]. In a
three-hour ablation the full method finds 24 against 14 [arxiv:2412.13802
§5.2.1] [arxiv:2412.13802 fig. 7]. The authors name one system and one map as
a limit on external validity [arxiv:2412.13802 §5.3].

### Wrapper feature selection with swarm methods (review)

A feature subset is the candidate, and a classifier trained on the subset
scores it. The review by Rostami, Berahmand and Forouzandeh covers 11 swarm
families (PSO, ACO, ABC, DE, GSA, FA, BA, COA, GWO, WOA and SSA) and the
feature selection work built on each [arxiv:2008.04103 §3] [arxiv:2008.04103
tab. 2]. Its own experiment runs one wrapper per family and four filters on six
UCI datasets, with SVM, Naive Bayes and AdaBoost, 10 runs each and a random
66/34 train/test split [arxiv:2008.04103 §4] [arxiv:2008.04103 §4.3]. The paper
does not state population sizes, iteration counts or stopping rules for any
method, so the original method papers are needed to reproduce it
[arxiv:2008.04103 §4]. Card:
[Review of Swarm Intelligence-based Feature Selection Methods](/papers/2008.04103).

Author-reported, averaged over the six datasets: PSO has the highest wrapper
accuracy on SVM (89.35%) and AdaBoost (88.92%). On Naive Bayes, COA is first
(89.24%) and PSO second (89.08%) [arxiv:2008.04103 §4.4] [arxiv:2008.04103
fig. 1] [arxiv:2008.04103 fig. 2] [arxiv:2008.04103 fig. 3]. The text says PSO
does better than the other wrappers in most cases, but the paper gives no
significance test, and the gaps are within the per-dataset standard deviations
[arxiv:2008.04103 §4.4] [arxiv:2008.04103 tab. 4]. Among filters, ACO has the
highest average on SVM (79.52%) against 78.82% for PSO [arxiv:2008.04103 §4.4].

### Cuttlefish feature selection and elephant-herd weight tuning (clinical)

The heart-disease card combines two population searches. A modified cuttlefish
algorithm (MCFA) selects features, and an elephant-herd variant (AEHO) sets
the weights of a small fully connected network that the paper calls MDCNN
[arxiv:2012.05999 §II-B] [arxiv:2012.05999 §II-C] [arxiv:2012.05999 §II-D].
The paper does not state population sizes, generation limits, clan counts or
the fitness function for AEHO [arxiv:2012.05999 §II-D] [arxiv:2012.05999 §II-E].
Card: [An IoT Framework for Heart Disease Prediction based on MDCNN Classifier](/papers/2012.05999).

Author-reported: 98.2% accuracy on the 4000-record Framingham set, against
88.3% for logistic regression and 83.8% for the baseline deep network
[arxiv:2012.05999 tab. 8]. These are single results without variance across
runs, and the train/test split and the baseline architecture are not stated
[arxiv:2012.05999 §IV-B]. Part of the sensor data is generated with
pseudo-random numbers [arxiv:2012.05999 §IV-A].

## When to use which

The wiki has eight papers on this page, so the table compares their methods
with the constraints they report. It does not rank metaheuristics against each
other.

| Situation | Use | Why |
|---|---|---|
| Objective is multimodal and has no usable gradient, and the budget covers the population size times the iteration count (the FDO setup is 30 agents over 500 iterations) | A population method such as the swarm variant | Designed for local-optima problems; the FDO paper reports benchmark wins over PSO, GA and DA [arxiv:1904.05226 §I] [arxiv:1904.05226 §V.1] |
| Each evaluation is an expensive simulator, but a trained surrogate is much cheaper | GA or NSGA-II over the surrogate, then verify the chosen designs with the simulator | The compressor card ran the GA and NSGA-II on the surrogate and checked every optimum with CFD [arxiv:2609.16066 §4.3]; about 0.9 ms per prediction against about 800 s per CFD run [arxiv:2609.16066 tab. 3] [arxiv:2609.16066 §2.2] |
| Several objectives that trade off against each other | NSGA-II | The compressor card used it for three tasks and reported the highest-efficiency point of each solution set [arxiv:2609.16066 §4.3] [arxiv:2609.16066 tab. 10] |
| Choosing a feature subset for a classifier you can retrain for each candidate, and you want the search to decide the subset | A swarm wrapper; PSO is the review's strongest on two of its three classifiers | Author-run and without a significance test: PSO has the best mean wrapper accuracy on SVM and AdaBoost over six UCI sets, but not on Naive Bayes [arxiv:2008.04103 §4.4] [arxiv:2008.04103 fig. 1] [arxiv:2008.04103 fig. 3] |
| Feature selection where each classifier fit is too costly to repeat per candidate | A filter score, accepting that features are treated as independent | The review says filters are cheap but usually reach lower-quality subsets [arxiv:2008.04103 §2.1] [arxiv:2008.04103 §5]. The best filter on SVM is ACO, at 79.52% against 78.82% for PSO [arxiv:2008.04103 §4.4] |
| Clinical tabular data, where the reported accuracy is the reason to pick a method | Treat the heart-disease card's numbers as the authors' claim, not as a target | Its 98.2% comes from one dataset with no variance across runs, and the split and baseline architecture are not stated [arxiv:2012.05999 tab. 8] [arxiv:2012.05999 §IV-B] |
| A hard limit on one quantity, such as mass flow | Add the limit to the search as a constraint, then check the result with the simulator | Two of the three multi-objective optima moved above the reference mass flow, and the constrained one stayed near it [arxiv:2609.16066 tab. 10] [arxiv:2609.16066 §4.3]. How the constraint is enforced is not stated [arxiv:2609.16066 §4.3] |
| Finding failing inputs for a simulated system, where one simulated run costs minutes | GA over the scenario parameters, compared with random search under the same budget | Author-reported: about 50% and 26% more failing tests than random search [arxiv:2410.19277 tab. 2] [arxiv:2410.19277 tab. 3]. At 280 to 310 s per test, 220 runs take about 17 to 19 hours if run one after another [arxiv:2410.19277 §3.1] |
| Fuzzing a driving stack, where distinct violations matter more than one summary score | NSGA-II with a learned violation score as one of several objectives | Author-reported: 35 unique violations in six hours on one system and one map, against 3 to 26 for three earlier fuzzers [arxiv:2412.13802 §5.2.2] [arxiv:2412.13802 §5.3] |
| Vehicle routing with pickups before deliveries, capacity and time windows, where answers are needed within seconds and training for hours on one GPU is acceptable | A learned route builder, compared against OR-Tools' metaheuristic as the baseline | Author-reported: better early solutions than OR-Tools at every size tested, but final quality close to OR-Tools only up to 200 customers. Training takes 3 to 336 hours per model on one A40 [arxiv:2608.14156 §5.1] [arxiv:2608.14156 §5.3] [arxiv:2608.14156 tab. 1] |
| Routing with 400 or 1000 customers and a long time budget | Keep the metaheuristic search of OR-Tools, or check the learned route builder against it | Author-reported: at 400 s the learned route builder stays about 20% behind OR-Tools, and OR-Tools' metaheuristic finds no first solution within 60 s [arxiv:2608.14156 §5.3] [arxiv:2608.14156 fig. 4] |
| Need to know whether the failures are varied, not just many | Measure feature and severity spread of the failures, as the MARTENS card does | Its GA raised feature spread over random search, but not severity spread [arxiv:2410.19277 tab. 4] |
| Failures found, and the model must be repaired before deployment | Fine-tune on failing and near-failing inputs, then re-run them | Author-reported: more than 99% of the re-run failing tests pass, and a repaired model needs fewer training epochs on real images [arxiv:2410.19277 tab. 5] [arxiv:2410.19277 tab. 8] |
| Little time for hand-tuning | Swarm variant with the default weight factor wf = 0 | The FDO paper says wf is the only parameter to tune and gives wf = 0 as the default [arxiv:1904.05226 §IV] [arxiv:1904.05226 §V.1] |
| Need a result with formal guarantees | Not covered here | The FDO paper gives no guarantees and cites the no-free-lunch argument [arxiv:1904.05226 §I] |
| Hyperparameter or architecture search with expensive trials | See [Bayesian optimization](/concepts/bayesian-optimization) | The FDO paper's experiments are on benchmark and signal-design objectives, not on training runs [arxiv:1904.05226 §V] |
| Engineering problem similar to antenna placement or FM sound fitting | Swarm variant as a first try | The FDO paper reports these two examples, with the FM result given without a numeric objective value [arxiv:1904.05226 §V.5A] [arxiv:1904.05226 §V.5B] |
| Multilevel image thresholding with Kapur or Otsu as the score, population size 100 | Membrane variant (MAAPO), or plain APO as the baseline | Author-reported: MAAPO has the best Kapur ranks on all three metrics, but the Otsu results are mixed [arxiv:2609.12756 tab. 11] [arxiv:2609.12756 tab. 12]. Its runtime is about 1.7 times APO's [arxiv:2609.12756 tab. 7] |
| Continuous objective where the population stalls early, and the extra runtime is acceptable | Membrane variant (MAAPO) | Against its own ablations it wins 5 of 30 functions and loses none, for both the membrane-only and the roulette-only variant [arxiv:2609.12756 tab. 5] |
| Dimension above 10 | Not covered by this card | CEC2017 was run only at 10-D [arxiv:2609.12756 §4.1] |
| Choosing between the top few methods on ranks alone | Do not decide on rank | MAAPO's average rank is 0.02 below MAQUATRE's, and the two have 10 wins and 10 losses against each other [arxiv:2609.12756 §4.5] |

Choose the weight factor per problem. The FDO paper uses wf = 1 for two
benchmark functions and wf = 0 elsewhere [arxiv:1904.05226 §V.1], so a single
default is not shown to transfer.

A surrogate in the loop has a cost too. At the optimum, the surrogate can be
wrong: for pressure loss, the surrogate predicts 0.115 and CFD gives 0.103, a
related error of 11.87% [arxiv:2609.16066 tab. 9]. The paper also says the
optimal solutions lie outside the training-sample range [arxiv:2609.16066 §4.3],
so check the chosen designs with the simulator before trusting them.

## Implementation sketch

Language-agnostic pseudocode of the swarm variant's core. The zero-fitness rule
and the retry step follow the paper's figure [arxiv:1904.05226 fig. 3]. Check
the signs in the step equations against the PDF before coding
[arxiv:1904.05226 eq. 4] [arxiv:1904.05226 eq. 5].

```pseudocode
# Population search, minimisation  [arxiv:1904.05226 §IV]
def swarm_search(f, n, T, wf, lower, upper):
    # Random start inside the bounds; bounds handling is not stated  [§IV]
    x = random_uniform(lower, upper, shape=(n, dims))
    # Last accepted step per agent, empty at the start  [fig. 3]
    pace = [None] * n
    for t in range(T):
        # Best candidate of this iteration  [§IV]
        best = x[argmin(f(x))]
        for i in range(n):
            # Zero own fitness gives weight 0  [fig. 3]
            w = 0 if f(x[i]) == 0 else abs(f(best) / f(x[i])) - wf  # [eq. 2]
            # Random factor in [-1, 1]; the paper names a Levy flight  [§IV]
            r = random_uniform(-1, 1)
            # Weight 0 or 1 uses the position itself  [eq. 3]
            step = x[i] * r if w in (0, 1) else (x[i] - best) * w * sign(r)
            # Accept the new candidate only if it is better  [eq. 1] [fig. 3]
            cand = x[i] + step
            if f(cand) < f(x[i]):
                x[i], pace[i] = cand, step
            elif pace[i] is not None and f(x[i] + pace[i]) < f(x[i]):
                # Otherwise retry the last accepted step  [fig. 3]
                x[i] = x[i] + pace[i]
    return argmin(f(x))
```

Where variants differ: the random factor's distribution, bounds handling and
the exact sign convention in the step equations. The paper gives no bounds
rule [§IV], and the Lévy flight has no stated exponent or scale [§IV].

For the surrogate pattern, the same kind of loop runs with `f` replaced by the
surrogate's prediction, and the simulator checks only the returned designs
[arxiv:2609.16066 §4.3]. The GA's selection, recombination and mutation
operators are not stated, so the implementer has to choose them
[arxiv:2609.16066 §4.3].

For the simulation-testing loop, the shared core is: run each candidate in the
simulator, record pass or fail, drop near-duplicates, breed, and stop at a
budget [arxiv:2410.19277 §2.2] [arxiv:2412.13802 §5.1]. Neither card states
every operator. MARTENS does not give its parent-selection rule, its
replacement scheme or the number of generations, and its cut-point range is not
given [arxiv:2410.19277 §2.2]. SimADFuzz's stopping rule is the time budget
alone [arxiv:2412.13802 §5.2].

For the membrane variant, each iteration first computes the diversity value
[arxiv:2609.12756 eq. 15]. Below ε the population is updated as one group;
otherwise it is split into m random groups, each updated, and then merged
[arxiv:2609.12756 alg. 1]. The card's pitfalls list open points to settle before
coding: whether each solution gets one APO operator or all four per iteration
[arxiv:2609.12756 alg. 1] [arxiv:2609.12756 §2.1]; whether the pool fraction pf
is used at all [arxiv:2609.12756 eq. 11]; and which "best" the distance term
measures [arxiv:2609.12756 §3.2]. The paper does not state these.

## Contradictions

None between the cards on the same claim. Their results measure different
things: benchmark functions in the FDO card, a compressor-design task in the
second, benchmark suites plus image thresholding in the membrane card, and
failures found in simulators in the two testing cards, a routing
construction task in the routing card, and classifier accuracy on feature
subsets in the two feature-selection cards. Their numbers are therefore not
comparable. The review's and the heart-disease card's feature-selection
results are on different data and classifiers, so neither confirms the other.
The heart-disease card's own tables also disagree on feature counts
[arxiv:2012.05999 tab. 3] [arxiv:2012.05999 tab. 7]. The routing card's early-solution gains also differ by size: about
up to 3% at 50 customers [arxiv:2608.14156 §5.1], 15 to 200 percent at 100 and 200
[arxiv:2608.14156 §5.2], and about 50% at 400 and 1000 [arxiv:2608.14156 §5.3].
The paper gives these in the text and plots rather than in a table. Within the FDO card, the PSO, GA
and DA classical numbers come from another study, not from the authors' runs
[arxiv:1904.05226 §V.1], so those comparisons mix sources. The compressor card
compares its optimisation only with the authors' earlier work, not with other
metaheuristics [arxiv:2609.16066 §4.3]. The membrane card's ranking margin over
MAQUATRE is 0.02 [arxiv:2609.12756 §4.5], and the card's own win-loss counts
against MAQUATRE are even at 10 and 10 [arxiv:2609.12756 §4.5].

Inside the testing cards, the printed numbers do not always add up. In the
MARTENS tables, the row sums do not match the printed totals, so the gains over
random search are the card's reading of the counts [arxiv:2410.19277 tab. 2]
[arxiv:2410.19277 tab. 3]. In SimADFuzz, the text gives a margin of 27 over
DriveFuzz, but its six-hour table gives 18 for DriveFuzz, which implies 17
[arxiv:2412.13802 §5.2.2] [arxiv:2412.13802 §7]. Check the source before
quoting either margin.

## Papers

- [Fitness Dependent Optimizer: Inspired by the Bee Swarming Reproductive Process](/papers/1904.05226): a swarm method whose step is scaled by a fitness-derived weight, with a random factor and a reused step after success; author-reported benchmark results.
- [MAAPO: an innovative membrane algorithm based on artificial protozoa optimizer for multilevel threshold image segmentation](/papers/2609.12756): APO with membrane-style splitting and merging of the population, and a roulette fitness-distance rule for the guide; author-reported CEC2017 and thresholding results.
- [Neural-operator surrogate for compressor-cascade flow fields](/papers/2609.16066): GA and NSGA-II run over a trained neural operator for compressor-blade design; author-reported optima, each checked with CFD.
- [In-Simulation Testing of Deep Learning Vision Models in Autonomous Robotic Manipulators](/papers/2410.19277): a single-objective GA searches a simulated pick-and-place scene for detector failures, then fine-tunes the detector on them; author-reported gains over random search and on real images.
- [SimADFuzz: Simulation-Feedback Fuzz Testing for Autonomous Driving Systems](/papers/2412.13802): NSGA-II genetic fuzzer for self-driving systems in CARLA, with a Transformer score over the simulation trace; author-reported violation counts against three fuzzers on one system.
- [Attention-based RL for pickup-and-delivery routing with time windows](/papers/2608.14156): an attention-based reinforcement-learning route builder with a pickup-order mask and a soft penalty; OR-Tools, including its metaheuristic search, is the baseline. Author-reported results only.
- [Review of Swarm Intelligence-based Feature Selection Methods](/papers/2008.04103): a survey of 11 swarm families for feature selection, with one wrapper and one filter per family run on six UCI datasets; author-run averages, no significance test.
- [An IoT Framework for Heart Disease Prediction based on MDCNN Classifier](/papers/2012.05999): cuttlefish-based feature selection and elephant-herd tuning of a small network for heart-disease classification; author-reported accuracy, with key settings not stated.