MOSHO: A Native Discrete Shark-Inspired Metaheuristic for Hardware-Aware Neural Architecture Search

Nazim Abdeerhmane Aouni; Zakaria Soualah Mohammed; Maroua Ogab; Nour El Imane Elbar; Rayane Rahmat Errahmane Smara; Billel Moussous; Adriane Anis Khaled; Malika Bessedik

cs.NEOct 23, 2026

MOSHO: A Native Discrete Shark-Inspired Metaheuristic for Hardware-Aware Neural Architecture Search

Authors: Nazim Abdeerhmane Aouni, Zakaria Soualah Mohammed, Maroua Ogab, Nour El Imane Elbar, Rayane Rahmat Errahmane Smara, Billel Moussous, Adriane Anis Khaled, Malika Bessedik,

Organizations: Higher National School of Computer Science (ESI), Algiers, Algeria · IBM Research

Abstract

Hardware-aware neural architecture search (NAS) requires jointly optimizing predictive accuracy and device-specific latency over discrete search spaces. While multi-objective swarm optimizers show promise, continuous formulations such as the Multi-Objective White Shark Optimizer (MOWSO) can suffer from quantization noise when rounded to integer-encoded architecture vectors. To address this limitation, we propose MOSHO (Multi-Objective Shark Hunting Optimization), a native discrete metaheuristic that replaces continuous motion equations with discrete architecture-editing operators. MOSHO integrates adaptive operator scheduling, energy-regulated restarts, and deferred crowding-distance truncation to enhance exploration and search efficiency. On the merged NAS-Bench-201/HW-NAS-Bench benchmark across 18 contexts, MOSHO achieves a median normalized hypervolume of 0.9987 and IGD+ of 0.0064, yielding Pareto fronts competitive with NSGA-II while reducing search runtime by 96.4% (0.64 s vs. 17.72 s). These results demonstrate that tailored discrete search mechanisms can enable swarm optimizers to achieve high-quality multi-objective solution quality with substantially lower search cost in hardware-aware NAS.

Figures & tables

Panel of Figure 1 — Figure 1: State-of-the-art landscape considered before focusing on shark-inspired optimization for hardware-aware multi-objective NAS

Figure 2: Example NAS-Bench-201 cell (NONE: zeroize ), encoded as $\mathbf{x}=(3,1,0,0,2,4)$ with indices $0$ : zeroize , $1$ : skip-connect , $2$ : conv $1{\times}1$ , $3$ : conv $3{\times}3$ , $4$ : avg-pool $3{\times}3$ .

Panel of Figure 3 — Figure 3: System architecture of MOSHO. Dashed green arrows denote the archive-driven feedback loops that distinguish MOSHO from its ancestors.

Panel of Figure 4 — Figure 4: Workflow diagram of the MOSHO search cycle.

Metric	Description	Goal
HV	Measures both convergence and diversity by computing the objective volume dominated by the approximation front $\hat{P}$ relative to a reference point $(r_{1},r_{2})$ offset by $\varepsilon=10^{-9}$ from $P^{*}$	$\uparrow$
nHV	Normalizes HV by the hypervolume of the exact Pareto front ( $\mathrm{HV}(P)/\mathrm{HV}_{\max}$ ) to enable fair comparison across contexts and scales	$\uparrow$
$\text{IGD}^{+}$	Evaluates both proximity and coverage by computing the average minimum modified distance from $P^{*}$ to $\hat{P}$ while preserving weak Pareto compliance	$\downarrow$
Spacing ( $S$ )	Evaluates the uniformity of distribution between adjacent non-dominated solutions via the standard deviation of nearest-neighbour distances $d_{i}$	$\downarrow$
Execution Time	Measures computational efficiency and algorithmic overhead via median wall-clock runtime across complete search runs at each budget level	$\downarrow$
Note: $\uparrow$ means maximize; $\downarrow$ means minimize.

Table 1: Summary of Evaluation Metrics

Param	Description	Range	Value	Param	Description	Range	Value
$N$	Population size	$\{20,30,50,80,100\}$	50	$\gamma$	Energy reset factor	$[0,1]$	0.50
$M$	Archive capacity	$[10,N]$	50	$P_{\rm patrol}$	Patrol probability	$[0,1]$	0.20
$e_{0}$	Initial energy/agent	$[0.5,\,2.0]$	0.818	$P_{\rm scent}$	Scent probability	$[0,1]$	0.25
$e_{\min}$	Restart energy thresh.	$[0.05,\,0.5]$	0.500	$P_{\rm circle}$	Circle probability	$[0,1]$	0.15
$e_{\max}$	Energy cap	$[0.5,\,2.0]$	1.699	$P_{\rm burst}$	Burst probability	$[0,1]$	0.10
$\delta$	Energy decay (rejection)	$[0,\,0.1]$	0.0968	$P_{\rm crossover}$	Crossover probability	$[0,1]$	0.20

Table 2: MOSHO hyperparameter settings after Optuna tuning.

Single-unit ablations			Grouped variants
Rem.	Name	Var.	Rem.	Name	Var.
U01	Discrete operator kernels	ABL-U01	U01+U02	Search core removal	G-SEARCH
U02	Explicit acceptance policy	ABL-U02	U05+U06+U07	Adaptive block removal	G-ADAPT
U03	Energy-regulated restarts	ABL-U03	U08	K-means leader-selection removal	G-ARCHIVE
U04	Dual adaptive signal	ABL-U04	U08+U09	No-advance mode	G-NOADV
U05	Active archive feedback	ABL-U05	U01–U07	Core mechanism removal	G-NOBASE

Table 3: Ablation units and tested grouped variants.

Panel of Figure 5 — Figure 5: Ablation study results across all tested variants. Top: median nHV, IGD + , spacing, and execution time over 30 independent runs per variant across the 18 benchmark contexts. Middle: Vargha–Delaney $A_{12}$ effect sizes for IGD + (left) and nHV (right); values above 0.5 favor MOSHO, values below 0.5 favor the ablated variant, dashed line marks the no-effect threshold of 0.5. Bottom: Wilcoxon signed-rank $p$ -values for IGD + (left) and nHV (right); values below the significance threshold ( $\alpha=0.05$ , dashed line) indicate a statistically significant difference from MOSHO.

Panel of Figure 6 — Figure 6: Comparison of MOSHO with several multi-objective optimization algorithms across 18 contexts. Median nHV and IGD + (top), and execution time and spacing (bottom), are reported over 30 runs with a budget of 15000 evaluations.

Panel of Figure 7 — Figure 7: Sensitivity analysis of MOSHO with respect to the two primary hyperparameters. For visualization purposes, each metric is independently normalized to the interval $[0,1]$ , allowing the relative evolution of nHV, IGD + , spacing, and runtime to be compared on a common scale.

Figure 8: Data inflation procedure applied to the NAS-Bench-201 search space. A new intermediate node is inserted into the DAG, adding 4 new edges and expanding the architecture space from $5^{6}=15{,}625$ to $5^{10}=9{,}765{,}625$ candidate architectures.

Metric	MOSHO	NSGA-III	MOEA/D
nHV	0.9658	0.9350	0.9070
IGD +	0.042	0.063	0.066
Spacing	0.628	4.248	7.702
Runtime (s)	0.68	2.23	0.80

Table 4: Comparison of MOSHO against NSGA-III and MOEA/D across 18 contexts.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Dimension	WSO	MOWSO	SSO	MOSHO
Objective type	Single	Multi	Single	Multi
Search space	Continuous	Continuous	Continuous	Discrete (native)
Search mechanism	Velocity–position, factor $\mu$	Velocity–position with post-hoc rounding	Gradient-following with rotational search	Six discrete operator kernels
Crossover	None	None	None	Uniform, then mutation ( $p\!=\!0.3$ )
Archive strategy	None	Pareto archive, True Distance	None	Pareto archive, crowding distance
Truncation timing	N/A	Per candidate	N/A	End of iteration (batch)

Appendix

Table 5: Structural comparison between MOSHO and its ancestor methods.

$B$	HV	IGD +	Spacing	Runtime (s)	Best Latency
1,000	0.9881	0.1120	3.2454	0.0538	0.3571
2,000	0.9935	0.0674	3.0531	0.1150	0.3568
5,000	0.9974	0.0258	2.8476	0.3066	0.3567
7,000	0.9979	0.0162	2.8126	0.4265	0.3566
10,000	0.9989	0.0110	2.7859	0.6289	0.3567
15,000	0.9992	0.0069	2.7634	0.9779	0.3566

Appendix

Table 6: Effect of evaluation budget

B

on raw median metrics (

N=50

fixed).

$N$	HV	IGD +	Spacing	Runtime (s)	Best Latency
20	0.9992	0.0089	3.8056	0.8921	0.3565
30	0.9993	0.0067	3.2879	0.9756	0.3566
50	0.9992	0.0069	2.7634	1.0047	0.3566
80	0.9994	0.0092	2.7539	0.9571	0.3566
100	0.9993	0.0070	2.7348	0.9914	0.3566

Appendix

Table 7: Effect of population size

N

on raw median metrics (

B=15{,}000

fixed).

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