JANUS: Online Jacobian-Aligned Infill for Black-Box Optimization

Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution

Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--leader state. In leader-relative coordinates, the resulting operator provides a direct interpretation of interpolation, projection, overshooting, and coordinate masking. Under Bernoulli perturbation masks, we derive closed-form expressions for the proposal mean, covariance, expected squared step length, expected squared distance from the leader, active dimensionality, and coordinate coverage. For canonical DE/rand/1/bin, we derive the finite-population moments of differential mutation and characterize the additional covariance and coordinate dependence induced by forced-coordinate binomial crossover. Exact enumeration and Monte Carlo experiments verify the analytical identities and quantify the effects of mask conditioning, boundary repair, and fitness-based selection. The analysis further motivates geometry-controlled and rotation-aware SOMA variants, together with an adaptive population-reducing extension of iSOMA. Experiments on the complete noiseless BBOB benchmark show that these operator-guided variants substantially improve upon canonical SOMA and are competitive with established DE methods in several dimension--budget regimes. The results demonstrate how proposal-level operator analysis can support both the interpretation and design of population-based optimizers.

MLDGWO: a grey wolf optimizer with momentum, leader adjustment, and differential perturbation for global optimization problems

ADPSO-ERLS: A Hybrid Discrete PSO with Enhanced Local Search for the Traveling Salesman Problem

The Traveling Salesman Problem is a canonical setting for studying how a population-based method should allocate a fixed search budget between exploration and progressively stronger local intensification. We propose ADPSO-ERLS, a discrete swarm algorithm that treats this allocation as an explicit, tunable design variable. It couples memory-guided swap mutation, heterogeneous initialization, selective candidate-restricted 2-opt during evolution, and an incumbent-only final refinement combining candidate-restricted and optional full 2-opt with double-bridge perturbations. The method is PSO-inspired, using personal and global memories yet dispensing with velocity, inertia, and acceleration coefficients. All six algorithms are implemented in Rust, run on identical hardware, and stopped at a strict, recorded limit of 100,000 candidate-solution assessments, so that programming language, hardware, and evaluation budget are held common across methods; wall-clock time is reported separately because equal assessment counts need not correspond to equal arithmetic work. Over 50 runs on five symmetric TSPLIB instances under the integer \texttt{EUC\_2D} convention, ADPSO-ERLS attains the lowest best and mean cost on every instance, with best-tour Gap of $1.93$--$4.17\%$ and relative error of $3.04$--$5.50\%$. It ranks first under the Friedman test, and all twenty-five multiplicity-controlled Wilcoxon comparisons favor it with large, near-complete distributional separation. A paired ablation with common seeds links initialization, in-run local search, and final refinement to quality gains, while candidate restriction chiefly cuts runtime, by up to a factor of roughly $38$. Further experiments up to $16{,}862$ cities keep best-tour Gaps below $6.7\%$, solving the largest case in under eleven minutes.

Quantifying the Explore-Exploit Trade-off in Metaheuristics via Normalised Positional Diversity

A continuous development of metaheuristics necessitates a deeper understanding of internal search mechanisms, specifically the transition between exploration and exploitation, which is often overlooked in favour of final fitness values. This study introduces a standardized framework based on a Normalized Positional Diversity Index (D*) to quantify optimizer behaviour. We demonstrate that D* is a geometric generalization of existing measures, such as the one proposed by Hussain et al. [1], by replacing stochastic, path-dependent historical maximums with a fixed global upper bound anchored to the search space geometry. This transformation eliminates post-hoc bias and provides a scale-independent diagnostic. From D*, additional metrics including Area Under the Curve (AUC) and crossover point (txover) are derived to identify exact phase transitions. We evaluate five optimizers (GWO, DE, PSO, AGOA, and EES) across CEC 2020 benchmarks. Results confirm that D* offers consistent diversity monitoring with lower Coefficients of Variation compared to existing measures. Code and supplementary materials are available at: [https://github.com/saiddddd/D-Star-Metric-Optimization].

AutoPSO: A Meta-Framework for Automated Particle Swarm Optimization

Comprehensive experiments on numerical benchmarks and neuroevolution robotic control tasks demonstrate that AutoPSO consistently discovers novel PSO variants that significantly outperform strong baselines and confirm that AutoPSO achieves increasing performance gains with larger swarm sizes.

TSMOO: Solving Multi-Objective Experimentation with Constrained Thompson Sampling