Anna Maria Gianni

Continuous optimization now draws on a large and growing number of competing metaheuristic families, including differential-evolution lineages, covariance-matrix adaptation strategies, swarm-intelligence methods, and simulated annealing, yet no single method dominates across problem classes, a consequence of the No Free Lunch theorem. This motivates algorithm selection: choosing, for an unseen problem, the method most likely to perform best. Building on the OptimSolution framework, we assemble a headless, reproducible batch-execution pipeline coupled with Exploratory Landscape Analysis (ELA), enabling large-scale, statistically grounded benchmarking together with feature-based meta-learning. We evaluate a set of optimizers of comparable overall strength, drawn from distinct algorithmic families, across a broad benchmark suite spanning classical scalable functions and established competition test suites, under a consistent multi-run evaluation protocol. A Random Forest classifier trained on ELA features, validated under a Leave-One-Problem-Out cross-validation scheme, is shown to predict the best-performing optimizer for a previously unseen problem substantially more accurately than the naive Single Best Solver (SBS) baseline, closing a meaningful share of the gap toward the oracle Virtual Best Solver (VBS). Family-level analysis further shows that structured competition benchmarks and classical scalable functions tend to be won by different solvers, confirming that the underlying selection problem is genuine rather than trivial. These results indicate that landscape-aware selection can meaningfully outperform naive strategies when the candidate methods are drawn from heterogeneous algorithmic families of comparable strength.

SPARQ is an advanced global optimization algorithm, the direct evolution of an earlier method called ARQ2. It searches efficiently for the best solution to problems where the space of options is too vast to check exhaustively, such as tuning antenna arrays or planning fuel-efficient spacecraft trajectories. Like its predecessor, it works with a population of candidate solutions that improve generation after generation, alternating between two complementary search strategies. What sets SPARQ apart is that it makes nearly every part of this process adaptive. Its population shrinks intelligently as the search matures. Its internal settings draw from a memory of many past successful configurations, not a single average. Its escape-from-stagnation mechanisms come in graduated strength, from a gentle nudge to a deeper partial restart. It also adds capabilities its predecessor never had, including a dedicated phase that locally polishes the current best solution using its own memory of productive directions. Every addition is kept only where it showed an overall benefit during development, though a subsequent component-wise analysis shows this benefit varies markedly in size and statistical significance across mechanisms. The result is more reliable than its predecessor on the large majority of tested problems, while staying grounded in the same battle-tested core.

We present OptimSolution, an open-source, cross-platform framework for the systematic benchmarking and analysis of continuous optimisation methods, available for Windows, Linux and macOS and operable via both a command-line interface (CLI) and a Qt-based Graphical User Interface (GUI). The framework supports four execution modes: Single mode for single method–problem runs with convergence and distribution analysis; Batch mode for automated multi-method, multi-problem experimentation with aggregated statistical summaries; Method Sensitivity Analysis for quantifying the effect of algorithmic hyperparameters on solution quality; and Problem Sensitivity Analysis for assessing how problem-defining parameters influence instance difficulty and inter-method rankings. Complexity analysis is provided along two-axes method scalability across problem dimensionalities and problem difficulty profiles across method portfolios. Statistical validation is embedded natively through Wilcoxon signed-rank and Friedman tests with post-hoc pairwise analysis, complemented by rank tables and box-plot visualisations. All outputs are exportable as CSV files or publication-ready PNG figures. The framework is designed for extensibility: new methods and benchmark problems can be registered and activated through the GUI without modifications to the core codebase, supporting rapid experimental iteration.

This article presents a new literature-informed benchmark problem for continuous global optimization, inspired by the semantics of weather-aware irrigation scheduling. The problem is formulated as a continuous minimization task in which irrigation decisions are determined under synthetically generated but agronomically motivated weather-dependent water demand, rainfall effects, and nonlinear operational penalties. The proposed benchmark is intentionally synthetic and self-contained requiring no external datasets or field-calibrated parameters while its components are grounded in established concepts from irrigation science such as evapotranspiration-based demand estimation, yield response–water relationships, and weather-dependent scheduling principles. It is designed to be sufficiently challenging for numerical optimization while retaining a clear agronomic interpretation. The article provides the full mathematical formulation of the problem, explains its main components and parameters, and reports an experimental study focused on its optimization behavior using ten established continuous optimizers across five problem dimensions. From this perspective, the proposed problem is positioned within a clear framework for the study of real-world-inspired continuous optimization benchmarks, offering an additional case in which mathematical formulation, practical interpretation, and experimental investigation coexist in a coherent and systematic manner.

ARQ2 is introduced as a next-generation extension of the ARQ (Archive-guided Roulette-based with Quarantine) optimization framework, which was originally established as a cohesive strategy for achieving stable performance on difficult and noisy search landscapes. While rooted in the core principles of the original design, ARQ2 advances this foundation through a more refined integration of adaptive search, archive-guided exploration, controlled replacement, and robustness-aware population management. In doing so, it moves beyond the level of a simple algorithmic modification and emerges as a distinct methodological development within hybrid continuous optimization. Its significance lies in shaping a more mature and experimentally substantiated variant that promotes dependable behavior, consistent search quality, and balanced exploration–exploitation dynamics across diverse optimization environments. Empirical evaluation against nine established optimizers on 36 continuous optimization problems yields an overall average rank of 1.958, with 25 rank-1 placements and a mean-value improvement over ARQ on 21 out of 36 problems, confirming the stronger robustness and repeated-run reliability of the proposed design. As such, ARQ2 contributes to the ongoing development of stability-oriented optimization methodologies and reinforces the scientific relevance of this design line in the contemporary literature.

The proposed Adaptive RTR with Quarantine (ARQ) method integrates, within a single evolutionary scheme for continuous optimization, three mature ideas of pbest differential evolution with an archive, success-history parameter adaptation, and restricted tournament replacement (RTR) and extends them with a novel outlier quarantine mechanism. At the heart of ARQ is a combination of the following complementary mechanisms: (1) an event-driven outlier-quarantine loop that triggers on robustly detected tail behavior, (2) a robust center from the best half of the population to which quarantined candidates are gently repaired under feasibility projections, (3) local RTR-based replacement that preserves spatial diversity and avoids premature collapse, (4) archive-guided trial generation that blends current and archived differences while steering toward strong exemplars, and (5) success-history adaptation that self-regulates search from recent successes and reduces manual fine-tuning. Together, these parts sustain focused progress while periodically renewing diversity. Search pressure remains focused yet diversity is steadily replenished through micro-restarts when progress stalls, producing smooth and reliable improvement on noisy or rugged landscapes. In a comprehensive benchmark campaign spanning separable, ill-conditioned, multimodal, hybrid, and composition problems, ARQ was compared against leading state-of-the-art baselines, including top entrants and winners from CEC competitions under identical evaluation budgets and rigorous protocols. Across these settings, ARQ delivered competitive peak results while maintaining favorable average behaviour, thereby narrowing the gap between best and typical outcomes. Overall, this design positions ARQ as a robust choice for practical performance and consistency, providing a dependable tool that can meaningfully strengthen the methodological repertoire of the research community.

This paper introduces TRIDENT-DE, a novel ensemble-based variant of Differential Evolution (DE) designed to tackle complex continuous global optimization problems. The algorithm leverages three complementary trial vector generation strategies best/1/bin, current-to-best/1/bin, and pbest/1/bin executed within a self-adaptive framework that employs jDE parameter control. To prevent stagnation and premature convergence, TRIDENT-DE incorporates adaptive micro-restart mechanisms, which periodically reinitialize a fraction of the population around the elite solution using Gaussian perturbations, thereby sustaining exploration even in rugged landscapes. Additionally, the algorithm integrates a greedy line-refinement operator that accelerates convergence by projecting candidate solutions along promising base-to-trial directions. These mechanisms are coordinated within a mini-batch update scheme, enabling aggressive iteration cycles while preserving diversity in the population. Experimental results across a diverse set of benchmark problems, including molecular potential energy surfaces and engineering design tasks, show that TRIDENT-DE consistently outperforms or matches state-of-the-art optimizers in terms of both best-found and mean performance. The findings highlight the potential of multi-operator, restart-aware DE frameworks as a powerful approach to advancing the state of the art in global optimization.

The Sporulation-Inspired Optimization Algorithm (SIOA) is an innovative metaheuristic optimization method inspired by the biological mechanisms of microbial sporulation and dispersal. SIOA operates on a dynamic population of solutions (“microorganisms”) and alternates between two main phases: sporulation, where new “spores” are generated through adaptive random perturbations combined with guided search towards the global best, and germination, in which these spores are evaluated and may replace the most similar and less effective individuals in the population. A distinctive feature of SIOA is its fully self-adaptive parameter control, where the dispersal radius and the probabilities of sporulation and germination are dynamically adjusted according to the progress of the search (e.g., convergence trends of the average fitness). The algorithm also integrates a special “zero-reset” mechanism, enhancing its ability to detect global optima located near the origin. SIOA further incorporates a stochastic local search phase to refine solutions and accelerate convergence. Experimental results demonstrate that SIOA achieves high-quality solutions with a reduced number of function evaluations, especially in complex, multimodal, or high-dimensional problems. Overall, SIOA provides a robust and flexible optimization framework, suitable for a wide range of challenging optimization tasks.

This paper presents an innovative optimization algorithm based on differential evolution that combines advanced mutation techniques with intelligent termination mechanisms. The proposed algorithm is designed to address the main limitations of classical differential evolution, offering improved performance for symmetric or non-symmetric optimization problems. The core scientific contribution of this research focuses on three key aspects. First, we develop a hybrid dual-strategy mutation system where the first strategy emphasizes exploration of the solution space through monitoring of the optimal solution, while the second strategy focuses on exploitation of promising regions using dynamically weighted differential terms. This dual mechanism ensures a balanced approach between discovering new solutions and improving existing ones. Second, the algorithm incorporates a novel majority dimension mechanism that evaluates candidate solutions through dimension-wise comparison with elite references (best sample and worst sample). This mechanism dynamically guides the search process by determining whether to intensify local exploitation or initiate global exploration based on majority voting across all the dimensions. Third, the work presents numerous new termination rules based on the quantitative evaluation of metric value homogeneity. These rules extend beyond traditional convergence checks by incorporating multidimensional criteria that consider both the solution distribution and evolutionary dynamics. This system enables more sophisticated and adaptive decision-making regarding the optimal stopping point of the optimization process. The methodology is validated through extensive experimental procedures covering a wide range of optimization problems. The results demonstrate significant improvements in both solution quality and computational efficiency, particularly for high-dimensional problems with numerous local optima. The research findings highlight the proposed algorithm’s potential as a high-performance tool for solving complex optimization challenges in contemporary scientific and technological contexts.

In the dynamically evolving field of collective computational optimization, modern approaches increasingly incorporate bio-inspired techniques, such as Smell Agent Optimization (SAO), to address complex, high-dimensional problems inherent to contemporary scientific and industrial applications. While these methods are distinguished by their dynamic convergence and heuristic ability to explore vast solution spaces, their growing computational complexity hinders their application in real-world, large-scale scenarios where simultaneous speed and precision are critical. To overcome this challenge, the present research advances a pioneering parallel implementation of SAO, which transcends simple workload distribution by integrating dynamic collaboration mechanisms and intelligent information dispersal among autonomous subpopulations. Concurrently, the method is enriched with innovative rules for exchanging optimal solutions between subpopulations. These rules not only prevent premature convergence to local minima but also establish a continuous flow of information that accelerates the global exploration of the solution space. Experimental validation of the proposed method demonstrated that, through optimized parameterization of the diffusion mechanisms, SAO’s efficiency can exceed 50%, achieving simultaneous reductions in both the number of objective function evaluations and total execution time. This outcome holds particular significance in high-dimensional problems, where balancing computational cost and accuracy is a decisive factor. These findings not only underscore the potential of parallel SAO to deliver sustainable solutions to real-world challenges but also open new horizons in the theory and practice of collective optimization. The implications extend to domains such as large-scale data analysis, autonomous systems, and adaptive resource management, where rapid and precise optimization is paramount.