genetic algorithm initialization

To address the slow convergence and premature convergence to local optima in evolutionary algorithms (EAs) on high-dimensional complex optimization problems—largely attributable to suboptimal population initialization—this paper proposes a hybrid initialization strategy integrating opposition-based learning (OBL) and empty-space-aware search (ESA). For the first time, ESA and OBL are synergistically incorporated into the EA initialization phase to actively explore underexplored “unconventional regions,” thereby significantly enhancing both diversity and structural rationality of the initial population. Experimental evaluations on multiple high-dimensional benchmark functions demonstrate that the proposed strategy achieves, on average, a 37% acceleration in convergence speed and a 21% improvement in solution quality over state-of-the-art initialization methods. The core contribution lies in overcoming the diversity bottleneck inherent in conventional random or uniform initialization, establishing an interpretable, reusable, and structurally principled design paradigm for EA initialization.

In binary evolutionary optimization, the quality of the initial population critically affects algorithm performance under low-budget conditions (i.e., limited function evaluations), yet existing initialization methods often rely on problem-specific prior knowledge or fail to generalize across diverse real-world problems. Method: This paper proposes an adaptive, experience-based transfer initialization method that requires no problem-specific prior knowledge. It introduces a generalizable framework for representing, selecting, and transferring solution patterns—dynamically accumulating high-quality empirical knowledge from canonical benchmark problems into an experience repository—and employs a hybrid transfer strategy to adapt these patterns to unseen, complex, real-world problems and high-dimensional instances. Contribution/Results: Seamlessly integrated with standard evolutionary algorithms, the method demonstrates consistent effectiveness across six benchmark problem classes. Notably, it significantly outperforms state-of-the-art generic initialization approaches on three previously unseen real-world problems—validating its strong cross-problem generalization capability and computational efficiency under stringent evaluation budgets.

This work addresses the limitation of conventional survival selection in evolutionary diversity optimization, which often fails due to its dependence on pairwise solution diversity. To overcome this issue, we propose a novel framework that enables the synchronous generation of multiple candidate solutions per generation, along with a tailored survival selection mechanism designed specifically for this setting. By moving beyond the traditional paradigm of single-solution, sequential updates, our approach effectively handles the dynamic nature of each solution’s contribution to population diversity. Experimental results demonstrate that, under certain conditions, the proposed multi-solution generation strategy accelerates convergence toward diverse solutions and significantly improves both the spread and quality balance of the final solution set.

This study investigates the impact of population initialization methods on the performance of genetic programming for symbolic regression. Within the NSGA-II multi-objective evolutionary framework, it systematically compares three random initialization strategies against an initialization based on small-scale optimized solutions from Exhaustive Symbolic Regression (ESR) across multiple synthetic and real-world datasets. The findings reveal that although ESR-based initialization offers a modest advantage in early evolutionary stages, the choice of initialization strategy does not significantly affect the accuracy or complexity of the final Pareto front; differences between strategies vanish within a few generations. These results challenge the common assumption that sophisticated initialization substantially enhances symbolic regression performance, suggesting instead that the structure of the initial population has limited influence on long-term evolutionary outcomes.

Bio-inspired optimization algorithms—spanning evolutionary, swarm intelligence, and physics-based paradigms—are widely applied to complex optimization problems, yet lack systematic classification and rigorous comparative assessment. Method: This paper introduces the first eight-dimensional unified taxonomy framework, categorizing over 300 algorithms into eight canonical paradigms. It integrates bibliometric analysis, cross-domain case studies, and paradigm-level comparison to synthesize algorithmic principles, applications (e.g., machine learning, engineering design), and emerging research directions—including hybridization, adaptive parameter control, and interpretability. Contribution/Results: The work identifies three fundamental challenges—scalability, convergence guarantees, and reliability—and constructs a structured knowledge graph. It delivers a comprehensive, authoritative survey for researchers and delineates key breakthrough pathways for the next five years, enabling principled algorithm selection, design, and advancement.

This work addresses the inefficiency of traditional genetic algorithms in solving optimization problems due to their reliance on random mutation and recombination, which lack goal-directedness. The authors formulate the problem through the lens of query complexity and propose objective-guided mutation and recombination operators informed by the optimization target. Leveraging reinforcement learning and formal language theory, they analyze the theoretical properties of these operators. For the first time, the study mathematically characterizes the mechanism of goal-directed genetic operators and demonstrates the necessity of population diversity for certain classes of optimization problems. A general model of genetic algorithms is established, enabling the design of a tight algorithm for a specific problem class, and proving that the synergy among generation, mutation, and recombination is essential for efficient optimization.

This study addresses the lack of theoretical foundation for parameter selection in the bat algorithm, which has traditionally relied on empirical tuning. For the first time, it integrates dynamical systems theory with population variance evolution analysis to construct a theoretical framework characterizing the influence of key parameters. Within this framework, analytically derived effective ranges for critical parameters are established. Numerical experiments confirm that the theoretical predictions align closely with the observed convergence behavior in practice. The work further uncovers the intrinsic mechanisms governing the trade-off between exploration and exploitation and the algorithm’s convergence properties, thereby providing the first systematic theoretical guidance for parameter configuration in the bat algorithm.

This work addresses the challenges in black-box optimization posed by heteroscedastic noise—namely, uncertain fitness evaluations, inaccurate solution ranking, and excessive computational cost—by introducing a confidence-driven dynamic sampling mechanism. The proposed approach integrates adaptive budget allocation and explicit averaging strategies within both CMA-ES and genetic algorithm frameworks. It further presents the first systematically constructed benchmark suite for heteroscedastic noise, thereby overcoming the conventional reliance on homoscedasticity and function smoothness assumptions. Experimental results demonstrate that the method consistently outperforms state-of-the-art algorithms under both homoscedastic and heteroscedastic noise conditions, achieving superior robustness and computational efficiency.

This work addresses the challenge of modeling fitness progress in evolutionary strategies when operating far from the global optimum, where traditional assumptions often fail. To capture the search dynamics in complex optimization problems—such as hyperparameter tuning—the paper introduces a homogenous progress model, positing that the fitness improvement of offspring over parents follows a stationary distribution. The authors innovatively develop an analytical framework tailored to steady-state $(\mu+1)$-ES, establishing for the first time provable upper and lower bounds on its expected rate of progress, thereby overcoming limitations of conventional approaches in handling intergenerational dependencies. Leveraging probabilistic modeling and asymptotic analysis, they rigorously derive a tight bound under the condition $Z \sim \mathcal{N}(-\delta, 1)$ with $\mu \le e^\delta$: $\mathcal{R}_\mu = \frac{\log^{1 + o(1)} \mu}{\mu} \mathcal{R}_1$.

This work addresses the lack of theoretical foundations for dynamic population sizing in multi-objective evolutionary algorithms by introducing a novel bi-objective benchmark problem, CLIMB. Through rigorous runtime analysis, it compares the performance of GSEMO and NSGA-II under both fixed and dynamic population strategies. The study provides the first provable super-constant speedup of GSEMO over fixed-population NSGA-II and proposes a new variant, NSGA-II-DYN. Leveraging diversity-based evolutionary analysis, family-tree lower-bound techniques, and tools from single-objective optimization theory, the paper establishes that both NSGA-II-DYN and GSEMO converge to the Pareto front in expected $O(n \log n)$ fitness evaluations, whereas fixed-population NSGA-II requires $\Omega(n^{1.5})$, yielding an asymptotic speedup of $\Omega(\sqrt{n} / \log n)$.