population initialization

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.

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 paper addresses two key bottlenecks in the initialization phase of Bayesian optimization: (1) conventional space-filling designs poorly reduce predictive uncertainty of surrogate models, and (2) they exhibit objective misalignment with hyperparameter learning. To resolve these issues, we propose HIPE—a novel active sampling strategy that for the first time integrates information-theoretic principles into initialization design. HIPE unifies hyperparameter learning and uncertainty reduction within a Gaussian process framework, yielding a closed-form acquisition function. Compared to state-of-the-art methods, HIPE significantly improves predictive accuracy, hyperparameter estimation quality, and downstream optimization efficiency—especially under low-sample, large-batch, few-iteration settings typical in practical deployment. Extensive experiments across multiple benchmark tasks demonstrate consistent superiority over Sobol sequences, Latin Hypercube Sampling (LHS), and entropy-based initialization approaches.

To address the slow convergence and suboptimal solutions of local optimization methods in real-time control—stemming from reliance on a single, fixed initial solution—this paper proposes a learning-based framework for multi-initial-solution prediction. Methodologically, it formulates diverse initial-solution generation as a supervised learning task for the first time and incorporates meta-learning to enhance cross-task generalization. Two complementary execution strategies are introduced: (i) adaptive selection of a single optimizer and (ii) parallel execution of multiple optimizers—both rigorously guaranteeing that the final solution is no worse than that obtained from default initialization. The framework is compatible with various optimal control optimizers, including DDP, MPPI, and iLQR. Evaluated on cart-pole, reacher, and autonomous driving benchmarks, it significantly improves both convergence speed and solution quality under strict time constraints, while scaling efficiently to larger numbers of initial solutions.

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 work proposes GAReg, a unified genetic algorithm framework designed to address high-dimensional discrete regression optimization problems where traditional gradient-based methods fail due to non-differentiable, non-convex objective functions or the presence of numerous local optima. GAReg employs compact chromosome encoding, constraint-preserving crossover and mutation operators, a steady-state population update mechanism, and supports island-model parallelization. This approach effectively overcomes the computational bottlenecks of enumeration and dynamic programming in high-dimensional spaces. Experimental results demonstrate that GAReg efficiently explores the model space in scenarios where standard methods are inapplicable, yielding near-optimal solutions and significantly outperforming conventional approaches such as exhaustive search and integer programming.

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 study investigates the intrinsic mechanisms underlying the efficiency of genetic algorithms in high-dimensional spaces. By analyzing the dynamics of the elitist (1+M) genetic algorithm in the small-mutation limit, the work establishes—for the first time—a theoretical equivalence between the algorithm and a truncated gradient descent process driven by anisotropic Gaussian white noise. This equivalence demonstrates that the algorithm implicitly follows the gradient direction of the loss function without explicitly computing or averaging gradients. Integrating tools from stochastic processes, Hessian spectral analysis, and high-dimensional optimization theory, the paper reveals that the algorithm’s efficiency depends on the effective rank of the loss function’s Hessian matrix rather than the total number of parameters. In high-dimensional problems such as neural networks, the Hessian spectrum is highly concentrated, rendering the effective rank much smaller than the ambient parameter dimension, thereby suppressing noise and explaining the scalability of genetic algorithms.

This work addresses the barren plateau problem in quantum neural network training caused by poor parameter initialization by proposing a first-moment–based analytical framework. Combining operator concentration theory with numerical experiments, the study systematically evaluates and compares the efficacy of various initialization strategies—including identity, Gaussian, and several shifted or asymmetric distributions. For the first time, it establishes an operator-level criterion for initialization validity, demonstrating that viable initializations avoiding barren plateaus are highly non-unique and form exponentially many inequivalent families. Moreover, the research reveals that initializations with distinct first moments can converge to different local minima, indicating that intelligent initialization effectively transforms the exponential concentration challenge into a selection problem among numerous trainable regions.