population 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.

Iterative generative models—such as diffusion models and flow matching—suffer from low inference efficiency due to hundreds of function evaluations per sample. To address this, we propose a warm-start mechanism that replaces the conventional random noise initialization with a context-conditioned prior distribution $mathcal{N}(mu, sigma)$, where the mean $mu$ and standard deviation $sigma$ are predicted in a single forward pass by a lightweight network. Conditional normalization enables model-agnostic, plug-and-play integration without modifying the original generator or sampler—ensuring compatibility across diverse iterative frameworks. In image inpainting, our method achieves performance on par with a 1000-step DDPM baseline using only one warm-start initialization plus ten sampling steps (11 total function evaluations), substantially accelerating strongly conditioned generation. Our core contribution is the first introduction of a context-aware, learnable initial prior into the general iterative generative paradigm.

This work proposes a population-based neural combinatorial optimization framework that addresses the limited exploratory capacity and robustness of traditional neural approaches, which typically operate on a single solution. By leveraging neural networks to jointly represent a set of candidate solutions, the framework incorporates a population-aware hierarchical classification mechanism to explicitly model inter-solution information sharing and diversity control. This design simultaneously reinforces high-quality solutions and preserves population diversity, effectively bridging the gap between neural optimization and classical population-based metaheuristics. Experimental results on the Max-Cut and Maximum Independent Set problems demonstrate that the proposed framework substantially improves both solution quality and algorithmic robustness.

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 generalized iterative algorithms for high-dimensional nonconvex optimization featuring mixed first-order and saddle-point updates. We propose the first rigorous State Evolution (SE) analysis framework applicable to non-coordinate-separable structures. Methodologically, we introduce a Hilbert-space parameterization model, integrating Bolthausen’s conditioning technique with the sequential form of Gordon’s Gaussian comparison inequality—thereby overcoming classical SE limitations restricted to purely first-order or separable settings. Theoretically, we establish the first rigorous SE trajectory derivation under nonseparable, finite-sample conditions and derive an explicit upper bound on the deviation between empirical iterates and the theoretical SE path. This framework provides a unified, verifiable, and precise performance guarantee for a broad class of complex optimizers, including gradient methods augmented with saddle-point corrections.

This work addresses the lack of a unified convergence analysis framework for population-based optimization algorithms, which hinders systematic comparison and generalization. The authors propose an operator calculus framework that models diverse algorithms as compositions of three fundamental operators—mutation, selection, and recombination—acting on probability measures. By leveraging mean-field limits, they derive a continuous-time transport-reaction-jump partial differential equation governing the algorithmic dynamics. Building upon operator semigroup theory and functional analysis on spaces of probability measures, they develop a modular Lyapunov method that enables dissipativity verification operator by operator. Under explicit stability and regularity conditions, they establish exponential decay of both a state-space Lyapunov functional and the search error, thereby providing a unified guarantee of exponential convergence for a broad class of distributed optimization algorithms.

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.

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.

Population-Based Training (PBT)-style hyperparameter optimization (HPO) relies on manually specified hyperparameter update intervals—a critical meta-hyperparameter whose optimal value varies across tasks and lacks general design principles. Method: We propose AutoPBT, a fully adaptive PBT framework that eliminates manual configuration of update intervals. Its core innovations include: (i) a task-agnostic weight reset mechanism; (ii) time-varying Bayesian optimization to dynamically schedule hyperparameter updates; and (iii) reuse of historical population weights to improve training efficiency. Contribution/Results: AutoPBT removes the need for tuning this key meta-hyperparameter, enhancing both generality and adaptability. Evaluated on eight benchmark tasks—including image classification and reinforcement learning—AutoPBT consistently outperforms five state-of-the-art PBT variants and other HPO methods, achieving comparable or superior performance without incurring additional computational overhead.