evolutionary algorithms

Multi-objective optimization requires simultaneously ensuring solution quality and inter-solution diversity; however, existing methods struggle to achieve optimal fitness under minimum distance constraints—and sometimes perform worse than random sampling. Method: We propose a cascaded CMA-ES framework that runs multiple CMA-ES instances in parallel, dynamically inherits forbidden regions to enforce spatial separation among solutions, and incorporates distance-aware trajectory optimization—enabling cooperative exploration of high-fitness, strictly separated solution batches without compromising single-solution optimality. Contribution/Results: This is the first CMA-ES-based co-optimization architecture to explicitly model and satisfy hard minimum distance constraints. On standard benchmarks, our method significantly outperforms random sampling, multimodal optimization algorithms, and vanilla CMA-ES in both solution quality and pairwise separation.

This paper investigates whether deterministic population update mechanisms in multi-objective evolutionary algorithms (MOEAs) can be replaced by stochastic ones to improve search efficiency. Method: We conduct theoretical runtime analysis and empirical evaluation of stochastic population updates on the SMS-EMOA and NSGA-II frameworks, applied to the bi-objective OneJumpZeroJump and RealRoyalRoad benchmark problems. Our approach integrates rigorous runtime analysis, modeling of nondominated sorting, and probabilistic selection mechanisms. Contribution/Results: We provide the first strict runtime proof showing that stochastic updates reduce the expected optimization time of SMS-EMOA on OneJumpZeroJump from exponential to polynomial—achieving exponential speedup. This challenges the long-standing paradigm of relying exclusively on deterministic updates in MOEAs. Empirical results further demonstrate that multiple MOEA variants adopting stochastic updates exhibit significantly improved convergence and diversity across benchmarks.

Combinatorial optimization problems pose significant challenges for deep reinforcement learning (DRL) due to their discrete, exponentially large solution spaces, often leading DRL to premature convergence to local optima. While genetic algorithms (GAs) offer strong global exploration, they suffer from low sample efficiency. To bridge this gap, we propose the Evolutionary Augmentation Mechanism (EAM)—a plug-and-play framework enabling dynamic, closed-loop coupling of DRL and GA during training. EAM integrates policy-based sampling, customized genetic operators, and solution re-injection to jointly optimize policy and solution distributions. Crucially, we derive an upper bound on the KL divergence between the policy distribution and the evolutionary solution distribution, theoretically guaranteeing distributional stability. Compatible with mainstream DRL architectures (e.g., Attention Model, POMO) and GA operators, EAM achieves state-of-the-art performance on TSP, CVRP, PCTSP, and OP benchmarks—simultaneously improving convergence speed and solution quality.

Existing data-driven evolutionary algorithms still rely on handcrafted heuristics, suffering from limited generality and insufficient automation. Method: This paper proposes EvoGO—the first fully data-driven generative evolutionary optimization framework—decoupling optimization into three stages: training-data construction, generative model training, and population generation. EvoGO replaces conventional mutation and crossover operators entirely with a customized generative model. By constructing diversity-enhanced pairwise training data, it enables parallel, zero-evaluation-cost population generation. Contribution/Results: On diverse benchmark tasks—including continuous, discrete, and combinatorial optimization—EvoGO achieves convergence within only 10 generations, significantly outperforming classical evolutionary algorithms, Bayesian optimization, and reinforcement learning–based methods. Empirical results demonstrate its superior efficiency, generalizability across problem domains, and strong scalability to high-dimensional and large-population settings.

Metaheuristic algorithms lack a systematic application framework for combinatorial optimization, particularly regarding result reliability and statistical interpretability. Method: This paper proposes the Exploration-Exploitation-Evaluation (EEE) tri-stage general framework, integrating uncertainty quantification into the evaluation stage—enabling, for the first time, statistical inference of the probability of discovering the global optimum. Grounded in Ant Colony Optimization (ACO), the framework incorporates a parameter-space adaptive search strategy. Contribution/Results: Evaluated on TSPLIB benchmarks, it achieves a 2.5% probability of finding the optimal solution in a single run on berlin52, rising to 20% after ten independent runs. The EEE framework establishes a scalable, principled algorithmic paradigm and bridges a critical gap in metaheuristics by introducing quantifiable confidence assessment—thereby enhancing result credibility and enabling rigorous performance interpretation.

This work addresses the limitations of traditional numerical methods—which rely heavily on gradients and initial guesses—and the slow convergence of evolutionary algorithms in high-dimensional constrained optimization. To overcome these challenges, the paper proposes embedding a population-based stochastic optimizer, such as CMA-ES, into an augmented Lagrangian (AL) framework, replacing local solvers in AL subproblems with gradient-free global search. This approach represents the first systematic integration of the AL method’s robust constraint-handling capabilities with the strong exploratory power of evolutionary algorithms, effectively balancing feasibility enforcement and global exploration. Experimental results demonstrate that the proposed method significantly outperforms both pure evolutionary algorithms and state-of-the-art solvers like IPOPT on standard benchmark problems, particularly excelling in high-dimensional nonconvex landscapes riddled with numerous local minima and saddle points.

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 addresses the lack of effective search-region guidance in existing meta black-box optimization methods for expensive constrained multi-objective problems. The authors propose MetaSG-SAEA, a novel bi-level framework that, for the first time, enables cross-problem, region-level search guidance and generalization. The approach introduces a problem-agnostic MM-CCI region abstraction and a scalable attention-based state representation, leveraging a diffusion model for initialization and employing MM-CCI-constrained calibration inequalities to guide a surrogate-assisted evolutionary algorithm. Experimental results demonstrate that MetaSG-SAEA significantly outperforms state-of-the-art methods across multiple benchmarks, achieving superior optimization performance while exhibiting strong generalization across diverse problem distributions.

Current large language model (LLM)-driven approaches to automated heuristic design struggle to effectively solve complex optimization problems characterized by tightly coupled subproblems. This work proposes CoupleEvo, a novel framework that extends LLM-guided heuristic evolution to coupled optimization scenarios for the first time. It introduces three cooperative evolution strategies—sequential, iterative, and integrated—and systematically investigates how different coordination mechanisms affect search stability and solution quality. Experimental results on two representative classes of coupled optimization problems demonstrate that decomposition-based strategies (sequential and iterative) significantly outperform the integrated approach, exhibiting both more stable convergence behavior and superior solution quality.

This work addresses the challenge of adapting to non-stationary environments in streaming data-driven optimization, where concept drift undermines model stability and performance. To tackle this issue, the authors propose a multi-island evolutionary framework that integrates meta-learning with generative replay. The approach employs a bi-level meta-learning strategy to rapidly initialize surrogate models and incorporates a linear residual component to enhance dynamic modeling capabilities. Concurrently, a generative replay mechanism preserves and reuses historical knowledge, enabling efficient knowledge transfer and robust optimization upon detecting concept drift. Experimental results on standard SDDO benchmarks demonstrate that the proposed method significantly outperforms existing techniques in both adaptation speed and optimization stability.