enhanced genetic algorithm

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 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 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 opacity of search dynamics in traditional swarm intelligence and evolutionary algorithms, where nonlinear selection and adaptive mechanisms obscure the intrinsic geometric structure underlying candidate solution generation. To resolve this, the authors propose an operator–selection decomposition framework that decouples fitness-independent variation operators from boundary handling and fitness-dependent selection, thereby systematically uncovering the proposal geometry of SOMA and Differential Evolution (DE). They reveal, for the first time, that SOMA exhibits a linear structure in the migrant–leader space, derive closed-form expressions for key statistical quantities, and leverage these insights to design a geometrically controllable, rotation-aware SOMA variant along with an adaptive population reduction strategy. On the noiseless BBOB benchmark suite, the resulting algorithm significantly outperforms the original SOMA and matches or exceeds state-of-the-art DE variants across multiple dimensions and evaluation budgets.

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.

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 work addresses the limited generalization capability of existing constrained multi-objective evolutionary algorithms (CMOEAs), which typically rely on fixed operators, as well as the inefficiency of current adaptive approaches that select only a single operator per generation, often leading to premature convergence and wasted evaluation budgets. To overcome these limitations, we propose CMOEA-AOP, a novel deep reinforcement learning–based method that dynamically allocates multiple optimization operators in each generation according to the current population state, thereby synergistically enhancing both convergence and diversity. The approach encodes population characteristics—including objective and constraint information—as states and uses overall improvement as the reward signal to train a deep neural network that maps states to cumulative rewards. Extensive experiments on 33 benchmark problems demonstrate that CMOEA-AOP significantly outperforms state-of-the-art CMOEAs, exhibiting superior stability and adaptability.

This work addresses the limitation of quality-diversity (QD) algorithms in effectively propagating high-quality genetic modules due to their reliance on incremental mutation, which often leads to premature stagnation in exploration. Inspired by biological meiosis, the authors propose a novel discrete genetic crossover operator that introduces gene-level recombination into the QD framework for the first time. This operator synergistically complements existing variation strategies by preserving elite genetic material while enabling efficient cross-behavioral exploration. By transcending the constraints of traditional incremental mutation, the method significantly improves QD scores, coverage, and peak fitness across three locomotion control tasks. Notably, it demonstrates superior performance gains and sustained diversity maintenance during late-stage optimization, highlighting its capacity to enhance both exploration efficacy and solution quality in complex behavioral spaces.

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.

Traditional evolutionary game analysis relies on closed-form payoff expressions derived from queueing systems, which are infeasible in complex scenarios. This work proposes a Discrete-Event Population Update (DEPU) framework that directly embeds a single discrete-event simulation into the evolutionary dynamics, enabling efficient analysis of strategy evolution in systems lacking closed-form solutions without resorting to nested simulations. The framework encompasses two implementation mechanisms: Discrete-Event Replicator Dynamics (DERD) and Discrete-Event Moran Replacement (DEMR). Evaluated on a multi-server jockeying queue model, DEPU achieves computational speedups of an order of magnitude over conventional methods while preserving comparable accuracy, substantially enhancing the feasibility and efficiency of large-scale parameter sweeps.