Exploring Elitism Strategies in Nested Tournament Selection for Multi-Objective Genetic Programming

Hybridizing Genetic Algorithms with Pareto Local Search for Multi-Objective Rule Learning

This work investigates the hybridization of a Genetic Algorithm with Pareto Local Search to improve the exploration of non-dominated rulesets and provides a documented baseline for hybrid metaheuristics in rule mining.

QDEvo: A Multi-Objective Quality-Diversity Framework for Automated Heuristic Design

Large Language Models (LLMs) are opening new directions for automated heuristic design (AHD), allowing evolutionary methods to create and enhance heuristics for constrained optimization problems (COPs). However, most existing approaches face the challenge of the exploration-exploitation balance, where the evolution needs to escape convergence to homogeneous populations and discover as large a heuristic landscape as possible. To address this challenge, we introduce Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-based AHD. At its core, QDEvo employs a semantic survival selection mechanism that clusters algorithms by functional similarity, then applies local Pareto competition. Evaluation on well-known COPs benchmarks and real-world problems shows that our method consistently outperforms the state-of-the-art baseline in both Hypervolume and Inverted Generational Distance metrics. These results facilitate further exploration of the algorithmic design space, while ensuring competitive solution quality and efficiency.

Provable Speedups From Dynamic Population Sizes in Evolutionary Algorithms for Multiobjective Optimization

This paper investigates the role of dynamic population sizes in evolutionary multi-objective optimization. Although such approaches are widely used in practice, their benefits remain poorly understood, and rigorous runtime analyses explaining when and why they help are still scarce. To address this, we introduce the bi-objective problem class CLIMB and analyze the runtime of GSEMO and the widely used NSGA-II on this problem. Our results show that allowing a dynamic population size for NSGA-II can lead to a moderate improvement, yielding a speedup of order $\Omega(\sqrt{n}/\log n)$. In particular, we prove that GSEMO and NSGA-II-DYN, a version of NSGA-II with dynamic population sizes we propose in this paper, can find the Pareto front of CLIMB in expected $O(n \log n)$ fitness evaluations, whereas NSGA-II with a fixed population size requires $\Omega(n^{1.5})$ fitness evaluations in expectation. To the best of our knowledge, this is the first rigorous runtime analysis in multi-objective optimization demonstrating a super-constant speedup of GSEMO over NSGA-II. Our analysis builds on concepts from single-objective optimization, like the evolution of population diversity over time, and employs the well-known family-three method to prove the lower bound.

Dropout-Inspired Strategies For Enhanced Exploration In Evolutionary Algorithms

Finding the right balance between exploration and exploitation is a crucial challenge in evolutionary algorithms (EAs), as it strongly impacts solution quality and the ability to escape local optima. While diversity-preserving mechanisms are commonly employed, high population diversity does not necessarily translate into improved performance across problem landscapes. Recent empirical evidence suggests that effective EA optimization largely depends on predominantly exploitative search dynamics, with exploration being most beneficial during the early iterations. Nevertheless, sporadic exploratory bursts may help reintroduce diversity and enhance solution quality. In this study, inspired by dropout regularization in neural networks (NNs), we introduce three mechanisms—and their variants— that stochastically deactivate entire individuals or subsets of decision variables with the expectation of enhancing exploration. We assess the effectiveness of dropout in genetic algorithms (GAs) on twelve single-objective and five multi-objective benchmark functions. We empirically demonstrate that per-variable stochastic deactivation, termed Individual Dropout (IDrop), significantly outperforms a standard GA on single-objective problems with exploitable global structure and improves convergence toward the theoretical Pareto front in multi-objective settings. We also show that, while dropout alone is not exempt from the curse of dimensionality, combinations of dropout mechanisms can partially alleviate this limitation in most of the tested functions.

Advanced and Classical Selection Methods in Genetic Algorithms: A Comprehensive Comparative Analysis

Selection mechanisms critically influence the convergence behavior and solution quality of Genetic Algorithms (GAs). This study presents a rigorous empirical comparison of six selection methods: three classical methods—Random Selection, Roulette Wheel Selection (RWS), and Tournament Selection (TS)—and three adaptive methods: Fitness-Distance Balance (FDB), Dynamic FDB (dFDB), and Functional Weight-based Selection (FW). Experiments were conducted across 23 classical benchmark functions (F1–F23) and 10 CEC2019 functions (cec01–cec10), with each configuration executed 30 times using consistent GA parameters. Performance was assessed using Best, Mean, Median, and Standard Deviation, with statistical significance determined by the Wilcoxon rank-sum test (α = 0.05). The results reveal that TS consistently achieved the best or statistically equivalent performance in 30 out of 33 functions, outperforming both classical and adaptive alternatives. Notably, RWS showed surprising competitiveness, outperforming adaptive methods such as FDB and dFDB in several scenarios. While dFDB and FW improved over static FDB, they failed to consistently outperform TS. These findings confirm TS as a robust default choice for diverse optimization landscapes and provide new empirical evidence regarding the limited practical advantage of current adaptive strategies within GAs. This study contributes the first controlled GA-based evaluation of adaptive selection mechanisms on both classical and CEC2019 benchmarks, offering insights for practitioners designing efficient evolutionary systems. Limitations related to fixed GA settings, function diversity, and adaptive method complexity are acknowledged, and future work is suggested to explore hybrid and problem-aware selection strategies.

MLDGWO: a grey wolf optimizer with momentum, leader adjustment, and differential perturbation for global optimization problems