On the Impact of Mutation-Selection Balance on the Runtime of Evolutionary Algorithms

Per Kristian Lehre; Xin Yao

Home/Archive/arXiv

arXiv · 1012.3098

On the Impact of Mutation-Selection Balance on the Runtime of Evolutionary Algorithms

Per Kristian Lehre·Xin Yao

View original source ↗Read source document ↗Export metadata ↓

Abstract

The interplay between mutation and selection plays a fundamental role in the behaviour of evolutionary algorithms (EAs). However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a non-elitist population-based EA that uses the linear ranking selection mechanism. The analysis focuses on how the balance between parameter $η$, controlling the selection pressure in linear ranking, and parameter $χ$ controlling the bit-wise mutation rate, impacts the runtime of the algorithm. The results point out situations where a correct balance between selection pressure and mutation rate is essential for finding the optimal solution in polynomial time. In particular, it is shown that there exist fitness functions which can only be solved in polynomial time if the ratio between parameters $η$ and $χ$ is within a narrow critical interval, and where a small change in this ratio can increase the runtime exponentially. Furthermore, it is shown quantitatively how the appropriate parameter choice depends on the characteristics of the fitness function. In addition to the original results on the runtime of EAs, this paper also introduces a very useful analytical tool, i.e., multi-type branching processes, to the runtime analysis of non-elitist population-based EAs.

Explore related subjects

cs.NE nlin.AO q-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Per Kristian Lehre, Xin Yao. 2010-12-14. On the Impact of Mutation-Selection Balance on the Runtime of Evolutionary Algorithms. https://arxiv.org/abs/1012.3098

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Genetic Programming with Behaviour-based Niching for Learning Guided Local Search in Vehicle Routing Problems

Genetic Programming Guided Local Search (GPGLS) learns utility functions that guide local search for vehicle routing. Its evolving programs can have similar fitness while inducing different search behaviour, making fitness alone an incomplete basis for population diversity management. We propose GPGLS with Behaviour-based Niching (BN-GPGLS), which characterises programs through six operator-level descriptors collected during local search. A current-generation archive selects fitness-competitive, compact representatives from strata of a behaviour score. Fixed policies use archive parents continuously, whereas adaptive policies activate them using training-fitness and standardised behaviour-dispersion signals, optionally with a tree-size condition. We compare four behaviour-based variants with a no-archive GPGLS control and fitness-based niching over 30 seed-matched runs on generated 200-customer instances. BN-Adaptive achieves the best descriptive average rank on a separate 90-instance monitoring set; aggregate routing-cost differences are small. All five archive policies produce lower final-population median tree sizes than the GPGLS control, with paired Wilcoxon comparisons remaining significant after Holm adjustment. These results identify useful solution-quality and program-size trade-offs within the evaluated setting, without attributing the size reductions to behaviour representation alone.

cs.NE↗

arXiv2026

DCL-GPGLS: Dynamic Curriculum Learning for Genetic Programming Guided Local Search in Large-Scale Vehicle Routing

Genetic Programming Guided Local Search (GPGLS) uses genetic programming to evolve utility functions for guided local search in large-scale vehicle routing problems (LSVRPs). Evaluating every GP individual on every training instance at every generation is expensive, so GPGLS is usually trained on small instance batches. Existing curriculum-based GPGLS orders these batches mainly by instance size. Adaptive Curriculum Learning GPGLS (ACL-GPGLS) improves training efficiency by adapting when the search moves between fixed curriculum stages, but the instance difficulty order remains predefined. We propose DCL-GPGLS, which estimates the difficulty of each training instance from the current population's solution quality and updates the estimates during evolution. Each generation then receives a batch near a scheduled difficulty level, with a correction that limits repeated selection of the same instances. Experiments on a fixed training-test split of the CVRPLIB X set show that DCL-GPGLS achieves the best observed average rank and mean test cost among six training policies. It obtains the lowest mean cost on 36 of 65 unseen test instances and is significantly better than the static feedback-derived curriculum, matched in total evaluator calls, on 6 instances, with no significant difference on the remaining 59.

cs.NE↗

arXiv2026

Meta-Representational Predictive Coding: Neuroscience-Informed Self-Supervised Learning

Self-supervised learning has become an important paradigm in the domains of machine intelligence and computational neuroscience. Nevertheless, current work on self-supervised learning (SSL) relies on biologically implausible credit assignment, i.e., backpropagation of errors, and feedforward inference, i.e., a sequential, non-parallel flow of information. Predictive coding (PC) offers a biologically plausible means to avoid backprop-specific limitations. However, unsupervised PC requires learning a generative model of raw input, which entails predicting high dimensional input; on the other hand, supervised PC learns a mapping between inputs to target labels and thus requires human annotation and incurs the drawbacks of supervised learning. In this work, we present a neuroscience-informed SSL model based on PC and active perception that we call meta-representational predictive coding (MPC). MPC sidesteps the need for a generative model of sensory input by learning to predict representations of data across parallel streams, resulting in an encoder-only learning-and-inference scheme.

cs.NE↗