Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1301.0939

Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm

Iztok Fister·Marjan Mernik·Bogdan Filipič
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper proposes a hybrid self-adaptive evolutionary algorithm for graph coloring that is hybridized with the following novel elements: heuristic genotype-phenotype mapping, a swap local search heuristic, and a neutral survivor selection operator. This algorithm was compared with the evolutionary algorithm with the SAW method of Eiben et al., the Tabucol algorithm of Hertz and de Werra, and the hybrid evolutionary algorithm of Galinier and Hao. The performance of these algorithms were tested on a test suite consisting of randomly generated 3-colorable graphs of various structural features, such as graph size, type, edge density, and variability in sizes of color classes. Furthermore, the test graphs were generated including the phase transition where the graphs are hard to color. The purpose of the extensive experimental work was threefold: to investigate the behavior of the tested algorithms in the phase transition, to identify what impact hybridization with the DSatur traditional heuristic has on the evolutionary algorithm, and to show how graph structural features influence the performance of the graph-coloring algorithms. The results indicate that the performance of the hybrid self-adaptive evolutionary algorithm is comparable with, or better than, the performance of the hybrid evolutionary algorithm which is one of the best graph-coloring algorithms today. Moreover, the fact that all the considered algorithms performed poorly on flat graphs confirms that this type of graphs is really the hardest to color.

Explore related subjects

cs.NE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Iztok Fister, Marjan Mernik, Bogdan Filipič. 2013-01-05. Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm. https://doi.org/10.1007/s10589-012-9496-5

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

KEEP EXPLORING

Related papers

arXiv2026

Rethinking Pairwise Token Interaction in Spiking Transformers

Spiking Transformers inherit token interaction mechanisms from conventional Transformers, yet their sparse binary representations fundamentally alter how token-to-token communication is established. In particular, spike-based query-key matching produces highly sparse and input-dependent interaction patterns, coupling information propagation to the instantaneous availability of matching spike events. This motivates a different interaction paradigm in which long-range communication does not rely solely on pairwise spike coincidence. We therefore propose Gated Spike Axial Propagation (GSAP), a spike-native token interaction mechanism that decouples information propagation from context selection. Instead of directly determining communication through query-key matching, GSAP first propagates spike-based context along the horizontal and vertical axes, allowing information to reach distant tokens through structured sequential propagation. A receiver-conditioned gate then determines how much of the propagated context is incorporated at each token, while a lightweight local pathway preserves fine-grained neighborhood information. In this way, GSAP reformulates token interaction as a propagate-then-select process, enabling structured long-range communication while retaining the sparse event-driven nature of spiking representations. Code is available at https://github.com/Fancyssc/GSAP.

cs.NE↗
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↗