Shortest Edit Path Crossover: A Theory-driven Solution to the Permutation Problem in Evolutionary Neural Architecture Search

Evolutionary algorithms (EAs) have gained attention recently due to their success in neural architecture search (NAS). However, whereas traditional EAs draw much power from crossover operations, most evolutionary NAS methods deploy only mutation operators. The main reason is the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This work conducts the first theoretical analysis of the behaviors of crossover and mutation in the NAS context, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown to overcome the permutation problem, and as a result, offspring generated by the SEP crossover is theoretically proved to have a better expected improvement in terms of graph edit distance to global optimum, compared to mutation and standard crossover. Experiments further show that the SEP crossover significantly outperforms mutation and standard crossover on three state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of evolution in NAS, and potentially other similar design problems as well.Comment: 17 pages, 6 figure

Evolved Art with Transparent, Overlapping, and Geometric Shapes

In this work, an evolutionary art project is presented where images are approximated by transparent, overlapping and geometric shapes of different types, e.g., polygons, circles, lines. Genotypes representing features and order of the geometric shapes are evolved with a fitness function that has the corresponding pixels of an input image as a target goal. A genotype-to-phenotype mapping is therefore applied to render images, as the chosen genetic representation is indirect, i.e., genotypes do not include pixels but a combination of shapes with their properties. Different combinations of shapes, quantity of shapes, mutation types and populations are tested. The goal of the work herein is twofold: (1) to approximate images as precisely as possible with evolved indirect encodings, (2) to produce visually appealing results and novel artistic styles.Comment: Proceedings of the Norwegian AI Symposium 2019 (NAIS 2019), Trondheim, Norwa

Finding Near-Optimal Independent Sets at Scale

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.Comment: 17 pages, 1 figure, 8 tables. arXiv admin note: text overlap with arXiv:1502.0168

Automated Generation of Cross-Domain Analogies via Evolutionary Computation

Analogy plays an important role in creativity, and is extensively used in science as well as art. In this paper we introduce a technique for the automated generation of cross-domain analogies based on a novel evolutionary algorithm (EA). Unlike existing work in computational analogy-making restricted to creating analogies between two given cases, our approach, for a given case, is capable of creating an analogy along with the novel analogous case itself. Our algorithm is based on the concept of "memes", which are units of culture, or knowledge, undergoing variation and selection under a fitness measure, and represents evolving pieces of knowledge as semantic networks. Using a fitness function based on Gentner's structure mapping theory of analogies, we demonstrate the feasibility of spontaneously generating semantic networks that are analogous to a given base network.Comment: Conference submission, International Conference on Computational Creativity 2012 (8 pages, 6 figures

Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances