Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation

Evidence for the Effects of Wind on the Biogeography of Soil Mites in Urban Tree Wells

The theoretical predictions of island biogeography have been applied successfully by a number of researchers studying the population and community structures of invertebrates living in large urban parks and remnant natural areas. Few, however, have examined the biogeography of smaller patches and the role that specific dispersal techniques play in shaping species distributions. In this study, I examine the impact of several biogeographical and environmental factors, including wind channelization effects, on the abundance of soil mites in small, urban tree wells in Westminster, Maryland. By testing five models that include the variables of well area, isolation, and dominate wind direction, I account for all possible directions in which channelization effects may be directing wind flow most frequently, therefore accounting for the impact of wind dispersal on mite distribution. As one would expect if mite abundances were impacted by the dominate direction of wind flow on a given street, only one of these models significantly explained the pattern of mite abundances found from sampling the tree wells. While the low power of the models requires that these results be viewed as inconclusive, the unusually high amount of variance explained by the significant model (R2 = 0.76), along with its agreement with better established biogeographical relationships, does suggest that future research into the role of wind as a factor in the biogeography of passively dispersing urban invertebrates may be worthwhile

Local Optima Networks for Continuous Fitness Landscapes

Local Optima Networks (LONs) have been proposed as a coarsegrained model of discrete (combinatorial) fitness landscapes, where nodes are local optima and edges are search transitions based on an exploration search operator. This paper presents one of the first complex network analysis of continuous fitness landscapes. We use benchmark functions with well-known global structure, and an existing implementation of a Basin-Hopping algorithm to extract the networks. We also explore the impact of varying the Basin-Hopping perturbation step-size. Our results suggest that the landscape's connectivity pattern (global structure) strongly varies with the perturbation step-size, with extreme values of this parameter being detrimental to search and fragmenting the global structure. Our LON visualisations strikingly illustrate the landscape's global (funnel) structure, indicating that LONs serve as a tool for visualising high-dimensional functions

Scale-specific spatial density-dependence in parasitoids: a multi-factor meta-analysis

1. Within a landscape, the risk of an insect being attacked by a parasitoid varies with the local density of the host species. This relationship should be strongest when observed at medium extents and resolutions with respect to the parasitoids’ foraging range, and turn negative at fine resolutions. The relationship is also hypothesised to depend on certain traits of the host and parasitoid taxa – e.g. being more positive for more specialised hosts or parasitoids and more negative for mobile hosts or gregarious parasitoids. Building on earlier literature reviews, it is now possible to investigate these hypotheses using meta-analysis. 2. We performed a multi-factor meta-analysis on 151 analyses of parasitism rates with respect to host densities at specified scales, from 61 empirical studies published from 1988 to 2012. We explored how the correlation between host density and parasitism rate may be related to the explanatory variables already mentioned, plus parasitoid body-size and various other characteristics of both hosts and parasitoids. 3. Correlations (Pearson’s r) between host density and parasitism rate ranged from –0.88 to 0.98 (mean 0.16, standard deviation 0.39). The correlation was more often negative where the host was exotic or in the orders Lepidoptera or Diptera, where the parasitoid was larger or exotic, or where the study was conducted at a finer grain-size. Hymenoptera and Homoptera were the most likely host orders to reveal positive associations, with Coleoptera and Diptera intermediate. 4. The fact that increased observational grain-size had similar effects to decreased parasitoid body length could be taken as evidence that parasitoids’ foraging ranges increase with their body-length. However, the hypothesis about scale-specific foraging was not supported by studies that compared multiple scales. 5. We conclude that parasitism most commonly produces positive (compensatory) spatial density-dependence, but ecological context is all-important. These findings should help improve the design and interpretation of field experiments on parasitism as well as their application to the modelling of population dynamics and the practice of biological control

Algorithm Instance Footprint: Separating Easily Solvable and Challenging Problem Instances

In black-box optimization, it is essential to understand why an algorithm instance works on a set of problem instances while failing on others and provide explanations of its behavior. We propose a methodology for formulating an algorithm instance footprint that consists of a set of problem instances that are easy to be solved and a set of problem instances that are difficult to be solved, for an algorithm instance. This behavior of the algorithm instance is further linked to the landscape properties of the problem instances to provide explanations of which properties make some problem instances easy or challenging. The proposed methodology uses meta-representations that embed the landscape properties of the problem instances and the performance of the algorithm into the same vector space. These meta-representations are obtained by training a supervised machine learning regression model for algorithm performance prediction and applying model explainability techniques to assess the importance of the landscape features to the performance predictions. Next, deterministic clustering of the meta-representations demonstrates that using them captures algorithm performance across the space and detects regions of poor and good algorithm performance, together with an explanation of which landscape properties are leading to it.Comment: To appear at GECCO 202

Landscape Analysis for Surrogate Models in the Evolutionary Black-Box Context

Surrogate modeling has become a valuable technique for black-box optimization tasks with expensive evaluation of the objective function. In this paper, we investigate the relationship between the predictive accuracy of surrogate models and features of the black-box function landscape. We also study properties of features for landscape analysis in the context of different transformations and ways of selecting the input data. We perform the landscape analysis of a large set of data generated using runs of a surrogate-assisted version of the Covariance Matrix Adaptation Evolution Strategy on the noiseless part of the Comparing Continuous Optimisers benchmark function testbed.Comment: 25 pages main article, 28 pages supplementary material, 3 figures, currently under review at Evolutionary Computation journa