Counteracting genetic drift and disruptive recombination in (μpluskommaλ)-EA on multimodal fitness landscapes

Abstract

The impact of operator disruption and genetic drift on the extinction of EA subpopulations on multimodal landscapes is estimated by means of idealized two-peak landscape models. To establish upper and lower bounds for extinction times the behavior of an EA that employs (µ + , λ) selection and recombination mechanisms is studied, assuming disruptive recombination. Markov chain and statistical simulation studies reveal that panmictic selection mechanisms as used in evolution strategies (ES) do not allow for maintaining several populations of similar fitness at the same time. Moreover, when using comma selection, good individuals might easily get lost if forming the minority of a population, an effect seemingly amplified by recombination. Niching techniques are suggested to facilitate coexistence of populations on distant attractors; conducted studies confirm their aptitude.

Searching for good and diverse game levels

“…It has been introduced in [17] and consists of two phases that are repeated until the algorithm is stopped: in the initial phase, a relatively large population (here: 100 random samples) is employed for determining basins of attraction by means of the nearest-better clustering algorithm (NBC, [18]). Based on a distance matrix, we connect every solution to the nearest one within the sample that is better.…”

“…Large maps consist of 256 tiles and must contain 2-10 bases and 4-30 resources; since it is very likely that large maps contain many bases and resources, they are very unlikely to be feasible (13 feasible in 10 6 randomly initialized large maps). For the two distance-oriented algorithms (NEA2, Novelty search), 6 different distance measures are tested: tile-based distance, objective-based distance, visual impression (VI) distance (including all features), and visual impression distance with only balance/symmetry (indices 1-8), concentration (indices 9-17), and grouping dimensions (indices [18][19][20], respectively. From the returned set of best solutions, we select only the valid ones and determine 6 representatives by k-medoids (k = 6) clustering.…”

Attraction basin sphere estimation approach for niching CMA-ES

“…To do this, we propose a method, named as SIC, to calculate the importance of a seed. The method is based on the assumption proposed in nearest-better clustering (Preuss et al 2005) that the distance from small peaks to big peaks is shorter than the distance between big peaks. Given a point p and an array of points T that have been tested with p. For each point i in T, if i and p are a 2-modal pair, and i is better than p, then we record i in a set V. After that, we find the nearest point to p in V and record the distance between them as the importance of p. The process is shown in Algorithm 4.…”

Diversified Virtual Camera Composition

“…We call the original version (also labelled as NBC-CMA) niching evolutionary algorithm 1 (NEA1) here to differentiate it from the newer version we term NEA2. NEA1 highly relies on the CMA-ES as local searcher, but uses a much larger starting population (40×D) on which the nearest-better clustering method is run to separate it into populations representing different basins of attraction [18]. This topological clustering method connects every search point in the population to the nearest one that is better and cuts the connections that are longer than 2× the average connection.…”