A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization

We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical optimization of non-linear, non-convex optimization problems in continuous domain. Inspired by the limited memory BFGS method of Liu and Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a covariance matrix reproduced from $m$ direction vectors selected during the optimization process. The decomposition of the covariance matrix into Cholesky factors allows to reduce the time and memory complexity of the sampling to $O(mn)$, where $n$ is the number of decision variables. When $n$ is large (e.g., $n$ > 1000), even relatively small values of $m$ (e.g., $m=20,30$) are sufficient to efficiently solve fully non-separable problems and to reduce the overall run-time.Comment: Genetic and Evolutionary Computation Conference (GECCO'2014) (2014

Replicated evolution of integrated plastic responses during early adaptive divergence

Colonization of a novel environment is expected to result in adaptive divergence from the ancestral population when selection favors a new phenotypic optimum. Local adaptation in the new environment occurs through the accumulation and integration of character states that positively affect fitness. The role played by plastic traits in adaptation to a novel environment has generally been ignored, except for variable environments. We propose that if conditions in a relatively stable but novel environment induce phenotypically plastic responses in many traits, and if genetic variation exists in the form of those responses, then selection may initially favor the accumulation and integration of functionally useful plastic responses. Early divergence between ancestral and colonist forms will then occur with respect to their plastic responses across the gradient bounded by ancestral and novel environmental conditions. To test this, we compared the magnitude, integration, and pattern of plastic character responses in external body form induced by shallow versus open water conditions between two sunfish ecomorphs that coexist in four postglacial lakes. The novel sunfish ecomorph is present in the deeper open water habitat, whereas the ancestral ecomorph inhabits the shallow waters along the lake margin. Plastic responses by open water ecomorphs were more correlated than those of their local shallow water ecomorph in two of the populations, whereas equal levels of correlated plastic character responses occurred between ecomorphs in the other two populations. Small but persistent differences occurred between ecomorph pairs in the pattern of their character responses, suggesting a recent divergence. Open water ecomorphs shared some similarities in the covariance among plastic responses to rearing environment. Replication in the form of correlated plastic responses among populations of open water ecomorphs suggests that plastic character states may evolve under selection. Variation between ecomorphs and among lake populations in the covariance of plastic responses suggests the presence of genetic variation in plastic character responses. In three populations, open water ecomorphs also exhibited larger plastic responses to the environmental gradient than the local shallow water ecomorph. This could account for the greater integration of plastic responses in open water ecomorphs in two of the populations. This suggests that the plastic responses of local sunfish ecomorphs can diverge through changes in the magnitude and coordination of plastic responses. Although these results require further investigation, they suggest that early adaptive evolution in a novel environment can include changes to plastic character states. The genetic assimilation of coordinated plastic responses could result in the further, and possibly rapid, divergence of such populations and could also account for the evolution of genes of major effect that contribute to suites of phenotypic differences between divergent populations