We consider the problem of devising an approach for handling inequality constraints in evolution strategies that allows converging linearly to optimal solutions on sphere functions with a single linear constraint. An analysis of the single-step behaviour of the (1 + 1)-ES shows that the task of balancing improvements in the objective with those in the constraint function is quite delicate, and that adaptive approaches need to be carefully designed in order to avoid failure. Based on the understanding gained, we propose a simple augmented Lagrangian approach and experimentally demonstrate good performance on a broad range of sphere functions as well as on moderately ill-conditioned ellipsoids with a single linear constraint.

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Bright field cellular microscopy is a simple and non-invasive method for capturing cytological images. However, the resulting micrographs prove challenging for image segmentation, especially with samples that have tightly clustered or overlapping cells. Filamentous cyanobacteria grow as linearly arranged cells forming chain-like filaments that often touch and overlap. Existing bright field cell segmentation methods perform poorly with these bacteria, and are incapable of identifying the filaments. Existing filament tracking methods are rudimentary, and cannot reliably account for overlapping or parallel touching filaments. We propose a new approach for identifying filaments in bright field micrographs by combining information about both filaments and cells. This information is used by an evolutionary strategy to iteratively construct a continuous spline representation that tracks the medial line of the filaments. We demonstrate that overlapping and parallel touching filaments are segmented correctly in many difficult cases.

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