Standardized microplates are used to conduct large-scale biomedical research. The design of microplate layouts plays an essential role in handling so-called plate effects, i.e., systematic variations across the geometry of a microplate. An effective layout allows us to detect and negate plate effects. The randomized placement of controls and compounds produces layouts of limited effectiveness, so specific approaches are needed. A previously developed system, PLAID, proposed a constraint satisfaction model to construct effective plate layouts. However, PLAID does not scale well with microplate dimensions. To improve on PLAID, we propose Constraint Optimization of MicroPlate Designs (COMPD), which allows for greater flexibility and higher quality of the layouts.

Given a table with a minimal set of input columns that functionally determines an output column, we introduce a method that tries to gradually decompose the corresponding minimal functional dependency (mfd) to acquire a formula expressing the output column in terms of the input columns. A first key element of the method is to create sub-problems that are easier to solve than the original formula acquisition problem, either because it learns formulae with fewer inputs parameters, or as it focuses on formulae of a particular class, such as Boolean formulae; as a result, the acquired formulae can mix different learning biases such as polynomials, conditionals or Boolean expressions. A second key feature of the method is that it can be applied recursively to find formulae that combine polynomial, conditional or Boolean sub-terms in a nested manner. The method was tested on data for eight families of combinatorial objects; new conjectures were found that were previously unattainable. The method often creates conjectures that combine several formulae into one with a limited number of automatically found Boolean terms.

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