What objective function does Optimeal use when trying to stay close to the reference diet?
When minimizing deviation from a reference diet, Optimeal Open Access uses an objective function that minimizes absolute changes in food quantities (e.g. grams per person per day), rather than relative changes.
This choice is motivated by both numerical and conceptual considerations. From a numerical perspective, relative deviation requires dividing by baseline intake, which can lead to instability when foods are consumed in very small amounts or not consumed at all. Using absolute deviation avoids these issues and ensures robust behavior across datasets.
From a modeling perspective, relative deviation disproportionately penalizes foods with low baseline consumption. This makes it difficult for new or currently marginal foods to enter the optimized diet, and tends to reinforce the status quo by concentrating changes in foods already consumed in large quantities. Because many Optimeal applications are forward-looking and exploratory, absolute deviation provides a more neutral playing field in which alternative products can realistically replace existing ones.
When interpreting results, it is important to keep in mind that:
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Deviations are minimized in absolute, not relative, terms
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Foods consumed in larger quantities may absorb more of the adjustment
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Minimum and maximum constraints at the food level play a key role in shaping realistic outcomes
This objective function supports transparent, stable, and interpretable diet optimization, but results should always be evaluated in the context of the chosen objective, constraints, and input data.