Model Selection using Multi-Objective Optimization

Choices in scientific research and management require balancing multiple, often competing objectives.Multiple-objective optimization (MOO) provides a unifying framework for solving multiple objective problems. Model selection is a critical component to scientific inference and prediction and concerns balancing the competing objectives of model fit and model complexity. The tradeoff between model fit and model complexity provides a basis for describing the model-selection problem within the MOO framework. We discuss MOO and two strategies for solving the MOO problem; modeling preferences pre-optimization and post-optimization. Most model selection methods are consistent with solving MOO problems via specification of preferences pre-optimization. We reconcile these methods within the MOO framework. We also consider model selection using post-optimization specification of preferences. That is, by first identifying Pareto optimal solutions, and then selecting among them. We demonstrate concepts with an ecological application of model selection using avian species richness data in the continental United States.