Observations on the Feasibility of Exact Pareto Optimization with Applications to RNA folding

Pareto optimization combines independent objectives by computing the Pareto front of its search space, defined as the set of all candidates for which no other candidate scores better under both objectives. This gives, in a precise sense, better information than an artificial amalgamation of different scores into a single objective, but is more costly to compute. We define a general Pareto product operator ∗Par on scoring schemes. Independent of a particular algorithm, we prove that for two scoring schemes A and B used in dynamic programming, the scoring scheme A ∗Par B correctly performs Pareto optimization over the same search space. We show that a “Pareto-eager” implementation of dynamic programming can achieve the same asymptotics as a single-objective optimization which computes the same number of results. For RNA structure prediction under the minimum free energy versus the maximum expected accuracy model, we show that the empirical size of the Pareto front remains within reasonable bounds. Without artificial amalgamation of objectives, and with no heuristics involved, Pareto optimization is faster than computing the same number of answers separately for each objective.