The Pareto front (or Pareto frontier) is the set of all Pareto-efficient solutions in a multi-objective optimization problem — solutions where no other solution outperforms them across every objective simultaneously. The concept is widely used in engineering and economics. The formal definition involves a compact feasible decision set and a criterion vector space, with dominance relationships between solutions. In economics, a key property is that at a Pareto-optimal allocation, the marginal rate of substitution is equal for all consumers. Algorithms for computing the exact Pareto front exist but can be computationally expensive; approximate methods using ε-approximations with bounded Hausdorff distance are also studied, with various algorithms compared on criteria like scaling invariance and monotonicity.
