Nondomination

Nondomination is a concept used in multiobjective optimization and decision analysis to describe a relationship between alternatives across multiple criteria. An option A dominates option B if A is at least as good as B in all objectives and strictly better in at least one. Nondomination occurs when neither A dominates B nor B dominates A, meaning there is a trade-off between criteria: each option is better than the other in some respect and worse in another.

The set of all nondominated options forms the Pareto-optimal set, also called the Pareto frontier. No single solution is best across all criteria; instead, improving one objective typically requires compromising another. For example, with two objectives—minimizing cost and maximizing quality—an option with both lower cost and higher quality than another dominates it, while two options can be nondominated if one is cheaper but of lower quality, and the other is higher quality but more costly.

Nondomination is central to many multiobjective methods, including evolutionary algorithms such as NSGA-II and SPEA2, which aim to approximate the Pareto frontier without relying on arbitrary weights for objectives. It provides a way to present a decision-maker with a set of diverse, noninferior solutions from which a choice can be made based on preferences not encoded in the objectives themselves.

Limitations include the potential abundance of nondominated solutions in large or finely scaled problems, sensitivity to objective scaling, and the need for additional decision criteria or preferences to select a final choice from the frontier.