nondominated

Nondominated refers to a solution in a multiobjective optimization context that is not worse than any other feasible solution across all objectives, and is strictly better in at least one objective. In other words, no other solution Pareto-dominates it. A solution that is not nondominated is said to be dominated.

In problems with multiple objectives, solutions are compared using Pareto dominance: a solution A dominates B if A is at least as good as B in every objective and strictly better in at least one. The set of all nondominated solutions forms the Pareto frontier (or Pareto front). The frontier represents trade-offs where improving one objective would worsen at least one other. Nondominated solutions are considered equally preferable from a purely technical perspective, with no single best choice without additional preferences.

Computing nondominated sets often involves sorting or filtering a population of candidate solutions. One common approach is nondominated sorting, which identifies the first front of solutions not dominated by any other, removes them, and repeats to find subsequent fronts. The complexity depends on the number of solutions and the number of objectives. In practice, many evolutionary algorithms, such as NSGA-II, use nondominated sorting to guide search toward the Pareto frontier.

Example: consider two objectives to minimize. Solutions A = (1, 2), B = (2, 1), and C = (3, 3). Neither A nor B dominates the other, and C is dominated by both A and B. Thus A and B are nondominated, forming the first frontier, while C lies outside the frontier.

Nondomination is central to multiobjective decision making, where a set of diverse, nondominated solutions provides a spectrum of trade-offs. It does not prescribe a single best solution; further preferences or decision criteria are needed to select among frontier members.