twocriterion

Twocriterion is a term used in optimization and decision analysis to denote problems that involve optimizing two objective functions simultaneously. In a twocriterion problem, one seeks solutions that balance competing goals, such as cost and quality, time and reliability, or risk and return. Unlike single-objective optimization, where a single best solution is sought, twocriterion problems typically yield a set of Pareto-optimal solutions, known as the Pareto frontier, in which no objective can be improved without worsening the other.

Common approaches to solving twocriterion problems include scalarization, where the two objectives are combined into a single objective through a weighting of f1 and f2; and the epsilon-constraint method, which optimizes one objective while constraining the other. Other techniques include goal programming, lexicographic optimization, and evolutionary multiobjective optimization. The choice of method depends on the decision maker's preferences, problem structure, and required guarantees.

Applications of twocriterion frameworks span operations research, engineering, economics, and computer science. Examples include production planning with cost and throughput, vehicle routing with distance and fuel consumption, and portfolio selection balancing expected return and risk. In practice, practitioners may present the Pareto frontier to stakeholders with a visualization or select a preferred compromise based on additional criteria.

Relation to terminology: twocriterion is closely related to bi-criteria or two-objective optimization. It is a specific case within the broader field of multiobjective optimization.