Scalarointi

Scalarointi, or scalarization, is a family of techniques in multiobjective optimization that transform a vector-valued objective into a single scalar objective. This enables the use of standard single-objective optimization methods to search for preferred trade-offs among competing goals. Scalarization does not remove the underlying multiple objectives, but encodes the decision maker’s preferences into the scalar objective or constraints.

Common methods include:

- Weighted sum: combine objectives as F(x) = sum_i w_i f_i(x) with weights w_i ≥ 0. Varying the weights aims to trace different Pareto-efficient solutions, typically when the objective set is convex.

- Epsilon-constraint: optimize one objective while enforcing upper bounds on the others, f_i(x) ≤ ε_i. By changing the thresholds ε_i, the Pareto front can be explored.

- Lexicographic: optimize objectives in a predefined order of priority, fixing higher-priority levels while optimizing lower-priority ones.

- Tchebychev (min-max) scalarization: minimize the maximum weighted deviation, often used to improve coverage of non-smooth fronts.

Advantages and caveats:

Scalarization is conceptually simple and computationally efficient, and it provides explicit control of preferences through weights or thresholds. However, it can be sensitive to the scale of objectives and may require normalization. The weighted-sum method can miss non-convex portions of the Pareto frontier, whereas alternative scalarizations like epsilon-constraint or goal programming can address some limitations.

Applications span engineering design, operations research, economics, and decision support, wherever trade-offs between conflicting objectives must be analyzed and communicated. In Finnish literature, the term scalarointi is used to denote these methods of converting multiple goals into a single evaluative criterion.