Nonlinear Multiobjective Optimization¶
Miettinen, K. (1998). Nonlinear Multiobjective Optimization. Springer.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Multiobjective Optimization
- (1) Multiobjective optimization is the generalization of single-objective optimization to problems with two or more distinct objectives that cannot be reduced to a single scalar without imposing additional value judgments — producing, in general, a set of Pareto-optimal (non-dominated) solutions rather than a single optimum, each representing a different trade-off among the competing objectives, and requiring either a-priori preference articulation, a-posteriori preference articulation (choose after seeing the Pareto frontier), or interactive preference articulation (choose through iterative dialogue with the solver) to select a specific solution from the Pareto set, in the formulation systematized by Miettinen (1999).
This sourceCanonical comprehensive reference for nonlinear MOO; systematizes definitions of Pareto-optimality, dominance, scalarization, and a-priori, a-posteriori, and interactive preference articulation.
- (1) Multiobjective optimization is the generalization of single-objective optimization to problems with two or more distinct objectives that cannot be reduced to a single scalar without imposing additional value judgments — producing, in general, a set of Pareto-optimal (non-dominated) solutions rather than a single optimum, each representing a different trade-off among the competing objectives, and requiring either a-priori preference articulation, a-posteriori preference articulation (choose after seeing the Pareto frontier), or interactive preference articulation (choose through iterative dialogue with the solver) to select a specific solution from the Pareto set, in the formulation systematized by Miettinen (1999).
Mechanisms¶
- Dominance Screening
- Its strength is decisiveness without overreach: it can prove that a whole set of familiar compromise options are strictly inferior
This sourceFormalizes Pareto dominance for identifying alternatives that are no better on every modeled objective and worse on at least one.
- Its strength is decisiveness without overreach: it can prove that a whole set of familiar compromise options are strictly inferior
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