Nonlinear Multiobjective Optimization¶
Miettinen, K. (1998). Nonlinear Multiobjective Optimization. Springer US.
Cited by¶
4 citations across 4 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.
Supported in partVerified against the publisher's abstract
Publisher abstract confirms MOO deals with conflicting objectives single-objective methods cannot handle, but not Pareto optimality or the three preference-articulation types.
“many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough”
- (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¶
- Design Space Map
- Its strength is generativity: by defining the space through dimensions rather than through the options already on the table, it can reveal feasible regions no one proposed, and it makes trade-off frontiers — where improving one axis costs another — legible as geometry.
This sourceFormalizes Pareto optimality for conflicting objectives and treats graphical representations that make multiobjective trade-offs visible.
- Its strength is generativity: by defining the space through dimensions rather than through the options already on the table, it can reveal feasible regions no one proposed, and it makes trade-off frontiers — where improving one axis costs another — legible as geometry.
- Dominance Filtering
- Its strength is a guarantee earned without any absolute measurement: it removes only options that are provably worse than a specific alternative, so the surviving frontier is exactly the set of defensible choices.
This sourceInternational Series in Operations Research & Management Science 12. Kluwer Academic Publishers (1998). Defines Pareto filtering by removing alternatives dominated by a specific feasible alternative, leaving the nondominated frontier without requiring a single aggregate measure.
- Its strength is a guarantee earned without any absolute measurement: it removes only options that are provably worse than a specific alternative, so the surviving frontier is exactly the set of defensible choices.
- 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
Verification¶
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