Daniel Hoff – Optimization Online

Enclosures and Local Lower and Upper Bound Sets in Multiobjective Optimization

Published: 2026/08/26

Multi-Criteria Optimization enclosure, global optimization, Local Lower Bound Set, Local Upper Bound Set, Nonlinear Multiobjective Optimization, Width

One goal of multiobjective optimization is to approximate the nondominated set in the image space. One widely used approximation concept is that of enclosures. These are unions of closed boxes that cover the nondominated set. The bounds of these boxes form the lower and upper bound sets of the enclosure. The quality of an enclosure … Read more

Properties of Enclosures in Multiobjective Optimization

Published: 2025/09/05, Updated: 2026/04/27

Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization enclosure, global optimization, multiobjective optimization

A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we … Read more