In multi-objective evolutionary algorithms (MOEAs) with elitism, the data structures for storing and updating archives may have a great impact on the required computational (CPU) time, especially when optimizing higherdimensional problems with large Pareto-sets. In this chapter, we introduce Quad-trees as an alternative data structure to linear lists for storing Paretosets. In particular, we in...

This paper describes how we maintain color and spatial index information on more than 1,000,000 images and how we allow users to browse the spatial color feature space. We break down all our images in color-based quad trees and we store all quad trees in our main-memory database. We allow users to browse the quad trees directly, or they can pre-select images through our color bit vector, which ...

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

The pair-wise comparison technique is a common approach for completing multi-attribute evaluations. However, this approach has limitations, especially for larger attribute sets, where the use of the technique is time-consuming because it requires a relatively large number of comparisons. The authors conducted an experiment to test the efficacy of three alternative approaches for eliciting prefe...

In MOEAs with elitism, the data structures and algorithms for storing and updating archives may have a great impact on the CPU time, especially when optimizing continuous problems with larger population sizes. In this paper, we introduce Quad-trees as an efficient data structure for storing Pareto-points. Apart from conventional linear lists, we have implemented three kinds of Quad-trees for th...