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Related Experiment Video

Updated: May 30, 2026

Quantitative Hardness Measurement by Instrumented AFM-indentation

Quantitative Hardness Measurement by Instrumented AFM-indentation

Published on: November 22, 2016

Formal analysis, hardness, and algorithms for extracting internal structure of test-based problems.

Wojciech Jaśkowski¹, Krzysztof Krawiec

¹Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60965 Poznań, Poland. wjaskowski@cs.put.poznan.pl

Evolutionary Computation

|August 6, 2011

Summary

This study introduces a coordinate system to understand problem dimensions in computational intelligence. Researchers developed an exact algorithm and a superior heuristic for finding minimal coordinate systems, revealing lower problem dimensions than expected.

Related Experiment Videos

Last Updated: May 30, 2026

Quantitative Hardness Measurement by Instrumented AFM-indentation

Quantitative Hardness Measurement by Instrumented AFM-indentation

Published on: November 22, 2016

Area of Science:

Computational Intelligence
Artificial Life
Machine Learning
Multi-Objective Optimization

Background:

Test-based problems are common in computational intelligence, involving interactions between elementary entities.
These problems can be framed as multi-objective optimization, where each test case represents a distinct objective.
Understanding the internal structure of these problems is crucial for efficient optimization.

Purpose of the Study:

To investigate the formalism and properties of coordinate systems for test-based problems.
To develop an exact algorithm for finding a minimal coordinate system.
To introduce a heuristic algorithm that outperforms existing methods for determining problem dimension.

Main Methods:

Formalizing underlying objectives and internal problem structure using a coordinate system.
Relating coordinate system properties to partially ordered sets.
Designing an exact algorithm and a novel heuristic for finding minimal coordinate systems.
Proving the NP-hard nature of the minimal coordinate system problem.

Main Results:

The dimension of a problem, defined by the minimal coordinate system, is typically much lower than the number of test cases.
The proposed heuristic algorithm demonstrates superior performance compared to the best previously known algorithm.
For certain problems, the dimension converges to an intrinsic, a priori parameter.

Conclusions:

The concept of problem dimension, derived from a minimal coordinate system, offers a more parsimonious representation of complex computational intelligence problems.
The developed algorithms provide effective tools for analyzing and understanding the intrinsic complexity of these problems.
This research contributes to a deeper theoretical understanding and practical optimization of test-based problems.