What is the Right Context for an Engineering Problem: Finding Such a Context is NP-Hard

Authors

Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Hung T. Nguyen, New Mexico State University - Main CampusFollow
Songsak Sriboonchitta, Chiang Mai UniversityFollow
Rujira Ouncharoen, Chiang Mai UniversityFollow

Publication Date

6-2015

Comments

Technical Report: UTEP-CS-15-44

Abstract

In the general case, most computational engineering problems are NP-hard. So, to make the problem feasible, it is important to restrict this problem. Ideally, we should use the most general context in which the problem is still feasible. In this paper, we prove that finding such most general context is itself an NP-hard problem. Since it is not possible to find the appropriate context by utilizing some algorithm, it is therefore necessary to be creative -- i.e., to use some computational intelligence techniques. On three examples, we show how such techniques can help us come up with the appropriate context. Our analysis explains why it is beneficial to take knowledge about causality into account when processing data, why sometimes long-term predictions are easier than short-term ones, and why often for small deviations, a straightforward application of a seemingly optimal control only makes the situation worse.