Data mining based framework to assess solution quality for the rectangular 2D strip-packing problem

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Alvaro Neuenfeldt Júnior (Author) Other; Elsa Silva (Author) Other; António Miguel Gomes (Author) FEUP; Carlos Soares (Author) FEUP; José Fernando Oliveira (Author) FEUP

Journal

Title: Expert Systems with Applications

Vol. 118

Pages: 365-380

ISSN: 0957-4174

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 21 Citations

Scopus - 23 Citations

Other information

Authenticus ID: P-00P-RAK

DOI: 10.1016/j.eswa.2018.10.006

Abstract (EN): In this paper, we explore the use of reference values (predictors) for the optimal objective function value of hard combinatorial optimization problems, instead of bounds, obtained by data mining techniques, and that may be used to assess the quality of heuristic solutions for the problem. With this purpose, we resort to the rectangular two-dimensional strip-packing problem (2D-SPP), which can be found in many industrial contexts. Mostly this problem is solved by heuristic methods, which provide good solutions. However, heuristic approaches do not guarantee optimality, and lower bounds are generally used to give information on the solution quality, in particular, the area lower bound. But this bound has a severe accuracy problem. Therefore, we propose a data mining-based framework capable of assessing the quality of heuristic solutions for the 2D-SPP. A regression model was fitted by comparing the strip height solutions obtained with the bottom-left-fill heuristic and 19 predictors provided by problem characteristics. Random forest was selected as the data mining technique with the best level of generalisation for the problem, and 30,000 problem instances were generated to represent different 2D-SPP variations found in real-world applications. Height predictions for new problem instances can be found in the regression model fitted. In the computational experimentation, we demonstrate that the data mining-based framework proposed is consistent, opening the doors for its application to finding predictions for other combinatorial optimisation problems, in particular, other cutting and packing problems. However, how to use a reference value instead of a bound, has still a large room for discussion and innovative ideas. Some directions for the use of reference values as a stopping criterion in search algorithms are also provided.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16