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ItemData mining based framework to assess solution quality for the rectangular 2D strippacking problem( 2019) Alvaro Luiz Júnior ; José Fernando Oliveira ; Carlos Manuel Soares ; António Miguel Gomes ; Elsa Marília Silva ; 5001 ; 265 ; 5675 ; 6300 ; 1249In 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 twodimensional strippacking problem (2DSPP), 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 miningbased framework capable of assessing the quality of heuristic solutions for the 2DSPP. A regression model was fitted by comparing the strip height solutions obtained with the bottomleftfill 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 2DSPP variations found in realworld applications. Height predictions for new problem instances can be found in the regression model fitted. In the computational experimentation, we demonstrate that the data miningbased 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. © 2018 Elsevier Ltd

ItemThe twodimensional strip packing problem: What matters?( 2018) Alvaro Luiz Júnior ; José Fernando Oliveira ; António Miguel Gomes ; Elsa Marília Silva ; 6300 ; 5675 ; 265 ; 1249This paper presents an exploratory approach to study and identify the main characteristics of the twodimensional strip packing problem (2DSPP). A large number of variables was defined to represent the main problem characteristics, aggregated in six groups, established through qualitative knowledge about the context of the problem. Coefficient correlation are used as a quantitative measure to validate the assignment of variables to groups. A principal component analysis (PCA) is used to reduce the dimensions of each group, taking advantage of the relations between variables from the same group. Our analysis indicates that the problem can be reduced to 19 characteristics, retaining most part of the total variance. These characteristics can be used to fit regression models to estimate the strip height necessary to position all items inside the strip. © Springer International Publishing AG 2018.