Abstract

HERRERA-FRANKLIN, Jorge; ROSETE-SUAREZ, Alejandro; GARCIA-BORROTO, Milton  and  CABRERA-GARCIA, Suitberto. Influence of statistical distributions in the hardness of instances of the variable size and cost bin packing problem. Ingeniería Mecánica [online]. 2020, vol.23, n.2  Epub Aug 01, 2020. ISSN 1815-5944.

The Variable Size and Cost Bin Packing Problem consists of minimizing the cost of all the containers used to pack a set of items. In the previous works, several algorithms have been presented and studied, to solve different instances of this problem where the weights of the elements to be packed follow Uniform Distribution. The objective of this work is to study the influence of the statistical distribution that the components of the instances of the problem follow in their complexity. For this, three sets of reference instances were designed that follow different statistical distributions and the SCIP solver was used to solve them. From these experiments, it was obtained that the instances where the weights of the elements follow the Normal Distribution and the capacities of the containers follow the Weibull Distribution are more difficult to solve than the instances with characteristics similar to those studied in the previous articles.

Keywords : combinatorial optimization; variable size and cost bin packing problem; benchmark instances; statistical analysis.

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