A Storage Pattern-Based Heuristic Algorithm for Solving Instances of Hard28 Datasets for the Bin Packing Problem

Abstract

In this paper, we propose a heuristic algorithm that obtains the optimal solution for 5 instances of the set of instances Hard28, for the problem of packing objects in containers of a dimension (1DBPP). This algorithm is based on storage patterns of objects in containers. To detect how objects are stored in containers, the HGGA-BP algorithm [8] was used. A tool for monitoring and analyzing the HGGA-BP algorithm was also developed. With the help of the user, this tool performs the monitoring and analysis of the intermediate solutions that are generated with the algorithm HGGA-BP [8]. The proposed algorithm uses the inherent characteristics of the objects, that is, the weight value of the objects of the set of instances Hard28 can be: a prime number, an even number or an odd number. As well as, the weights of some of the objects are bigger than half of the capacity of the containers. The set Hard28 consists of 28 instances and the optimal value was found in 5 of them. For 19 instances, a container is missing to reach the optimum solution. For 3 instances, two containers were missing to reach the optimal solution and in one of the obtained solutions, 3 containers were missing to reach the optimal solution. For each of the optimal solutions found, the calculated time is less or equal than one millisecond.