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In this paper a hybrid algorithm is proposed to find the optimal solution for any instance of the bin packing problem one-dimensional. The hybrid algorithm considers the use of a heuristic method and a mathematical model based on flow arcs technique to find the optimal solution for an instance of 1D-BPP. The hybrid algorithm makes use of the lower bound of an instance as an element that allows it to identify if it have found the optimum or starting from this value it must find the optimal solution. The experiments were performed using the instances of the hard28 set, finding it the optimal solutions for all instances. The results show that the developed algorithm, called AHR, used 75% less time than using the Valerio model. [ABSTRACT FROM AUTHOR]

The problem of Bin Packing is a problem that is still open. Different strategies have been proposed using heuristic algorithms and metaheuristics to solve it without any of them can get the optimal solutions for all instances of hard28 set. This paper presents a heuristic strategy that solves instances of the hard28 set in less time than that obtained by the best algorithm. This heuristic strategy uses two types of patterns that contain instances of the hard28; approximately one sixth of the values of the objects are prime numbers, and also, about a third of their values are greater than half the capacity of the container, these features allows to fill containers before applying First Fit Decreasing heuristic. The presented heuristic significantly reduces the time needed to obtain the optimal value of some instances. The 28 instances of the hard28 set are used to evaluate the heuristic and the optimal values were obtained five them. [ABSTRACT FROM AUTHOR]