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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]

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]

Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. In this paper we have performedan experimental studythat indicates the use of genetic algorithms for the two dimensional bin packing problem. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. We propose a new solution of the problem by a genetic algorithm. [ABSTRACT FROM AUTHOR]

In this article the solution of Bin Packing problem of one dimension through a weighted finite automaton is presented. Construction of the automaton and its application to solve three different instances, one synthetic data and two benchmarks are presented: N1C1W1_A.BPP belonging to data set Set_1; and BPP13.BPP belonging to hard28. The optimal solution of synthetic data is obtained. In the first benchmark the solution obtained is one more container than the ideal number of containers and in the second benchmark the solution is two more containers than the ideal solution (approximately 2.5%). The runtime in all three cases was less than one second. [ABSTRACT FROM AUTHOR]