Abstract
This study brings an implementation of a metaheuristic procedure to solve the Number Partitioning Problem (NPP), which is a classic NP-hard combinatorial optimization problem. The presented problem has applications in different areas, such as: logistics, production and operations management, besides important relationships with other combinatorial problems. This paper aims to perform a comparative analysis between the proposed algorithm with others metaheuristics using a group of instances available on the literature. Implementations of constructive heuristics, local search and metaheuristics ILS with path relinking as mechanism of intensification and diversification were made in order to improve solutions, surpassing the others algorithms.
Highlights
The Partition Problem is: given a set of numbers N, the goal is to divide it in 2 or more subsets so that the difference between the sums of the numbers inside each partition be the minimum.The problem’s definition sounds very simple but it is a combinatorial optimization problem that belongs to NP-hard class
Considering the importance of the Partition Problem, this paper aims to perform a comparative analysis between the proposed algorithm and others metaheuristics to solve a group of instances available on the literature
The first column defines the size of the instances and the other abbreviations has the meaning as follow: Hill-Clibing (HIC), Randon Generated Test (RGT), Simulated Annealing (SA), Tabu Search with Short Term Memory (TSSTM), Genetic Algorithms (GA), Memetic Algorithms (MA), Iterated Local Search (ILS), Iterated Local Search with Path Relinking (ILS+PR)
Summary
The Partition Problem is: given a set of numbers N, the goal is to divide it in 2 or more subsets (known as partitions) so that the difference between the sums of the numbers inside each partition be the minimum.The problem’s definition sounds very simple but it is a combinatorial optimization problem that belongs to NP-hard class. The Partition Problem is: given a set of numbers N, the goal is to divide it in 2 or more subsets (known as partitions) so that the difference between the sums of the numbers inside each partition be the minimum. To a set with n numbers, we have 2n ways to divide these numbers in two or more partitions. A feasible solution can be represented by a vector of bits which size is n, the position of an element in the solution’s vector points to partition associated to the number in the same position of the set that will be allocated. In industry, according to Ducha (2014), a possible application is the raw material partitioning between two machines in the production line, such way that the raw material can be processed faster
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