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    A Comparative Analysis of Metaheuristic Approaches for Multidimensional Two-Way Number Partitioning Problem
    (Springer Heidelberg, 2018) Hacibeyoglu, Mehmet; Alaykiran, Kemal; Acilar, Ayse Merve; Tongur, Vahit; Ulker, Erkan
    In this study, a novel usage of four metaheuristic approaches Genetic algorithm (GA), Simulated annealing (SA), migrating bird optimization algorithm (MBO) and clonal selection algorithm (CSA) are applied to multidimensional two-way number partitioning problem (MDTWNPP). MDTWNPP is a classical combinatorial NP-hard optimization problem where a set of vectors have more than one coordinate is partitioned into two subsets. The main objective function of MDTWNPP is to minimize the maximum absolute difference between the sums per coordinate of elements. In order to solve this problem, GA is applied with greedy crossover and mutation operators. SA is improved with dual local search mechanism. MBO is specialized as multiple flock migrating birds optimization algorithms. CSA is applied with problem specific hyper mutation process. Furthermore, all instances are solved using an integer linear programming model which was previously presented in the literature. In the experiments, four metaheuristic approaches and integer linear programming model are used to solve 126 datasets with different sizes and coordinates. As a brief result, the GA and SA approaches designed for this problem outperformed all other heuristics and the integer programming model. Both the performance of GA and SA approaches are in a competitive manner where GA and SA yielded the best solution for 56 and 65 out of 125 datasets, respectively.
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    SOLVING THE BI-DIMENSIONAL TWO-WAY NUMBER PARTITIONING PROBLEM WITH HEURISTIC ALGORITHMS
    (IEEE, 2014) Hacibeyoglu, Mehmet; Tongur, Vahit; Alaykiran, Kemal
    The two-way number partitioning problem is to divide set of numbers into two subsets. As a result of the dividing process the sums of numbers in subsets must be as nearly equal as possible. The two-way number partitioning problem problem is NP-complete. The bi-dimensional two-way number partitioning problem is a kind of number partitioning problem. The sets have only two coordinates and the aim is minimized the differences of the sum of the numbers for both coordinates. This work presents two heuristic algorithm for solving bi-dimensional two-way number partitioning problem. Fist algorithm is best known and most used greedy algorithm. The other one is a novel genetic algorithm approach. These algorithms are analyzed, implemented and tested on randomly different 20 datasets.