Algorithms of Optimization Techniques for Bin Packing Problem: A Comparative Study

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EL Karmi, Yasmin
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جامعة النجاح الوطنية
One of the most critical optimization problems called Bin Packing Problem (BPP) attracts researchers attention because it is an NP-Complete problem means the solution can not be found in polynomial time. It has many applications such as storage and filling container. BPP aims to pick several items with different weights and pack them in a minimum number of bins without exceeding the bin’s capacity. One dimension BPP (1D-BPP) is one of its variations. Researchers have developed and proposed many algorithms to find an optimal solution or near-optimal solution. This research aims to make a comparison between six algorithms to solve one-dimensional BPP. Two heuristic algorithms proposed by Zehmakan [?] are approximation algorithms; one of them has an approximation ratio of 3/2, called A1 and A2. Those algorithms promise to perform more efficient and much better than other algorithms. Two classical approximation algorithms First Fit Decreasing (FFD) and Best Fit Decreasing (BFD) and two meta-heuristic algorithm namely Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) with specific parameters have been compared. In this work, several data sets have been used with the known optimal solution. They vary between random and arranged. Also, they vary in size. Some groups are small such as 9, 20 items, and medium such as 50, 100, 120 items and large such as 250, 500, 1000 items. Moreover, the sets vary in difficulty between easy and medium. So the number of bins used and running time have been compared to consider these algorithms’ performance. According to the number of bins used, A2 has performed better than A1 by comparing heuristic algorithms. However, it took much more running time than A1, especially in large data sets. Nevertheless, classical heuristics (BFD FFD) outperform both A1 and A2 in easy datasets, while in hard datasets A2 outperform the classical heuristics. By comparing meta-heuristic algorithms according to the number of bins used, in small data sets, PSO has performed better than GA but in large sets it’s almost the same. Also, PSO takes double running time than GA. PSO and GA have close results by the number of bins comparison and running time comparisons in other data sets. PSO is slightly better than GA when both the heuristics and the meta-heuristics are compared. Heuristic performs more efficient according to the number of bins and running time