A new optimization method, the Algorithm of Changes, for Bin Packing Problem

The Bin Packing Problem (BPP) is one of the classic NP-hard problems in combinatorial optimization. It is difficult to find the optimal solution even though the size of the problem is small. Many researchers applied the traditional evolutionary algorithm, Genetic Algorithms (GA), Evolution Strategy (ES) etc. to solve the BPP problem in recent research. In this study, a new optimization algorithm, Algorithm of Changes (AOC), was proposed for the BPP problems. The algorithm was developed by the authors based on the concept of I Ching. It is a work with originality. The hexagram operators in I Ching were generalized to binary string case and an iterative procedure which imitated the I Ching inference was also introduced in this study. With the data taken from OR-Library, the AOC method was applied for finding the optimal solution (i.e. the minimum number of bins used) of three BPP problems. All the results found by the AOC method were compared with the other optimization methods shown in the past studies. Overall, the AOC method was shown to provide the optimal solution for all the BPP problems, and even superior to the other evolutionary heuristic methods.