定和充足個体により連結された多段進化戦略に基づく効率的な魔方陣生成

抄録

The generation of magic squares of any size has been researched since ancient times. However，due to the need to solve complex combinatorial optimization problems，many existing methods are rule-based，and therefore can only generate a limited number of special magic squares. One of the non-rule-based generation methods is evolutionary computation，and this paper proposes a multi-stage evolutionary strategy that hierarchically classifies the constraints of magic squares into three stages of rows，columns，and diagonals，and uses the individuals satisfying each layer’s constraints as the initial individuals for the next layer. A magic square is a state in which the sum of each element in a square matrix in rows，columns，and diagonals is equal to a constant value. A square matrix that satisfies only the constraints in rows and columns is called a semi-magic square. In this research，the semi-magic square was divided into two layers，and by adding a lower layer that generates individuals satisfying only the row constraints，the need for exploration in the row direction was eliminated，resulting in a significant reduction in the number of searches. Experiments compared the necessary time and generation number between prior research and the proposed method，and achieved a significant reduction. Specifically，it was possible to generate a 90x90 magic square in about 232 times faster than prior research，with a successful generation in an average of 6 minutes and 57 seconds (10 trials).