Speed-Up Method for Magic Square Generation Using Multi-Stage Evolutionary Strategy Cascaded by Satisfiable Individuals for Magic Sum

In this paper, we 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. The proposed method’s efficiency is evidenced through experimental comparison of execution time and generations with a previous study, demonstrating substantial reductions in execution time.