Optimization of Rectangular Layout Based on an Improved Adaptive Genetic Algorithm in Stone Cutting

We present an improved adaptive genetic algorithm for rectangular layout in stone cutting process. Firstly, the mathematical model for stone layout is proposed and established. Secondly, a heuristic algorithm based on the area size and the length-width ratio is employed to initialize the population. Thirdly, in order to define the fitness function, we take into consideration three important ingredients: the layout length, layout center of gravity and layout uniformity. Then an adaptive strategy on crossover probability and mutation probability is presented based on the distribution of population fitness values. The adaptive strategy can help the algorithm avoid achieving a premature convergence of local optimal solution. Finally, actual project results on production data show consistent improvements in the utilization ratio of stones compared with traditional method.