Solving One-Dimensional Cutting Stock Problem Using Genetic Algorithm

In this section, we employ a genetic algorithm to solve the one-dimensional cutting stock problem, returning both total material consumption and cutting patterns. The genetic algorithm is an optimization technique inspired by biological evolution principles, simulating natural selection, crossover, and mutation processes to progressively search for optimal solutions. For the one-dimensional cutting problem, we model it as cutting materials along a single dimension to minimize waste while meeting specified requirements. Key implementation components include chromosome encoding (representing cutting patterns as sequences), fitness evaluation (calculating material utilization efficiency), and genetic operators like tournament selection, single-point crossover, and mutation mechanisms. Through genetic optimization, we identify optimal cutting schemes that minimize material usage while fulfilling demand constraints. The algorithm iteratively improves solutions by maintaining a population of candidate patterns, evaluating their performance using objective functions, and evolving better combinations through generations.