A Hybrid Algorithm for Solving the Optimal Layout Problem of Rectangular Pieces

In this paper, a hybrid algorithm, combined the adaptive simulated annealing genetic algorithm with the improved bottom-left algorithm, is presented for the optimal layout problem of rectangle pieces which is a NP-complete problem and possesses widespread applications in the industry. Adaptive genetic algorithm is adopted to change the probabilities of crossover and mutation automatically. Simulated annealing algorithm is used to modify the individuals whose fitness value is higher than the average fitness value of the population. The presented algorithm provides with global search capability of adaptive genetic algorithm and local search capability of simulated annealing algorithm. The computation results show that the optimal layout problem of rectangular pieces can be effectively solved by the hybrid algorithm.