Production scheduling problem and solver improvement via integration of the grey wolf optimizer into the augmented Lagrangian relaxation method

Abstract

In open-pit mines, the long-term production scheduling problem is a mixed-integer programming optimization problem. Usually, it is tricky to reach the true optimal solution to the long-term production scheduling problem due to its complexity and dimensions. However, owing to its high-dimensional and combinatorial nature, the long-term production scheduling problem hinders the development of a precise mathematical optimization technique that can solve the whole problem for any real-size block model. In this paper, a hybrid model is introduced to solve the long-term production scheduling problem, taking into account grade uncertainty assisted by the augmented Lagrangian relaxation and the grey wolf optimizer methods. The hybrid augmented Lagrangian relaxation–the grey wolf optimizer technique is recommended to solve the long-term production scheduling problem to improve its performance and, consequently, speed up the convergence. The proposed model has been compared with the results of the hybrid methods gained from the classic Lagrangian relaxation and augmented Lagrangian relaxation methods integrated with the bat algorithm, particle swarm optimization, genetic algorithm, the traditional subgradient method, and conventional method without using the Lagrangian approach. The fallouts point out that better presentation is gained by the augmented Lagrangian relaxation–the grey wolf optimizer method in terms of net present value, average ore grade, and CPU time. Moreover, the cumulative net present value by the proposed model is 13.39% more than the conventional method.