Document Type: Original Research Paper


1 Department of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mining Engineering, University of Kashan, Kashan, Iran


It is significant to discover a global optimization in the problems dealing with large dimensional scales to increase the quality of decision-making in the mining operation. It has been broadly confirmed that the long-term production scheduling (LTPS) problem performs a main role in mining projects to develop the performance regarding the obtainability of constraints, while maximizing the whole profits of the project in a specific period. There is a requirement for improving the scheduling methodologies to get a good solution since the production scheduling problems are non-deterministic polynomial-time hard. The current paper introduces the hybrid models so as to solve the LTPS problem under the condition of grade uncertainty with the contribution of Lagrangian relaxation (LR), particle swarm optimization (PSO), firefly algorithm (FA), and bat algorithm (BA). In fact, the LTPS problem is solved under the condition of grade uncertainty. It is proposed to use the LR technique on the LTPS problem and develop its performance, speeding up the convergence. Furthermore, PSO, FA, and BA are projected to bring up-to-date the Lagrangian multipliers. The consequences of the case study specifies that the LR method is more influential than the traditional linearization method to clarify the large-scale problem and make an acceptable solution. The results obtained point out that a better presentation is gained by LR–FA in comparison with LR-PSO, LR-BA, LR-Genetic Algorithm (GA), and traditional methods in terms of the summation net present value. Moreover, the CPU time by the LR-FA method is approximately 16.2% upper than the other methods.


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