Solving LTPSOP in open-pit mines using Gaussian process and human mental search

In this paper, to synthesize grade uncertainty into the strategic mine schedule, a stochastic mixed-integer programming framework (SMIP) is presented for the long-term production scheduling optimization problem (LTPSOP) in open-pit mines. The objective function maximizes the net present value and minimizes the risk of deviation from the production targets considering grade uncertainty simultaneously while satisfying all technical constraints and operational requirements. The current study has proposed a hybrid model to solve the LTPSOP with the incorporation of augmented Lagrangian relaxation (ALR) and the human mental search metaheuristic algorithm (HMS). The ALR function is formulated and the HMS is used to update the Lagrange multipliers. Besides, a Gaussian process machine learning method is applied to estimate the grade in a mineral deposit. The results obtained from a supercomputer have indicated that the ALR–HMS method conducted on real case studies generates 18.29% and 31.56% more cumulative net present value; 9.75% and 13.98% larger pit size than the conventional method, respectively. Finally, while improving the solvability and optimality gap, the analysis of the outcomes has demonstrated that the proposed model yields a near-optimal solution with a rational time.