Automated dig-limit optimization through simulated annealing
Thijs Hanemaaijer · Research Repository (Delft University of Technology) · 2018
As ore-bodies become more complex and difficult to extract, mining operations need to increase their efficiency and performance.Dig-limit design is part of the short-term mine planning in open pit mines.Dig-limits are the boundaries between material destinations in a mining bench.Common practice in the mining industry is that these are created manually by a mining engineer, this results in subjective and sub-optimal dig-limits.In this thesis an automated optimization program was written to optimize these dig-limit designs.The optimization of dig-limits is a combinatorial optimization problem which has proven to be NP-hard, it cannot be solved exact in a reasonable time-frame.Therefore the meta-heuristic method of simulated annealing has been used for the optimization program.A meta-heuristic optimization method is a problem independent method that uses a smart searching algorithm, such that not the whole solution space needs to be investigated.This cannot guarantee an absolute optimal solution but will produce a near optimal solution within reasonable computing time.Simulated annealing uses an initial solution, from where it makes a change into a neighboring solution.The new solution is then accepted or rejected based on the difference in the objective value.If the objective value increases, the solution is always accepted, if it decreases, the solution may still be accepted with a certain probability.This probability depends on the magnitude of the difference in objective value, and on the temperature.The temperature is a control parameter for the acceptance of worse solutions, and is regulated by the cooling schedule.Initially the temperature will be very high, such that most worse solutions are accepted and the algorithm makes a broad search of the solution space.During the course of the algorithm the temperature is lowered by the cooling schedule and less worse solutions are accepted.This will make the algorithm converge into the found optimum.The constraints in the simulated annealing program were enforced by applying a penalty to the objective value for constraint violations.Different varieties for the simulated annealing program have been tested to investigate their applicability for dig-limit optimization and their performance.These options are written as interchangeable modules which are all compatible to each other and can easily be implemented in the program.Different methods were investigated for the initial solution, the constraint penalty, the cooling schedule, the perturbation mechanism and the stop criteria of the algorithm.The best performing combination of modules was a random initial solution, with a quadratic cooling schedule, a random perturbation which stops after a certain number of consecutive rejected perturbations.To reduce or prevent frequent switching between destinations, a specific module for the penalty function was created.This module could successfully and in a controlled manner discourage the switching between destinations, while making the final solution comply to the spatial mining constraints.This will make the algorithm more applicable to mining operations where dilution is a problem.Another successful option was a pre-optimized initial solution in combination with a greedy algorithm, which does not accept any worse solutions.This created high quality dig-limit designs in a considerable smaller amount of computation time.The resulting automated dig-limit optimization program was successful in creating near-optimal dig-limit designs.The program is flexible and can be adjusted for multiple material destinations, multiple oretypes and different shapes and sizes for the spatial mining constraints.The objective function can be adjusted for different optimization goals.This makes the program potentially applicable for different types of open-pit mining operations.i First of all I would like to thank my initial supervisor Tom Wambeke, who introduced the topic of dig-limit optimization to me.He laid down the framework for the program that was written and gave me essential guidance to get familiar with the programming language python.I would also like to thank Jeroen van Duivenbode, for his assistance with the programming and for his constructive feedback throughout my thesis.