1. Global Optimization Overview

The general relation between the number of Constraints and NPV tends to be inversely proportional, which means that scenarios with fewer constraints imposed, the optimization tends to find higher NPV since the algorithm free to search for better solutions. Therefore, it is always recommended that the full potentials of the mining project are tested first, as recommended in the optimized workflow, which starts at the Data Validation generating results that could be used in further steps. Regarding these aspects, a pretty useful approach was done by the MiningMath team throughout 2000 simulations (Figure 1) on a project seeking to identify the main impacts that the constraints had.

In summary, these results illustrate the intuitive assumption that by adding more and more constraints the probability of getting higher NPVs decreases drastically that is why the users have to apply "smart" concepts and constraints to achieve such results.

MiningMath deals with multiple constraints and aims to maximize NPV simultaneously. Remember that it is computationally impossible to guarantee that all possible solutions are evaluated by any algorithm and, therefore, it is impossible to guarantee that the maximum NPV will be delivered by a single run. Having such concepts in mind, a simple modification on a single parameter can generate unexpected effects on NPV. Thus, is always worthwhile to identify tendency, what it is not possible to find with only two runs. Note that is required to create a curve with a set of runs if we wish to find tendencies of an algorithm that includes such heuristics.

The logic behind such analysis is quite simple: for any optimization algorithm that aims to solve such complex problems, if we put too many constraints, we give no freedom for the algorithm to explore the solution space. Therefore, we tend to find solutions with lower NPV. On the other hand, when we give too much freedom, the algorithm will have the whole space to search for solutions, with no guidance on what would be reasonable in real life, so good solutions might not be found. The best compromise is when the user starts free of constraints and, then, starts giving some reasonable guidance (Figure 2). Therefore, smart constraints might help the algorithm in focusing only on a certain part of the space and actually deliver higher NPVs.

The main suggestions to explore the potential is by running the first iterations and evaluations with as few constraints as possible and without geometries (most complex in the mathematical model). Then, starts to move gradually to detailed scenarios, by adding parameters one-by-one, which will allow you to understand the impact of each constraint in the NPV, and guide decisions through an Integrated Workflow. Thus, by measuring how much each assumption "costs" to the project in the long-term, the managers will be able to choose the best way to use them.

MiningMath is a technology composed of mathematical programming and heuristics, which do not disrespect the constraints imposed to increase the NPV as the hierarchy (Figure 3) disclosed on this content explains. Experienced users take advantage of this aspect and slowly place constraints that might even help the optimizer to find solutions with higher NPV. A scenario with the total movement/production free, for instance, results in the better distribution of waste over time while adding/modifying a total limit makes the algorithm search the best result within these capacities and even find surprising NPVs among them. Therefore, to assess tendencies, it's recommended to draw a curve of scenarios, such as free, 100 Mtpa, 90 Mtpa, 80 Mtpa, and so forth versus NPV.