Rock blasting, in particularly the drilling process, is one of the first processes in the stage of rock fragmentation and plays a fundamental role by influencing all the following stages. Given its importance, some proposals to optimize this process have been presented over the last few years. These proposals, while having different approaches, aim (in a large part) to minimize the costs of drilling and blasting respecting the limits of fragmentation required by primary crushing. Reviewing some recent articles leads us to an enriching experience, since the authors of these articles clearly model the problem, but do not address the mathematical solution of these models, which in turn, given their non-linear nature, have no directly and easy solution. Simple and even robust optimizers present in the market show different results and often do not converge to a single solution. To address this problem, an adapted gradient heuristic-based model was developed to try to find optimum values. Heuristics search for values of stemming, subdrilling, burden and spacing that minimize the costs of blasting and drilling. This search, which by the nature of the heuristic moves the solution in the direction of the gradient with maximum decrease to find optimal solution, found values that in turn, when compared with values presented by market solutions not only equaled them as, in some situations, even improved the proposed solution. The algorithm was tested and validated on the field, and although the results have already been presented in papers published in the last year by the authors of this paper, it is now presented with its mathematical formulation and comparison with the other solutions. This approach is expected to be able to improve (and even demystify) the process of pattern expansion and be the basis for future work in the continuation of the optimization process.
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