Determination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithm

• Autorzy: Azimi Y. , Osanloo M.

Warianty tytułu

PL

Określenie granicznej zawartości pierwiastka użytecznego w rudzie wydobywanej metodą odkrywkową w oparciu o połączenie programowania liniowego i algorytmów genetycznych

• Języki publikacji: EN

Abstrakty

EN

Determination of cut-off grade strategy is one of the most important stages of open pit mine planning and design. It is the parameter directly influencing the financial, technical, economic, legal, environmental, social and political issues in relation to mining operation. Choosing the optimum cut-off grade strategy (COGS) that maximizes the economic outcome has been a major topic for research workers of nearly one century. Many researchers have contributed in devising methods and algorithms, such as dynamic programming, linear programming, optimal control and so on for various aspects of its determination. In this paper, a nonlinear mathematical programming for cut-off grade strategy optimization is presented considering the three main stages of mining operation introduced by K.F. Lane. In this model maximization of net present value of mining operation, under the three constraints of mining stages' capacities, considered as the optimization criteria. Due to the discrete representation of the mining resource, the proposed nonlinear formulation is approximated by a nonlinear signomial geometric programming. According to nonconvexity and the complexity of the proposed model, an augmented Lagrangian genetic algorithm was used to find the optimum cut-off grade strategy under varying and fixed price circumstances. To validate the proposed nonlinear model efficiency, their results were compared with the results obtained by the K.F. Lane methodology. It was found that the proposed nonlinear model works efficiently in the determination of cut-off grade strategy. According to the simplicity of the structure of nonlinear programming modeling in comparison with dynamic programming it is hoped that, further development of this model would certainly provide the ability of considering managerial and technical flexibilities as well as incorporating more real mining conditions in the determination of cut-off grade strategy optimization.

PL

Opracowanie strategii określania granicznej zawartości pierwiastka użytecznego w rudzie jest jednym z najważniejszych zagadnień przy projektowaniu i planowaniu kopalni. Jest to parametr który w sposób bezpośredni wpływa na kwestie finansowe, techniczne, ekonomiczne, prawne, środowiskowe, społeczne oraz polityczne pozostające w związku z działalnością górniczą. Wybór optymalnej strategii określania granicznej zawartości pierwiastka użytecznego w rudzie zakładający maksymalizację zysków jest ważnym problemem badawczym od prawie stu lat. Liczni badacze opracowali użyteczne metody i algorytmy: programowanie liniowe, programowanie dynamiczne, kontrola optymalna. W obecnej pracy przedstawiono metodę nieliniowego programowania matematycznego z wykorzystaniem do optymalizacji strategii określania granicznej zawartości pierwiastka użytecznego w rudzie. Metoda ta uwzględnia trzy etapy prowadzenia działalności górniczej, wprowadzone przez K.F.Lane'a. W modelu tym jako kryterium optymalizacji przyjęto maksymalizację wartości bieżącej netto działalności górniczej, z uwzględnieniem trzech więzów - czyli wydajności kopalni na poszczególnych etapach. Ze uwagi na dyskretne przedstawienie zasobów górniczych, proponowana sformułowanie nieliniowe przybliżone jest nieliniowym signomialnym algorytmem programowania geometrycznego. Z uwagi na nie wypukłość i złożoność proponowanego modelu, wykorzystano rozbudowany algorytm genetyczny (Lagrangian) w celu znalezienia optymalnej strategii określania granicznej zawartości pierwiastka użytecznego w rudzie w stałych i zmiennych warunkach cenowych. Dla walidacji skuteczności proponowanego modelu nieliniowego, wyniki porównano z wynikami uzyskanymi przy użyciu metodologii K.F. Lane'a. Stwierdzono, że proponowany model nieliniowy jest skuteczny przy określaniu granicznej zawartości pierwiastka użytecznego w rudzie. Dzięki prostocie struktury modelu programowania nieliniowego w porównaniu do programowania dynamicznego, oczekiwać należy że po dopracowaniu model uwzględniać będzie także zagadnienia menedżerskie i techniczne a także, iż będzie w stanie uwzględniać większy zakres rzeczywistych warunków górniczych.

Słowa kluczowe

EN

cut-off grade strategy; geometric nonlinear optimization; genetic algorithm

PL

strategia określanie granicznej zawartości pierwiastka użytecznego w rudzie; nieliniowa optymalizacja geometryczna; algorytm genetyczny

• Wydawca: Instytut Mechaniki Górotworu PAN
• Czasopismo: Archives of Mining Sciences
• Rocznik: 2011
• Tom: Vol. 56, no 2
• Strony: 189--212
• Opis fizyczny: Bibliogr. 66 poz., rys., tab., wykr.

Twórcy

autor

Azimi Y.

autor

Osanloo M.

• Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran,

Bibliografia

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