تعيين عيار حد بهينه معادن روباز با هدف بيشينه كردن ارزش خالص فعلي با استفاده از الگوريتم رقابت استعماري

Determination of optimum cutoff grades to maximize net present value by using Imperialism Competitive Algorithm (ICA)

هدف اساسی برنامه‌ریزی تولید بلند مدت، اتخاذ تدابیری جهت اجرای عیارهای حد استخراجی و برنامه‌ریزی تولید كوتاه مدت است. یكی از مهمترین پارامترها در طراحی معادن روباز، تعیین عیار حد بهینه است. عیار حد بهینه منجر به بیشینه نمودن سود و یا بیشینه نمودن ارزش خالص فعلی می‌شود. بیشنه نمودن ارزش خالص فعلی كه در چند دهه اخیر مورد توجه قرار گرفته است، یك مساله برنامه‌ریزی غیرخطی است. لین برای تعیین عیار حد بهینه با احتساب عواملی همچون ظرفیت‌های هر یك از قسمت‌های مختلف معدن (ظرفیت‌های استخراج از معدن، كارخانه تغلیظ، كارخانه تصفیه و بازار)، ارزش زمانی پول و توزیع عیار كانسار، الگوریتم خود را  ارایه  داده است. روند محاسبه عیار حد با استفاده از الگوریتم لین بسیار طولانی است. در این مقاله به منظور تعیین عیار حد بهینه از روش الگوریتم بهینه‌سازی رقابت استعماری، كه در رده الگوریتم‌های هوشمند قرار می‌گیرد، استفاده شده است. نتایج نشان می‌دهد كه تعیین عیار حد با استفاده از این روش از دقت وسرعت بالایی برخوردار است.

Summary Mining production planning is a very vital subject of mine design process. One of the most important issues in mine production planning is the cutoff grade which is simply a grade used to distinguish between ore and waste. Waste materials may either be left in place or sent to waste dump. Ore is sent to the mill for further processing. Lower cutoff grade causes higher amounts of ore to be processed and subsequently lower amounts of waste materials to be dumped resulted in fluctuations in the cash flow of a mining project. The main goal of the long-term production planning is to determine strategies to implement the cutoff grade and short-term production planning. One of the most important aspects of mine design is to determine the optimum cutoff grade. The optimum cutoff grade leads to maximize the profit or the Net Present Value (NPV). Maximizing of NPV is a non-liner programing problem that has been considered in the recent decades. The main factors involved in the Lane algorithm are the capacities of each part of the mine (e.g. extraction capacity of mine, refinery plant, and market), time value of currency and distribution grad of deposit. Since Lane algorithm calculation steps are very time consuming, In this study a novel technique namely Imperialism Competitive Algorithm (ICA) is used to determine the optimum cut-off grade. The results show that optimum cut-off grade obtained by ICA is more accurate and faster than other simulation algorithms. In this paper a novel optimization algorithm based on imperialist competitive algorithm (ICA) is used to determine the optimum cut-off grade in the open-pit mines.   Introduction One of the important aspects of open-pit mine design is determination of cutoff grade, by definition cutoff grade is the grade at which the mineral reserve ca no longer be mined and processed at profit. A cutoff grade is used to assign the destination of material exploited from the mine. This destinations are: (1) to mill, (2) to the waste dump and (3) to the stockpiles. In this paper, determining the optimal cutoff grade of ore to maximize the NPV due to mining limitations, concentration and refining is described by using ICA algorithm.   Methodology and Approaches The ICA algorithm starts with an initial population. Each population in ICA is called country. Countries are divided in two groups: imperialists and colonies. In this algorithm the more powerful imperialist, have the more colonies. When the competition starts, imperialists attempt to achieve more colonies and the colonies start to move toward their imperialists. So during the competition the powerful imperialists will be improved and the weak ones will be collapsed. At the end just one imperialist will remain. In this stage the position of imperialist and its colonies will be the same. In this paper the cutoff grade of hypothetical deposit is calculated using ICA algorithm. This algorithm has 40 country, 6 imperialist and 34 colony. Finally the results is validated by dichotomous method.   Results and Conclusions One of the important parameters of open-pit mine design is determination of cutoff grade. In this paper imperialist competitive algorithm is used to optimize the cutoff grade. Since the roulette wheel mechanism is not used In the ICA algorithm and only a probability density function (PDF) is needed to reach the answer, the ICA algorithm converges faster and better to the optimum point compare with other algorithms.