A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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product that must be produced from the mine. MaximizeT X bx b (2) bB Subject to: gb Gmin x b 0 (3) bB i i imb immax x b 0, i 1,..., nim (4) bB x b 0,1 , b B (5) In this model, T is the total tonnage of final blended material to be maximized, b is the block identifier, and B is the set of potential ore blocks in the block model. X b is the tonnage of material in block b, and x b is the decision variable. If x b is equal to 1, then block b is included in the blended product, and if x b is equal to 0, then block b is not included in the blended product and it will be treated as a waste block. g b and G min are the grade of material in block b, and minimum allowable grade of final blended i i product respectively. n im , im b , and im max are the number of impurities in the ore deposit, grade of impurity i in block b, and maximum allowable amount of impurity i, in the final blended product respectively. The aim of the model is to maximize the total tonnage of the blended product (Equation 2). Equation 3 guaranties that the grade of the final product is greater than the minimum required. Equations 4, is used to make sure that the amount of impurities (contaminants) in the final product is lower than the maximum allowed. Equation 5, make sure that the decision variables are binary. The model presented in equations 2-5, selects a sub set of potential ore blocks that meets the blending requirements, and it does not consider the final outline of the mine (pit limit). The set of the selected potential ore blocks is the input of the pit optimization algorithms. The values of the potential ore blocks are assigned to be equal to the value of the final product, and those ore blocks that are not selected for blending are treated as waste blocks. Then it is possible to determine BEVs and the ultimate pit limit. In the next section the approach to combine pit and blend optimization is presented. 4 <strong>PIT</strong> AND BLEND OPTIMIZATION There are a number of pit design algorithms which is discussed in section 2. These algorithms require that the BEV of each block to be determined prior to applying the algorithms. In order to determine the BEV of the blocks, one needs to first select the set of blocks that can be blended. Then the BEV of these blocks is set to be equal to the value of final product. After this, one could apply any available methods to determine the ultimate pit limit (UPL). Figure 1 presents the procedure of determining the ultimate pit and blend limit according to Osanloo and Rahmanpour (2012). Figure 1. The procedure of determining the ultimate pit-blend limit According to figure 1 the steps of determining the ultimate pit-blend limit is as follow. Step 1) The potential ore blocks are selected from the block model based on characteristics such as rock type and ore grade. The set of these blocks are named S. Step 2) Set S is fed into the blend optimizing model to identify and select those block which satisfy the blending requirements. The set of those blocks that meet the blending requirements are called 122
23 rd BS. The mathematical model of blend optimization is given in equations 2-5 and a self-adapting differential evolution algorithm will be introduced to solve the blend optimization model. Step 3) The BEV of those blocks included in set BS are assigned to be equal to the value of the final product. Those block that are not a member of BS are waste blocks and their BEVs can also be calculated. Step 4) A UPL optimizing algorithms will be applied to determine the set of blocks that are economically profitable to be exploited be open pit mining. The sub set of BS which is inside the UPL is named PS. Step 5) In this step it should be checked that if the blocks in set PS, satisfies the blending requirement. Then, the UPL determined in step 4 is the optimum pit limit that satisfies both blending requirements and pit design constraints. If not, those blocks that are not profitable to be exploited by open pit mining are removed from set S, and the procedure repeats from step 2. Applying the procedure presented here one could achieve a pit limit that meets both blending requirements (the consumer’s requirements) and pit design constraints (including pit slope, and precedence of blocks). 4.1 Self-Adapting Differential Evolution Algorithm In step 2 of the procedure introduced for pitblend optimization, a genetic algorithm namely Self-adapting differential evolution is applied to solve the blending optimization problem (Equation 2-5). Differential evolution (DE) introduced by Storn and Price (1997), is a simple yet powerful evolutionary algorithm (EA) for global optimization. The DE algorithms are becoming more popular and are used in many practical cases, mainly because it has demonstrated good convergence properties and it is easy to understand. EAs are a broad class of stochastic optimization algorithms inspired by biology and have many advantages over other types of numerical methods. They only require information about the objective function itself. Other accessory properties such as differentiability or continuity are not necessary. As such, they are more flexible in dealing with a wide spectrum of problems (Back et al. 1997). When using an EA, it is also necessary to specify how candidate solutions will be changed to generate new solutions. Starting with a number of guessed solutions, the multipoint algorithm updates one or more candidate solutions in the hope of steering the population toward the optimum (Deb, 2005). DE creates new candidate solutions by combining the parent individual and several other individuals of the same population. A candidate replaces the parent only if it has better fitness (objective value). DE has three parameters: amplification factor of the difference vector (F), crossover control parameter (CR), and population size (NP). The values of these parameters greatly affect the quality of the solution obtained and the efficiency of the search. Choosing suitable values for these parameters is, frequently, a problem dependent task and requires previous experience of the user (Brest et al. 2006). In self-adaptive DE algorithm, the parameters to be adapted are encoded into the chromosome and they also undergo the actions of genetic operators. The better values of these parameters lead to better chromosomes which, in turn, are more likely to survive and produce offspring and propagate better values of the parameters as well. Brest et al. (2006) developed a selfadaptive DE algorithm based on the selfadaptation of two parameters F and CR, into the individuals, associated with the evolutionary process. In this algorithm called jDE (Qin et al. 2009), D is the set of optimization parameters and it is called an individual and is represented by a D-dimensional vector. A population consists of NP parameter vectors x i , G , i 1,...., NP and G denotes one generation and there is one population for each generation. NP is the number of members in a population, and it is not changed during the optimization process. 123
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Chapter - A OPEN PIT MINING
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23 rd 3.7 Results and Discussion T
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23 rd 4 DISCUSSION The results of
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A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

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