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The optimization of cut-off grades by means of memetic algorithms

Erhan Cetin Abdurrahman Dalgic
Gospodarka Surowcami Mineralnymi - Mineral Resources Management | 2022 | vol. 38 | No 1 | 107-122 | DOI: 10.24425/gsm.2022.140607
Keywords memetic algorithms optimization cut-off grades depletion rate rehabilitation cost
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Abstract

Cut-off grades optimization is a fundamental issue for mineral deposits. A cut-off grade is any grade that is used to separate two courses of action; to mine or not to mine, to process or to dump. In order to achieve the maximum discounted cash flow, generally a decreasing order of cut-off grades schedule takes place. Variable mining costs are applied to the extracted material, not to all of the depletion rate as some of the depletion can be left in-situ. B ecause of access constraints, some of the blocks that have an average grade less than the determined cut-off grade are left in-situ, some of them are excavated and dumped as waste material. The probability density function of an exponential distribution is used to find the portion of the material below the cut-off used that is left in situ. The parts of a mineral deposit that are excavated but will be dumped as waste material and tailings of ore incur some additional cost of rehabilitation. The method of memetic algorithms is a very robust optimization tool. It is a step further from the genetic algorithms. The crossover, mutation and natural selection behavior of the method ensures it escape from a local optimum point, and a further local search improves the optimum further. This paper describes the general problem of cut-off grades optimization, outlines the use of memetic algorithms in cut-off grades optimization and further extension of the method including partial depletion rates and variable rehabilitation cost. This paper is the first application of memetic algorithms to cut-off grades optimization in this context.
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Bibliography

Cetin, E . 2016. Cut-off grades optimization by means of memetic algorithms with uncertain market conditions. Middle East Journal of Technic 1(1).
Cetin, E . and Dowd, P. A. 2002. The use of genetic algorithms for multiple cut-off grade optimisation. Proceedings of the 30th International Symposium on the Application of Computers and Operations Research in the Minerals Industries, Littleton, Colorado, USA.
Cetin, E . and Dowd, P.A. 2016. M ultiple cut-off grade optimization by genetic algorithms and comparison with grid search method and dynamic programming. The Journal of the South African Institute of Mining and Metallurgy 116(7), pp. 681–688, DOI: 10.17159/2411-9717/2016/v116n7a10.
Dowd, P.A. 1976. Application of dynamic and stochastic programming to optimise cut-off grades and production rates. Transactions of the Institution of Mining and Metallurgy Section A: Mining Industry 81. pp. 160–179.
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Garg, P. 2009. A Comparison between Memetic algorithm and Genetic algorithm for the Cryptanalysis of Simplified Data Encryption Standard Algorithm. International Journal of Network Security & Its Applications (IJNSA), 1(1), pp. 34–42.
Gholamnejad, J. 2008. Determination of the optimum cutoff grade considering environmental cost. Journal of International Environmental Application and Science 3(3), pp. 186-194.
Gholamnejad, J. 2009. Incorporation of rehabilitation cost into the optimum cut-off grade determination. The Journal of the South African Institute of Mining and Metallurgy 109(2), pp. 89–94.
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Lane, K.F. 1988. The Economic Definition of Ore. Mining Journals Books Ltd., L ondon, UK.
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Authors and Affiliations

Erhan Cetin
1
ORCID: ORCID
Abdurrahman Dalgic
2
  1. Dicle University, Diyarbakır, Turkey
  2. Alanya Alaaddin Keykubat University, Alanya, Turkey

Controllability-Oriented Placement of Actuators for Active Noise-Vibration Control of Rectangular Plates Using a Memetic Algorithm

Stanisław Wrona Marek Pawełczyk
Archives of Acoustics | 2013 | vol. 38 | No 4 | 529-536 | DOI: 10.2478/aoa-2013-0062
Keywords active control flexible structures actuators placement controllability Gramian evolutionary algorithm memetic algorithm
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Abstract

For successful active control with a vibrating plate it is essential to appropriately place actuators. One of the most important criteria is to make the system controllable, so any control objectives can be achieved. In this paper the controllability-oriented placement of actuators is undertaken. First, a theoretical model of a fully clamped rectangular plate is obtained. Optimization criterion based on maximization of controllability of the system is developed. The memetic algorithm is used to find the optimal solution. Obtained results are compared with those obtained by the evolutionary algorithm. The configuration is also validated experimentally.
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Authors and Affiliations

Stanisław Wrona
Marek Pawełczyk

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