1. 28/09/2011Ivan S. Živković1 Artificial Neural Networks for Decision Support in Copper Smelting Process Ivan S. Živković Mathematical Institute of the Serbian Academy of Sciences and Arts

2. 28/09/2011 Ivan S. Živković 2 1. Introduction Considerable development of pyrometallurgical copper smelting process Enlargement of production plants capacities Increase of entire copper production in the world Increasing problems due to environmental pollution

3. 28/09/2011 Ivan S. Živković 3 1. Introduction Smelting plants with old technologies emit PM 10 and SO 2 far above the limited values World Health Organization (WHO, 2001) has prescribed limited values of SO 2, PM 10 content and heavy metals' content in the air EU standardized limits of these polluters in the air by their regulations

4. 28/09/2011 Ivan S. Živković 4 1. Introduction Multi-Criteria Decision Making (MCDM) methods in the analysis of problems of air pollution and soil The integration of the analysis: 1. technological criteria 2. social criteria 3. environmental criteria 4. economical criteria

5. 28/09/2011 Ivan S. Živković 5 2. The blending problem K1,...,Km concentrates Determining the amount of each of the available raw materials (concentrates) K1,...,Km which will be used for obtaining the useful products GOAL: achieve the greatest difference between profit from useful products sales and costs for obtaining specified quantities of raw materials.

6. 28/09/2011 Ivan S. Živković 6 2. The blending problem Take into account : 1. interactive relations between the quality of raw materials, 2. economical criteria, 3. the influence of the environmental criteria in the production process.

7. 28/09/2011 Ivan S. Živković 7 2. The blending problem

8. 28/09/2011 Ivan S. Živković 8 2. The blending problem Maximize the goal function F(x1,...xn)

9. 28/09/2011 Ivan S. Živković 9 3. Neural network model F(x1,...,xn) = ? F(x1,...,xn) = Artificial Neural Network (ANN)

10. 28/09/2011 Ivan S. Živković 10 4. Neural network training Generate training data Combination of concentrate amount in mixture (x1,...,x14) Calculate profit for combination Back propagation algorithm The trained network stores the nonlinear relationships between amounts of concentrates in mixture

11. 28/09/2011 Ivan S. Živković 11 5. Optimization Complex Method for Constrained Optimization (Richardson and Kuester) Sequential search technique No derivatives are required The initial set of points is randomly scattered throughout the feasible region

12. 28/09/2011 Ivan S. Živković 12 5. Optimization x1 = 0.0011503862654742391 x2 = 0.0000044659968334488122 x3 = 0.33686567686323504 x4 = 0.000065479997370932846 x5 = 0.000005457597151501704 x6 = 0.14504843643625098 x7 = 0.0031948514922107056 x8 = 0.073478464846484792 x9 = 0.00043238651034418812 x10 = 0.00046832857651410561 x11 = 0.00011146905884013261 x12 = 0.43769285709204886 x13 = 0.00043421539040961333 x14 = 0.000063306618389357238 Profit = 581.19142562842535

13. 28/09/2011 Ivan S. Živković 13 6. Advantage No need for explicit form of the goal function No derivatives are required Network can learn nonlinear relationships between amounts of concentrates in mixture Easy to implement