Abstract and keywords
Abstract (English):
The problem related to the conflict between sources group’s excessive emissions and region’s pollution standards has been considered. It is possible to resolve the conflict by emissions sources efficiencies restrictions or reduction of pollution standards. Both actions lead to economic losses. It has been proposed to ease the conflict by the optimal sources allocation, in comparison with the initial one. The sources’ efficiencies and the region’s standards have been preserved during optimization. The sources emissions were modeling by parabolic functions, thus was solving the geometric problem of optimizing the coordinates for allocation of paraboloids with constant volumes. Different sources coordinates usually lead to a multiextremal function of pollution excess over the region's standards. The optimization problem is reduced to excess function control. The sources coordinates are becoming the control parameter. The numerical integral of the excess function has been defined as optimization criterion. Assuming a unimodal relationship between the criterion and the parameter, the Nelder-Mead procedure has been chosen as an algorithm for multidimensional nonlinear optimization. The optimization criterion’s convinced convergence to zero has been established due to a change on the sources coordinates’ iterations. Numerical experiments have been carried out, in which a high level of conflict (pollution function’s multiple excesses over the standards) has been set by the initial parameters. The region has been divided into 6 regulatory zones with non-standard flexible boundaries. The excess function was generating by 24 sources with different emissions efficiencies. A series of iterations has been performed, at which the conflict level was reduced to 1.32% due to the sources displacement. Such a decrease has required a selective withdrawal of 18 sources out of the region. This withdrawal does not exclude further trans-boundary pollutions emissions into the controlled area. The problems of trans-boundary pollutions transfer have been discussed. Iterations results have been shown in 2D-3D graphics. Having at disposal detailed iterations tapes, including their visualization, a designer is free to choose different input data of the model and to achieve the required conflict level. The presentation of optimization results in numerical and graphical formats is a convenient tool for designing of areas with complex infrastructure.

region pollution, emissions sources, pollution standards, Nelder-Mead procedure, sources removal, trans-boundary pollution transfer.

В промышленной экологии распространены задачи конфликта выбросов источников с допустимыми нормативами загрязнения, которые действуют в различных зонах области [5; 10].


1. Bandi B. Metody optimizacii. Vvodny`j kurs. [Optimization methods. Introductory course]. Moscow, Radio i svjaz Publ., 1988. 128 p.

2. Emel'janov S.V., Korovin S.K., Bobylev N.A. Metody nelinejnogo analiza v zadachah upravlenija i optimizacii. [Methods of nonlinear analysis in control problems and optimization]. Moscow, Editorial URSS Publ., 2002. 120 p.

3. Zhilinskas A., Shaltjanis V.M. Poisk optimuma. [Search for optimum]. Moscow, Nauka Publ., 1989. 128 p.

4. Zavriev S.K., Novikova N.M., Fedosova A.V. Stohasticheskij algoritm reshenija vypuklyh zadach polubeskonechnoj optimizacii s ogranichenijami ravenstvami i neravenstvami [A stochastic algorithm for solving convex problems semi-infinite optimization with the limitations equalities and inequalities]. Vestnik Moskovskogo universiteta. Vy`chislitelnaja matematika i kibernetika [Bulletin of Moscow University. Computational Mathematics and Cybernetics]. 2000, I. 4, pp. 30–35.

5. Zamaj S.S., Jakubajlik O.J. Modeli ocenki i prognoza zagrjaznenija atmosfery promyshlennymi vybrosami v informacionno-analiticheskoj sisteme prirodoohrannyh sluzhb krupnogo goroda [Models of assessment and forecast atmospheric pollution by industrial emissions in the information-analytical system of environmental services of large kind]. Krasnojarsk, Krasnojarskij gos. un-t Publ., 1998. 109 p.

6. Zedgenidze, I.G. Planirovanie jeksperimenta dlja issledovanija mnogokomponentnyh sistem [Experimental Design for the study of multicomponent systems]. Moscow, Nauka Publ. 1976. 390 p.

7. Karpenko A.P. Sovremennye algoritmy poiskovoj optimizacii. Algoritmy, vdohnovlennye prirodoj [Modern search optimi- zation algorithms. Algorithms inspired by nature]. Moscow, MGTU im. N. Je. Baumana Publ. 2014. 446 p.

8. Klejmenova I.E. Optimizacija razmeshhenija ob#ektov neftegazovogo kompleksa v razlichnyh geojekologicheskih uslovijah [Optimizing the placement of oil and gas complex in the various geoecological conditions]. Bezopasnost` v tehnosfere [Safety in Technosphere]. 2012, V. 1, I. 4, pp. 30–34.

9. Malyshev V.V. Metody optimizacii v zadachah sistemnogo analiza i upravleniya. [Optimization Methods in problems of system analysis and management]. Moscow, MAI Publ., 2010. 44 p.

10. Nathina R.I. Modelirovanie processov rasprostraneniya mnogokomponentny`h promyshlenny`h vy`brosov [Modeling of the propagation of multicomponent industrial emissions]. Moscow, Nauka Publ., 2001. 234 p.

11. Panteleev A.V., Metlickaja D.V., Aleshina E.A. Metody` global'noj optimizacii. Metae`vristicheskie strategii i algoritmy`. [Methods of global optimization. Metaheuristic strategies and algorithms]. Moscow, Vuzovskaja kniga Publ. 2013. 244 p.

12. Petrova T.M. Razrabotka matematicheskoj modeli funkcionirovanija sistemy nabljudenija, kontrolja i regulirovanija zagrjaznenija atmosfery. Kand. Diss. [Development of a mathematical model of the functioning of the monitoring system, monitoring and control of air pollution. Cand. Diss.]. Volgograd, 1997. 115 p.

13. Samarskij A.A. Vvedenie v chislennye metody [Introduction to Numerical Methods]. St. Petersburg, Lan Publ. 2009. 288 p.

14. Skorohodov A.A. Chislennaja model' optimizacii rezhima raboty zagrjaznjajushhih atmosferu proizvodstv [Numerical model optimization mode polluting industries]. Chislennoe modelirovanie dlya zadach dinamiki atmosfery i ohrany okruzhajushhej sredy` [Numerical simulation for the problems of the dynamics of the atmosphere and the environment]. Novosibirsk, 1989. pp. 4–19.

15. Fedosov V.V., Fedosova A.V. Optimizaciya v sisteme gruppovy` h vy`brosov-zaborov zagryaznenij dlya proizvodstvennoj ploshhadki (territorii) [Optimization of group emissions system-fences for pollution production site]. Programmnaya inzheneriya [Software Engineering]. 2014, I. 4, pp. 19–25.

16. Bhattacharjee B., Lemonidis P., Green W.H., Barton P.I. Global solution of semi-infinite programs. Mathematical Programming. 2005, Vol. 103, pp. 283–307.

17. Goberna Miguel A., Uckmann Jan J.R. Semi-Infinite Programming. Kluwer Academic Publishers. 2011. 428 p.

18. Fang, F., Zhang, T., Pavlidis, D., Pain, C. C, Buchan, A. G., Navon, I. M. Reduced order modelling of an unstructured mesh air pollution model and application in 2D/3D urban street canyons. ELSEVIER. Atmospheric Environment. 2014, Vol. 96, pp. 96–106.

19. Fedosov V.V., Fedosova A.V. Semi-Infinite Optimization Algorithms for the Simulation of Industrial Ecology. Ciencia etecnica. Vitivinicola Journal. Lisboa, Portugal. 2015, Vol. 30, N. 3, pp.195–216.

20. Fedossova A., Kafarov V., Mahecha Bohórquez D.P. Solucion Numerica del Problema de Control de Contaminacion del Aire. Colombian Journal of Computation (RCC). 2003, Vol. 4, N. 2, pp. 21–28.

21. Nelder J. A., Mead R. A simplex method for function minimization. The Computer Journal. Oxford University Press. 1965, Vol. 7, N. 4, pp. 308–313.

22. Semi-infinite Programming. Edited by R.Reemtsen and J.-J. Ruckmann. Nonconvex Optimization and Its Applications. Kluwer Academic Publish-Ers. Boston/Dordrecht/London. 1998, Vol. 25. 413 p.

23. Spendley W., Hext G.R., Himsworth F.R. Sequential applications of simplex de-signs in optimization and evolutionary operation. Technometrics. 1962, No. 4, pp. 441–461.

24. Stein O. How to Solve a Semi-infinite Optimization Problem. Institute of Operations Research, Karlsruhe Institute of Technology (KIT). Germany. 2012, March 27. 30 p.

25. Vaz A. Ismael F., Ferreira E.C. Air pollution control with semi-infinite programming. Applied Mathematical Modelling. ELSEVIER. 2009, N 33, pp. 1957–1969.

26. Volkov Y.V., Zavriev S.K. A General Stochastic Outer Approximation Methods. SIAM Journal on Control and Optimization. 1997, Vol. 35, pp. 1387–1421.

Login or Create
* Forgot password?