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Method for Calculating the Air Pollution Emission Quotas

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1476))

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Abstract

The main purpose of quotas is to limit emissions for facilities that have a negative impact on the environment. When calculating emission quotas, it is necessary to solve a nonlinear programming problem with a nonlinear objective function and linear constraints. Variables of the problem are emission reduction coefficients for objects that have a negative impact on the environment. Constraints of the problem are determined by the admissibility of the emission contributions from objects to the concentration of pollutants in the air at the locations of quotas. As a rule, the number of constraints of this problem is significantly less than the number of variables (the problem can include up to 10,000 variables and 1,000 linear constraints). In this regard, it seems relevant to use the theory of duality for the purposes of substantive analysis and simplification of computational methods for problem solving.

We suggest the transition from primal to dual nonlinear programming. As a result, we gain a nonsmooth problem of unconstrained minimization of a much smaller order, and the solution can be obtained by effective subgradient minimization methods with an alteration in the space metric. We propose an effective method for solving the problem of emission quotas to be determined, and confirm its efficiency by a computational experiment on both test and applied data. The explicit form of the dependence of primal and dual variables is useful for the analysis of the solution and the selection of the object priority parameters by an expert.

Supported by the Ministry of Science and Higher Education of the Russian Federation (Project FEFE-2020-0013).

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Author information

Authors and Affiliations

  1. Kemerovo State University, 6 Krasnaya Street, Kemerovo, 650043, Russia

    Vladimir Krutikov

  2. Institute of Computational Technologies SB RAS, 21 Rukavishnikov Street, Kemerovo, 650025, Russia

    Anatoly Bykov

  3. Reshetnev Siberian State University of Science and Technology, prosp. Krasnoyarskiy Rabochiy 31, Krasnoyarsk, 660031, Russia

    Elena Tovbis & Lev Kazakovtsev

  4. Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, 660041, Russia

    Lev Kazakovtsev

Authors
  1. Vladimir Krutikov
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  2. Anatoly Bykov
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  3. Elena Tovbis
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  4. Lev Kazakovtsev
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Corresponding author

Correspondence to Lev Kazakovtsev .

Editor information

Editors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander Strekalovsky

  2. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  3. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Tatiana Gruzdeva

  4. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Andrei Orlov

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Krutikov, V., Bykov, A., Tovbis, E., Kazakovtsev, L. (2021). Method for Calculating the Air Pollution Emission Quotas. In: Strekalovsky, A., Kochetov, Y., Gruzdeva, T., Orlov, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2021. Communications in Computer and Information Science, vol 1476. Springer, Cham. https://doi.org/10.1007/978-3-030-86433-0_24

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  • DOI: https://doi.org/10.1007/978-3-030-86433-0_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86432-3

  • Online ISBN: 978-3-030-86433-0

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