Оптимальное позиционирование источников выбросов загрязнений в задачах промышленной экологии

Abstract

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.