Outer approximation algorithms to solve semi-infinite environmental pollution problems

Introduction- The traditional approaches of managing the integral estimation of a general function do no solve the problem of fulfilling the constraints in each point of the domain. This is achieved through a semi-infinite formulation of the problem, in which there are great possibilities in modeling many practical situations of industrial ecology. Some of them are presented in this paper. Objective- Based on detailed studies ([1]-[3]), the aim of this research paper is to examine the mentioned studies in order to contribute to disseminate SIP (Semi-Infinite Programming) applications in environmental pollution control. Methodology- With regard to the numerical solution a stochastic outer approximation algorithm was used, in addition numerical experiments were performed in MATLAB. Results- The obtained results of this work have showed three patterns, the first one enhances the power of emitting pollution sources, taking into account the area landscape, the second one also enhances the power of pollution sources using wind displacement of emissions, finally the third pattern operates by improving the pollution of 3D areas between a group of emission sources and purifiers. Conclusions- In conclusion, it can be said that the issue of power from emitting pollution sources, by considering the area landscape and wind displacement of emissions, should be modeled such as a semi-infinite programming trouble. The method used to calculate the algorithm stopping criterion, does not interpret this solution as an additional problem.