APPLICATIONS OF ACCELERATED OPTIMIZATION MODELS IN SOLVING THE WATER POLUTION PROBLEM
Keywords:
accelerated gradient method, line search, convergence rate, unconstrained optimizationAbstract
Human impacts on the living environment, habitats, land use and natural resource cause many
environmental issues (air pollution, biodiversity, climate change, energy, global warming, water pollution, etc.).
Among them, in this paper we chose the water resources planning as a general goal problem that we attempt to solve
using some chosen optimization models. Taking all needed parameters that define the measure of pollution, we
apply efficient accelerated gradient method and its hybrid version as a tool to solve the goal problem. The chosen
applicative methods are the transformed accelerated double step-size method (TADSS) and the hybrid TADSS, (i.e.
HTADSS) scheme. Good convergence and numerical properties of both models are confirmed in relevant papers.
The search directions of chosen methods are of the gradient descent form. With that, the iterative step lengths
parameters of the applicative methods are derived using the adequate Backtracking line search algorithms. In both of
these models we also use the initial improvement of the inexact line search procedure which additionally upgrades
the performance characteristics of the applied model. Finally, the relevant accelerated parameters of chosen models
are derived using the features of the second order Taylor’s expansions that are taken on the objective iterative rules.
The hybrid applicative method, HTADSS model, is defined using the Khan’s hybridization three-term principle.
Several contemporary researches show that from this hybrid rule at least eight efficient minimalization methods are
developed. Numerical comparations, taken on a large-scale test functions with application of the Dolan-Moré
benchmarking optimization software, confirmed that Khan’s hybrid approach is justified to use as a way of
improving the objective accelerated gradient minimization method. The both applicative optimization models, are
confirmedly efficient regarding usually analyzed performance metrics: the number of iterations, the CPU time and
the number of function evaluations. Proven good convergence and performance features, the efficiency, as well as,
the robustness of the objective minimization scheme were the guiding criteria in choosing the applicative
optimization methods for generating the relevant solver-models for the posed water resources planning problem.
Proposed idea of application of the TADSS and the HTADSS optimization models for solving water resources
planning problem can be used similarly for solving some other environmental issues mentioned above.
Furthermore, this approach is applicative on various methods of different optimization classes. Further researches
concerning this theme might consider studying of the appropriately chosen type of optimization method as an
adequate application for solving a certain environmental issue.
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