Lino J. Alvarez-Vázquez

Numerical Optimization for the Location of Wastewater Outfalls

In this paper we solve a constrained optimal control problem related to the location of the wastewater outfalls in a sewage disposal system. This is a problem where the control is the position and the constraints are non-convex and pointwise, which makes difficult its resolution. We discretize the problem by means of a characteristics-Galerkin method and we use three algorithms for the numerical resolution of the discretized optimization problem: an interior point algorithm, the Nelder-Mead simplex method and a duality method. Finally, we compare the numerical results obtained by applying the described methods for a realistic problem posed in the ría of Vigo (Galicia, Spain).

Multi-objective Pareto-optimal control: an application to wastewater management

This work treats, within a multi-objective framework, of an economical-ecological problem related to the optimal management of a wastewater treatment system consisting of several purifying plants. The problem is formulated as a multi-objective parabolic optimal control problem and it is studied from a cooperative point of view, looking for Pareto-optimal solutions. The weighting method is used here to characterize the Pareto solutions of our problem. To obtain them, a numerical algorithm—based in a characteristics-Galerkin discretization—is proposed and numerical results for a real world situation in the estuary of Vigo (NW Spain) are also presented.

Optimization methods for optimal transmitter locations in a mobile wireless system

A combination of a simple indoor propagation model with different optimization methods enables optimal single and multiple transmitter locations and antenna sectorization in wireless systems.

Optimal location of sampling points for river pollution control

Common methods of controlling river pollution include establishing water pollution monitoring stations located along the length of the river. The point where each station is located (sampling point) is of crucial importance and, obviously, depends on the reasons for the sample. Collecting data about pollution at selected points along the river is not the only objective; must also be extrapolated to know the characteristics of the pollution in the entire river. In this work we will deal with the optimal location of sampling points. A mathematical formulation for this problem as well as an efficient algorithm to solve it will be given. Finally, in last sections, we will present numerical results obtained by using this algorithm when applied to a realistic situation in a river mouth.

Numerical convergence for a sewage disposal problem

Abstract The management of sewage disposal and the design of wastewater treatment systems can be formulated as a constrained pointwise optimal control problem. In this paper we study the convergence of the numerical resolution for the corresponding state system by means of a characteristics Galerkin method. The main difficulty of the problem is due to the existence of Radon measures in the right-hand side of the state system. Finally, we present numerical results for a realistic problem posed in a r i a of Galicia, Spain.

THE WATER CONVEYANCE PROBLEM: OPTIMAL PURIFICATION OF POLLUTED WATERS

In this work we deal with the optimal purification of polluted areas of shallow waters by means of the injection of clear water in order to promote seawater exchange. This problem can be formulated as a control constrained optimal control problem where the control is the velocity of the injected water, the state equations are the shallow water equations together with that modelling the contaminant concentration, and the cost function measures the total amount of injected water and the fulfilment of the water quality standards. We analyze the solutions of the optimal control problem and give an optimality condition in order to characterize them. We also discretize the problem by means of a characteristics-mixed finite element method, focusing our attention on both the discrete and the discretized adjoint systems, and propose an algorithm for the numerical resolution of the discrete optimization problem. Finally, we present numerical results for some computational experiments.

On optimal location and management of a new industrial plant: Numerical simulation and control☆

Abstract Within the framework of numerical modelling and multi-objective control of partial differential equations, in this work we deal with the problem of determining the optimal location of a new industrial plant. We take into account both economic and ecological objectives, and we look not only for the optimal location of the plant but also for the optimal management of its emissions rate. In order to do this, we introduce a mathematical model (a system of nonlinear parabolic partial differential equations) for the numerical simulation of air pollution. Based on this model, we formulate the problem in the field of multi-objective optimal control from a cooperative viewpoint, recalling the standard concept of Pareto-optimal solution, and pointing out the usefulness of Pareto-optimal frontier in the decision making process. Finally, a numerical algorithm – based on a characteristics/Galerkin discretization of the adjoint model – is proposed, and some numerical results for a hypothetical situation in the region of Galicia (NW Spain) are presented.

Asymptotic justification of an evolution linear thermoelastic model for rods

Abstract The justification of a dynamic thermoelastic model for a linearized beam is presented using asymptotic analysis methods. We prove that the three-dimensional thermoelastic model converges weakly to a limit model introduced here and we deduce a compatibility condition in order to obtain strong convergence.

Optimal location of green zones in metropolitan areas to control the urban heat island

In this paper we analyze and numerically solve a problem related to the optimal location of green zones in metropolitan areas in order to mitigate the urban heat island effect. So, we consider a microscale climate model and analyze the problem within the framework of optimal control theory of partial differential equations. Finally we compute its numerical solution using the finite element method, with the help of the interior point algorithm IPOPT, interfaced with the FreeFem++ software package.

Optimal Management of a Bioreactor for Eutrophicated Water Treatment: A Numerical Approach

This paper presents a numerical algorithm for computing the optimal design variables in the management of a bioreactor for the treatment of eutrophicated water: initial and distributed quantities of phytoplankton added along the process, and total duration of the process. This real-world problem is formulated as a state-control constrained optimal control problem, whose numerical resolution is the main aim of this study. After discretizing the control problem, we present a structured algorithm for solving the discrete state systems, computing the corresponding derivatives, and minimizing the objective function. Finally, the good performance of the algorithm is shown by applying it to a realistic example with two pre-reservoirs.