N. García-Chan

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.

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.

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.

Improving the environmental impact of wastewater discharges with a specific simulation-optimization software

Wastewater treatment has become one of the most important environmental problems, especially for the particular case of urban areas. In this work we use numerical simulation, and combine optimal control theory of partial differential equations with multi-objective optimization techniques to formulate and solve this type of problems. Specifically, the main objective of this paper is to detail the mathematical tools that we can use in order to assess in decision making related to determining the sewage depuration intensities in a wastewater treatment system. We show the usefulness of our techniques by solving a realistic problem posed in the estuary of Vigo (NW Spain) with the free software SOS, recently developed by the authors.

SOS: A numerical simulation toolbox for decision support related to wastewater discharges and their environmental impact

Abstract Multi-objective optimization combined with numerical simulation are useful tools for environmental sciences. Using these methods, the treatment and discharge of wastewater in large waterbodies (estuaries, rivers, lakes…) - one of the essential problems in environmental management - can be analyzed in order to avoid the usual controversy between economic and ecological interests. In this article we present a decision support software system referred to as Simulating Optimal Solutions (SOS). Software SOS is a Matlab toolbox (interfaced with Fortran codes for mathematical computation of hydrodynamics and contaminant dispersion) to assess in decision making related to treatment intensity in different purifying plants. The program allows a flexible analysis both from a cooperative viewpoint (Pareto optimality) and a non-cooperative one (Nash equilibria).

Optimal control in wastewater management: a multi-objective study

This work deals with the management of a sewage treatment system consisting of several purifying plants discharging treated sewage into the same region, for instance, an estuary or a lake. The management of this system involves economical aspects (given by the treatment cost in the plants) and also environmental aspects (related to water quality in the sensitive areas of the region). By assuming a unique manager for all plants, the problem is formulated as a multi-objective parabolic optimal control problem, and it is studied from a cooperative viewpoint. Pareto-optimal solutions are completely characterized, a numerical algorithm to obtain the Pareto-optimal set is proposed and, finally, numerical experiences in the estuary of Vigo (NW Spain) are presented.

Numerical simulation of air pollution due to traffic flow in urban networks

Abstract As it is well known, traffic flow is the main pollution source in many urban areas, where the number of vehicles ranges from many thousands to millions. Thus, estimating the pollution emission rate due to traffic flow in big cities is a very hard task. To approach this environmental issue, in this paper we propose a methodology that consists of combining the 1D Lighthill–Whitham–Richards traffic model for road networks with a classical 2D advection–diffusion–reaction pollution model for the atmosphere. Here, the pollution model uses a source term that takes into account the traffic flow contamination by means of a Radon measure supported on a road network within an urban domain. Furthermore, we establish the existence of solution of the coupled model, and detail a complete numerical algorithm to compute it (mainly, interfacing a finite volume scheme based on the supply–demand method for the traffic model, with a characteristics-Lagrange finite element method for the pollution model). Finally, several numerical experiences for a real urban domain (the Guadalajara Metropolitan Area in Mexico) are presented.

An application of interactive multi-criteria optimization to air pollution control

In this paper a problem of air pollution control is studied, posing it as a multi-objective control problem of partial differential equations. The original problem, dealing with the optimal management of a set of industrial plants inside a populated area, is formulated by means of the diffusion transport equation, including a linear reaction term and source terms modelled by Dirac deltas. Introducing adjoint state techniques, the problem transforms into a problem of multi-objective optimization in Banach spaces, where the large number of objective functions discourages the complete search of its Pareto front. Therefore, in order to solve the problem, two interactive methods of multi-objective programming are proposed: the VIA and the STEM algorithms. Finally, the paper illustrates how to combine both algorithms to solve in a more effective way a realistic problem posed in the Metropolitan Area of Guadalajara (Mexico).

Stackelberg strategies for wastewater management

Management of wastewater has become a critical environmental problem during past decades, specially for the particular case of urban areas. In this work we use numerical simulation, and combine optimal control theory of partial differential equations with multi-objective optimization techniques to formulate and solve this type of problems from a new original hierarchical viewpoint with a leader and a follower (Stackelberg strategies). Specifically, the main aim of this paper deals with applying these Stackelberg techniques to the environmental problem related to determining the optimal location and the optimal purification profile when building a new treatment plant in a wastewater depuration system. We analyze the control problem, introduce a numerical algorithm, and show the possibilities of our approach by solving a realistic problem posed in the Estuary of Vigo (NW Spain).

Numerical Simulation for Evaluating the Effect of Traffic Restrictions on Urban Air Pollution

Traffic flow is the main pollution source in many urban areas, so when the pollutant concentration is above the permitted level, a common public policy consists of restricting the vehicular traffic. However, this restriction presents a negative impact on the economic activities and the inhabitants mobility. For these reasons different sectors question its efficiency arguing that the pollution reduction is due to wind changes and not to a lower vehicular traffic. In this work we estimate the pollution emission rate and pollutant concentration with a novel methodology that consists of combining the 1D Lighthill-Whitham-Richards (LWR) traffic model for road networks with a 2D advection-diffusion-reaction model for air pollution. This allows us to verify the efficiency of restrictions on vehicular traffic in the framework of numerical simulations in a real urban domain: the Guadalajara Metropolitan Area in Mexico.