Search results for " optimization"

Water distribution network robust design based on energy surplus index maximization

2015

The aim of this paper is to show that energy surplus indices, such as resilience index, besides providing a very good indirect measure of water distribution network reliability to be adopted during the design phase, represent also a valuable and effective indicator of the robustness of the network in alternative network scenarios, and can thus be profitably used in condition of future demands uncertainty. The methodology adopted consisted of (I) multi-objective design optimization performed in order to minimize construction costs while maximizing the resilience index; (II) retrospective performance assessment of the alternative solutions of the Pareto front obtained, under demand conditions…

Determination of Optimum Prices in the Commercial Distribution Sector in Spain: Application of an Asymetrical Competition Approach

2011

Teniendo en cuenta la importancia que adquieren las decisiones de precios en la distribución comercial minorista, en este trabajo se propone un modelo de decisión de precios óptimos en el que, a corto plazo, los efectos de los precios óptimos sobre la demanda y los márgenes del distribuidor maximizan la rentabilidad global de la categoría de productos. Tres aspectos fundamentales permiten describir esta propuesta: 1) se basa en una perspectiva agregada; 2) incorpora modelos de cuota de mercado con consistencia lógica -con el fin de aportar mayor robustez a la medición de la demanda- y 3) incluye el papel de la estructura competitiva mediante una modelización explícita de los efectos asimétr…

Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

2017

Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive …

Interactive methods for multiobjective robust optimization

2018

Practical optimization problems usually have multiple objectives, and they also involve uncertainty from different sources. Various robustness concepts have been proposed to handle multiple objectives and the involved uncertainty simultaneously. However, the practical applicability of the proposed concepts in decision making has not been widely studied in the literature. Developing solution methods to support a decision maker to find a most preferred robust solution is an even more rarely studied topic. Thus, we focus on two goals in this thesis including 1) analyzing the practical applicability of different robustness concepts in decision making and 2) developing interactive methods for sup…

Quantitative Approximation Properties for the Fractional Heat Equation

2017

In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…

The fractional Calderón problem: Low regularity and stability

2017

The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argumen…

Multi-marginal entropy-transport with repulsive cost

2020

In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.

Refined instability estimates for some inverse problems

2022

Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache [29]. In this work, based on Mandache's idea, we refine the instability estimates for two inverse problems, including the inverse inclusion problem and the inverse scattering problem. Our aim is to derive explicitly the dependence of the instability estimates on key parameters. The first result of this work is to show how the instability depends on the depth of the hidden inclusion and the conductivity of the background medium. This work can be regarded as a counterpart of the depth-dependent and conductivity-dependent stability estim…

Shape optimization utilizing consistent sensitivities

2010

Multi-objective parameter identification via ACOR algorithm

2009

The spreading of advanced constituive models, needed to model complex phenomena, makes necessary to solve difficult parameter identification problems. The need of multiple tests to fully characterize the experimental behaviour makes the parameter identification problem a multi objective one. Unlike conventional techniques, based on the formulation of an aggregate scalar ob- jective function, in the present work the problem is addressed using a new multi objective algorithm obtained extending the continuous Ant Colony Optimization algorithm. Mathematical tests and ap- plication to a real world problem are performed and different performance measures are used to asses the performance of the a…