Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics

The second MFO Oberwolfach Workshop on Mixed-Integer Nonlinear Programming (MINLP) took place between 2nd and 8th June 2019. MINLP refers to one of the hardest Mathematical Programming (MP) problem classes, involving both nonlinear functions as well as continuous and integer decision variables. MP is a formal language for describing optimization problems, and is traditionally part of Operations Research (OR), which is itself at the intersection of mathematics, computer science, engineering and econometrics. The scientific program has covered the three announced areas (hierarchies of approximation, mixed-integer nonlinear optimal control, and dealing with uncertainties) with a variety of tutorials, talks, short research announcements, and a special "open problems'' session

Optimization of Critical Infrastructure with Fluids

Many of the world's most critical infrastructure systems control the motion of fluids. Despite their importance, the design, operation, and restoration of these infrastructures are sometimes carried out suboptimally. One reason for this is the intractability of optimization problems involving fluids, which are often constrained by partial differential equations or nonconvex physics. To address these challenges, this dissertation focuses on developing new mathematical programming and algorithmic techniques for optimization problems involving difficult nonlinear constraints that model a fluid's behavior. These new contributions bring many important problems within the realm of tractability. The first focus of this dissertation is on surface water systems. Specifically, we introduce the Optimal Flood Mitigation Problem, which optimizes the positioning of structural measures to protect critical assets with respect to a predefined flood scenario. Two solution approaches are then developed. The first leverages mathematical programming but does not tractably scale to realistic scenarios. The second uses a physics-inspired metaheuristic, which is found to compute good quality solutions for realistic scenarios. The second focus is on potable water distribution systems. Two foundational problems are considered. The first is the optimal water network design problem, for which we derive a novel convex reformulation, then develop an algorithm found to be more effective than the current state of the art on select instances. The second is the optimal pump scheduling (or Optimal Water Flow) problem, for which we develop a mathematical programming relaxation and various algorithmic techniques to improve convergence. The final focus is on natural gas pipeline systems. Two novel problems are considered. The first is the Maximal Load Delivery (MLD) problem for gas pipelines, which aims at finding a feasible steady-state operating point that maximizes load delivery for a severely damaged gas network. The second is the joint gas-power MLD problem, which couples damaged gas and power networks at gas-fired generators. In both problems, convex relaxations of nonconvex dynamical constraints are developed to increase tractability.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169849/1/tasseff_1.pd

Control of spatio-temporal pattern formation governed by geometrical models of interface evolution

Numerous natural phenomena are characterized by spatio-temporal dynamics which give rise to time evolving spatial patterns. Although studies that address the problem of modelling these complex dynamics exist, a model based control approach for such systems is still a challenging task. The work in this thesis is concerned with the development of control methods for such spatio-temporal systems, where interface growth is represented using a geometric evolution law. In particular, the focus is set on the control of dendritic crystal growth and wind-aided wildfire sprea

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Decision-Making for Search and Classification using Multiple Autonomous Vehicles over Large-Scale Domains

This dissertation focuses on real-time decision-making for large-scale domain search and object classification using Multiple Autonomous Vehicles (MAV). In recent years, MAV systems have attracted considerable attention and have been widely utilized. Of particular interest is their application to search and classification under limited sensory capabilities. Since search requires sensor mobility and classification requires a sensor to stay within the vicinity of an object, search and classification are two competing tasks. Therefore, there is a need to develop real-time sensor allocation decision-making strategies to guarantee task accomplishment. These decisions are especially crucial when the domain is much larger than the field-of-view of a sensor, or when the number of objects to be found and classified is much larger than that of available sensors. In this work, the search problem is formulated as a coverage control problem, which aims at collecting enough data at every point within the domain to construct an awareness map. The object classification problem seeks to satisfactorily categorize the property of each found object of interest. The decision-making strategies include both sensor allocation decisions and vehicle motion control. The awareness-, Bayesian-, and risk-based decision-making strategies are developed in sequence. The awareness-based approach is developed under a deterministic framework, while the latter two are developed under a probabilistic framework where uncertainty in sensor measurement is taken into account. The risk-based decision-making strategy also analyzes the effect of measurement cost. It is further extended to an integrated detection and estimation problem with applications in optimal sensor management. Simulation-based studies are performed to confirm the effectiveness of the proposed algorithms

Classe de Ciências

info:eu-repo/semantics/publishedVersio

Modeling of Soil Erosion and Sediment Transport

The Special Issue entitled “Modeling of Soil Erosion and Sediment Transport” focuses on the mathematical modeling of soil erosion caused by rainfall and runoff at a basin scale, as well as on the sediment transport in the streams of the basin. In concrete terms, the quantification of these phenomena by means of mathematical modeling and field measurements has been studied. The following mathematical models (software) were used, amongst others: AnnAGNPS, SWAT, SWAT-Twn, TUSLE, WRF-Hydro-Sed, CORINE, LCM-MUSLE, EROSION-3D, HEC-RAS, SRC, WA-ANN. The Special Issue contains 14 articles that can be classified into the following five categories: Category A: “Soil erosion and sediment transport modeling in basins”; Category B: “Inclusion of soil erosion control measures in soil erosion models”; Category C: “Soil erosion and sediment transport modeling in view of reservoir sedimentation”; Category D: “Field measurements of gully erosion”; Category E: “Stream sediment transport modeling”. Most studies presented in the Special Issue were applied to different basins in Europe, America, and Asia, and are the result of the cooperation between universities and/or research centers in different countries and continents, which constitutes an optimistic fact for the international scientific communication