scholarly journals Finding events in temporal networks: segmentation meets densest subgraph discovery

2019 ◽  
Vol 62 (4) ◽  
pp. 1611-1639
Author(s):  
Polina Rozenshtein ◽  
Francesco Bonchi ◽  
Aristides Gionis ◽  
Mauro Sozio ◽  
Nikolaj Tatti
Keyword(s):  
Optimization Problem ◽  
Approximate Dynamic Programming ◽  
Problem Formulation ◽  
Network Activity ◽  
Total Density ◽  
Temporal Networks ◽  
Time Intervals ◽  
Dense Subgraphs ◽  
Approximation Guarantee ◽  
Densest Subgraph

Abstract In this paper, we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality.

scholarly journals Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

2021 ◽  
Author(s):  
Johanna Schultes ◽  
Michael Stiglmayr ◽  
Kathrin Klamroth ◽  
Camilla Hahn
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Mechanical Stability ◽  
Adjoint Equation ◽  
Tensile Load ◽  
Problem Formulation ◽  
State Equation ◽  
Efficient Solutions ◽  
Volume Stability ◽  
Shape Optimization Problem

AbstractIn engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

scholarly journals Optimization-Based Formulations for Short-Circuit Studies with Inverter-Interfaced Generation in PowerModelsProtection.jl

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2160
Author(s):  
Arthur K. Barnes ◽  
Jose E. Tabarez ◽  
Adam Mate ◽  
Russell W. Bent
Keyword(s):  
Optimization Problem ◽  
Short Circuit ◽  
Problem Formulation ◽  
Power Delivery ◽  
Fault Current ◽  
Protective Device ◽  
Protective Relaying ◽  
Overcurrent Protection ◽  
Short Circuits ◽  
Optimization Problem Formulation

Protecting inverter-interfaced microgrids is challenging as conventional time-overcurrent protection becomes unusable due to the lack of fault current. There is a great need for novel protective relaying methods that enable the application of protection coordination on microgrids, thereby allowing for microgrids with larger areas and numbers of loads while not compromising reliable power delivery. Tools for modeling and analyzing such microgrids under fault conditions are necessary in order to help design such protective relaying and operate microgrids in a configuration that can be protected, though there is currently a lack of tools applicable to inverter-interfaced microgrids. This paper introduces the concept of applying an optimization problem formulation to the topic of inverter-interfaced microgrid fault modeling, and discusses how it can be employed both for simulating short-circuits and as a set of constraints for optimal microgrid operation to ensure protective device coordination.

Optimization Problem Formulation

2016 ◽  
pp. 47-61
Author(s):  
Javier Contreras ◽  
Miguel Asensio ◽  
Pilar Meneses de Quevedo ◽  
Gregorio Muñoz-Delgado ◽  
Sergio Montoya-Bueno
Keyword(s):  
Optimization Problem ◽  
Problem Formulation ◽  
Optimization Problem Formulation

Combined Analysis and Optimization of Extended Heat Transfer Surfaces

1985 ◽  
Vol 107 (3) ◽  
pp. 527-532 ◽  
Author(s):  
A. N. Hrymak ◽  
G. J. McRae ◽  
A. W. Westerberg
Keyword(s):  
Optimization Problem ◽  
Radiative Heat ◽  
Inequality Constraints ◽  
Finite Element Approximation ◽  
Problem Formulation ◽  
Element Approximation ◽  
Problem Solution ◽  
Radiative Heat Loss ◽  
Equality And Inequality Constraints ◽  
Grid Points

This study presents an efficient numerical method to discover the optimal shape for a fin subject to both convective and radiative heat loss. Problem formulation is a finite element approximation to the conduction equation embedded within and solved simultaneously with the shape optimization problem. The approach handles arbitrary equality and inequality constraints. Grid points move to conform to the fin shape during the problem solution, reducing the number of elements required in the solution.

Predictive Control of a Laboratory Time Delay Process Experiment

2013 ◽  
Vol 11 (1) ◽  
pp. 29-36
Author(s):  
S. Enev
Keyword(s):  
Time Delay ◽  
Predictive Control ◽  
Control Algorithm ◽  
Optimization Problem ◽  
Problem Formulation ◽  
Practical Implementation ◽  
Control Law ◽  
Design And Implementation ◽  
Optimization Problem Formulation ◽  
Laboratory Time

Abstract The paper presents the design and implementation of a Model Predictive Control (MPC) scheme of a laboratory heatexchange process with a significant time delay in the input-output path. The optimization problem formulation is given and an MPC control algorithm is designed, achieving integral properties. Details, related to the practical implementation of the control law are discussed and the first experimental results are presented.

A nonlinear optimization shooting method for bifurcation tracking of nonlinear systems

2020 ◽  
pp. 107754632095674
Author(s):  
Haitao Liao ◽  
Mengyu Li ◽  
Ruxin Gao
Keyword(s):  
Periodic Solution ◽  
Optimization Problem ◽  
Continuation Method ◽  
Problem Formulation ◽  
Correlation Equation ◽  
Jeffcott Rotor ◽  
Optimization Formulation ◽  
Bifurcation Detection ◽  
Tuned Vibration Absorber ◽  
Optimization Problem Formulation

A continuation method for bifurcation tracking is presented based on the proposed optimization problem formulation which is designed to locate the bifurcation periodic solution. The bifurcation detection problem is formulated as a constrained optimization problem. The nonlinear constraints of the optimization problem are imposed on the shooting function and bifurcation conditions derived from the Floquet theory whereas the objective function associated with the pseudo-arclength correlation equation is devised to solution continuation. The proposed optimization formulation is integrated with the prediction–correction strategy to achieve bifurcation tracking. Two numerical examples about the Jeffcott rotor and the nonlinear tuned vibration absorber are illustrated to validate the effectiveness of the proposed methodology. Numerical results have demonstrated that the proposed method offers a convenient scheme to follow bifurcation periodic solution.

scholarly journals Path Tracking Algorithms for Non-Convex Waiter Motion Problem

2018 ◽  
Vol 62 (1) ◽  
pp. 16-23
Author(s):  
Ákos Nagy ◽  
Gábor Csorvási ◽  
István Vajk
Keyword(s):  
Motion Planning ◽  
Optimization Problem ◽  
Minimum Energy ◽  
Real Life ◽  
Problem Formulation ◽  
Energy Planning ◽  
Special Area ◽  
Time Optimal ◽  
Motion Problem ◽  
Optimal Approach

Originally, motion planning was concerned with problems such as how to move an object from a start to a goal position without hitting anything. Later, it has extended with complications such as kinematics, dynamics, uncertainties, and also with some optimality purpose such as minimum-time, minimum-energy planning. The paper presents a time-optimal approach for robotic manipulators. A special area of motion planning is the waiter motion problem, in which a tablet is moved from one place to another as fastas possible, avoiding the slip of the object that is placed upon it. The presented method uses the direct transcription approach for the waiter problem, which means a optimization problem is formed in order to obtain a time-optimal control for the robot. Problem formulation is extended with a non-convex jerk constraints to avoid unwanted oscillations during the motion. The possible local and global solver approaches for the presented formulation are discussed, and the waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm.

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