Bilevel Linear Optimization Under Uncertainty

2020 ◽  
pp. 485-511
Author(s):  
Johanna Burtscheidt ◽  
Matthias Claus
Keyword(s):  
Linear Optimization ◽  
Optimization Under Uncertainty ◽  
Bilevel Linear Optimization

scholarly journals Pessimistic Bilevel Linear Optimization

2018 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
S. Dempe ◽  
G. Luo ◽  
S. Franke
Keyword(s):  
Optimization Problem ◽  
Value Function ◽  
Linear Optimization ◽  
Equivalent Transformation ◽  
Optimal Solutions ◽  
Linear Optimization Problem ◽  
Optimal Value ◽  
Nonconvex And Nonsmooth Optimization ◽  
Bilevel Linear Optimization ◽  
Nonsmooth Optimization Problem

In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.  

scholarly journals Improving Law Enforcement Daily Deployment Through Machine Learning-Informed Optimization under Uncertainty

2019 ◽  
Author(s):  
Jonathan Chase ◽  
Duc Thien Nguyen ◽  
Haiyang Sun ◽  
Hoong Chuin Lau
Keyword(s):  
Machine Learning ◽  
Law Enforcement ◽  
Real World ◽  
Response Times ◽  
Linear Optimization ◽  
Temporal Distribution ◽  
Sample Average Approximation ◽  
Optimization Under Uncertainty ◽  
Mixed Integer ◽  
Peace Of Mind

Urban law enforcement agencies are under great pressure to respond to emergency incidents effectively while operating within restricted budgets. Minutes saved on emergency response times can save lives and catch criminals, and a responsive police force can deter crime and bring peace of mind to citizens. To efficiently minimize the response times of a law enforcement agency operating in a dense urban environment with limited manpower, we consider in this paper the problem of optimizing the spatial and temporal deployment of law enforcement agents to predefined patrol regions in a real-world scenario informed by machine learning. To this end, we develop a mixed integer linear optimization formulation (MIP) to minimize the risk of failing response time targets. Given the stochasticity of the environment in terms of incident numbers, location, timing, and duration, we use Sample Average Approximation (SAA) to find a robust deployment plan. To overcome the sparsity of real data, samples are provided by an incident generator that learns the spatio-temporal distribution and demand parameters of incidents from a real world historical dataset and generates sets of training incidents accordingly. To improve runtime performance across multiple samples, we implement a heuristic based on Iterated Local Search (ILS), as the solution is intended to create deployment plans quickly on a daily basis. Experimental results demonstrate that ILS performs well against the integer model while offering substantial gains in execution time.

Optimal Test Assembly in Practice

2013 ◽  
Vol 221 (3) ◽  
pp. 190-200 ◽  
Author(s):  
Jörg-Tobias Kuhn ◽  
Thomas Kiefer
Keyword(s):  
Particle Physics ◽  
Large Scale ◽  
Block Design ◽  
Linear Optimization ◽  
Mixed Integer ◽  
Optimal Test ◽  
Automated Test Assembly ◽  
Test Assembly ◽  
Block Level ◽  
Mixed Integer Linear Optimization

Several techniques have been developed in recent years to generate optimal large-scale assessments (LSAs) of student achievement. These techniques often represent a blend of procedures from such diverse fields as experimental design, combinatorial optimization, particle physics, or neural networks. However, despite the theoretical advances in the field, there still exists a surprising scarcity of well-documented test designs in which all factors that have guided design decisions are explicitly and clearly communicated. This paper therefore has two goals. First, a brief summary of relevant key terms, as well as experimental designs and automated test assembly routines in LSA, is given. Second, conceptual and methodological steps in designing the assessment of the Austrian educational standards in mathematics are described in detail. The test design was generated using a two-step procedure, starting at the item block level and continuing at the item level. Initially, a partially balanced incomplete item block design was generated using simulated annealing, whereas in a second step, items were assigned to the item blocks using mixed-integer linear optimization in combination with a shadow-test approach.

Order Constrained Linear Optimization

2014 ◽  
Author(s):  
Joe W. Tidwell ◽  
Michael Dougherty ◽  
Rick P. Thomas ◽  
Jeffrey S. Chrabaszcz
Keyword(s):  
Linear Optimization

Nonlinear and Mixed-Integer Optimization

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Nonlinear Optimization ◽  
Systems Engineering ◽  
Chemical Engineering ◽  
Applied Mathematics ◽  
Linear Optimization ◽  
Mixed Integer ◽  
Process Synthesis ◽  
Synthesis Process ◽  
Integer Optimization ◽  
Mixed Integer Optimization

Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.

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