A Mathematical Programming-Based Approach for Architecture Selection

2012 ◽  
Author(s):  
Aleksandr A. Kerzhner ◽  
Christiaan J. J. Paredis
Keyword(s):  
Mathematical Programming ◽  
Optimization Technique ◽  
Problem Formulation ◽  
Mixed Integer ◽  
Model Transformations ◽  
Continuous Variables ◽  
Solution Approach ◽  
Computational Support ◽  
Algebraic Constraints ◽  
Selection Of

Modern systems are difficult to design because there are a significant number of potential alternatives to consider. The specification of an alternative includes an architecture (which describes the components and connections of the system) and component sizings (the sizing parameter for each component). In current practice, designers rely mainly on their experience and intuition to select a desired architecture without much computational support and then spend most of their effort on optimizing component sizings. In this paper, an approach for representing an architecture selection as a mixed-integer linear programming optimization is presented; existing solvers are then used to identify promising candidate architectures at early stages of the design process. Mathematical programming is a common optimization technique, but it is rarely used for architecture selection because of the difficulty of manually formulating an architecture selection as a mathematical program. In this paper, the formulation is presented in a modular fashion so that model transformations can be applied to transform a problem formulation that is convenient for designers into the mathematical programming optimization. A modular superstructure representation is used to model the design space; in a superstructure a union of all potential architectures is represented as a set of discrete and continuous variables. Algebraic constraints are added to describe both acceptable variable combinations and system behavior to allow the solver to eliminate clearly poor alternatives and identify promising alternatives. The framework is demonstrated on the selection of an actuation subsystem for a hydraulic excavator, although the solution approach would be similar for most mechanical systems.

scholarly journals MIPaaL: Mixed Integer Program as a Layer

2020 ◽  
Vol 34 (02) ◽  
pp. 1504-1511 ◽  
Author(s):  
Aaron Ferber ◽  
Bryan Wilder ◽  
Bistra Dilkina ◽  
Milind Tambe
Keyword(s):  
Broad Class ◽  
Linear Constraints ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Linear Programs ◽  
Continuous Variables ◽  
Two Phase ◽  
Mixed Integer Linear Program ◽  
Submodular Optimization ◽  
Solution Approach

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures average accuracy between predicted values and ground truth values. Decision-focused learning explicitly integrates the downstream decision problem when training the predictive model, in order to optimize the quality of decisions induced by the predictions. It has been successfully applied to several limited combinatorial problem classes, such as those that can be expressed as linear programs (LP), and submodular optimization. However, these previous applications have uniformly focused on problems with simple constraints. Here, we enable decision-focused learning for the broad class of problems that can be encoded as a mixed integer linear program (MIP), hence supporting arbitrary linear constraints over discrete and continuous variables. We show how to differentiate through a MIP by employing a cutting planes solution approach, an algorithm that iteratively tightens the continuous relaxation by adding constraints removing fractional solutions. We evaluate our new end-to-end approach on several real world domains and show that it outperforms the standard two phase approaches that treat prediction and optimization separately, as well as a baseline approach of simply applying decision-focused learning to the LP relaxation of the MIP. Lastly, we demonstrate generalization performance in several transfer learning tasks.

Optimal Toll Design in Second-Best Link-Based Congestion Pricing

2003 ◽  
Vol 1857 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Hai Yang ◽  
Xiaoning Zhang
Keyword(s):  
Cost Minimization ◽  
Real Life ◽  
Research Area ◽  
User Equilibrium ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Second Best ◽  
Pricing Scheme ◽  
General Network ◽  
Selection Of

In the traffic assignment literature, it is well known that a marginal-cost toll is charged on each link to drive a user equilibrium flow pattern toward a system optimum in a general network. Although this principle is theoretically reasonable, it is not practically appealing for many reasons. In real life, a second-best pricing scheme is more attractive, where only a subset of links is subject to toll charge. Previously most studies in the research area of second-best pricing concern the determination of optimal toll levels on predetermined toll links, whereas very little attention has been devoted to the selection of toll locations. The second-best link-based pricing scheme that involves optimal selection of both toll levels and toll locations is described here. Travel cost minimization or social welfare maximization with and without inclusion of the implementation cost of the toll charge is sought in general networks. Optimization models with mixed (integer and continuous) variables are formulated for determining toll levels and toll locations simultaneously. A binary genetic algorithm is used to search optimal toll locations dynamically and a simulated annealing method is used to search optimal toll levels.

Generative Adversarial Networks (GANs)

2021 ◽  
Vol 54 (3) ◽  
pp. 1-42
Author(s):  
Divya Saxena ◽  
Jiannong Cao
Keyword(s):  
Optimization Technique ◽  
Generative Models ◽  
Generative Adversarial Networks ◽  
Network Architectures ◽  
Research Directions ◽  
Research Issues ◽  
Design And Optimization ◽  
Adversarial Networks ◽  
Comprehensive Survey ◽  
Selection Of

Generative Adversarial Networks (GANs) is a novel class of deep generative models that has recently gained significant attention. GANs learn complex and high-dimensional distributions implicitly over images, audio, and data. However, there exist major challenges in training of GANs, i.e., mode collapse, non-convergence, and instability, due to inappropriate design of network architectre, use of objective function, and selection of optimization algorithm. Recently, to address these challenges, several solutions for better design and optimization of GANs have been investigated based on techniques of re-engineered network architectures, new objective functions, and alternative optimization algorithms. To the best of our knowledge, there is no existing survey that has particularly focused on the broad and systematic developments of these solutions. In this study, we perform a comprehensive survey of the advancements in GANs design and optimization solutions proposed to handle GANs challenges. We first identify key research issues within each design and optimization technique and then propose a new taxonomy to structure solutions by key research issues. In accordance with the taxonomy, we provide a detailed discussion on different GANs variants proposed within each solution and their relationships. Finally, based on the insights gained, we present promising research directions in this rapidly growing field.

scholarly journals Optimising the selection of food items for FFQs using Mixed Integer Linear Programming

2014 ◽  
Vol 18 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Johanna C Gerdessen ◽  
Olga W Souverein ◽  
Pieter van ‘t Veer ◽  
Jeanne HM de Vries
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Selection Process ◽  
Saturated Fat ◽  
Mixed Integer ◽  
Monounsaturated Fat ◽  
Food Items ◽  
Milp Model ◽  
Selection Of

AbstractObjectiveTo support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible.DesignSelection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium.ResultsThe food lists generated by the MILP model have good performance in terms of length, coverage and R2 (explained variance) of all nutrients. MILP-generated food lists were 32–40 % shorter than a benchmark food list, whereas their quality in terms of R2 was similar to that of the benchmark.ConclusionsThe results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

1993 ◽  
Author(s):  
B. K. Kannan ◽  
Steven N. Kramer
Keyword(s):  
Lagrange Multiplier ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Augmented Lagrange Multiplier

Abstract An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

Computerized Selection of Optimum Machining Conditions for a Job Requiring Multiple Operations

1978 ◽  
Vol 100 (3) ◽  
pp. 356-362 ◽  
Author(s):  
S. S. Rao ◽  
S. K. Hati
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Machine Tools ◽  
Machining Conditions ◽  
Coupling Constraints ◽  
Programming Techniques ◽  
Mathematical Programming Problems ◽  
The Individual ◽  
The Cost ◽  
Selection Of

The problem of determining the optimum machining conditions for a job requiring multiple operations has been investigated. Three objectives, namely, the minimization of the cost of production per piece, the maximization of the production rate and, the maximization of the profit are considered in this work. In addition to the usual constraints that arise from the individual machine tools, some coupling constraints have been included in the formulation. The problems are formulated as standard mathematical programming problems, and nonlinear programming techniques are used to solve the problems.

scholarly journals Can benchmarking Australian hospitals for quality identify and improve high and low performers? Disseminating research findings for hospitals

2020 ◽  
Vol 32 (Supplement_1) ◽  
pp. 84-88 ◽  
Author(s):  
Peter Hibbert ◽  
Faisal Saeed ◽  
Natalie Taylor ◽  
Robyn Clay-Williams ◽  
Teresa Winata ◽  
...  
Keyword(s):  
Quality Improvement ◽  
Health Services Research ◽  
Large Scale ◽  
Logic Model ◽  
Continuous Variables ◽  
Services Research ◽  
High Performer ◽  
Research Findings ◽  
Multiple Domains ◽  
Selection Of

Abstract This paper examines the principles of benchmarking in healthcare and how benchmarking can contribute to practice improvement and improved health outcomes for patients. It uses the Deepening our Understanding of Quality in Australia (DUQuA) study published in this Supplement and DUQuA’s predecessor in Europe, the Deepening our Understanding of Quality improvement in Europe (DUQuE) study, as models. Benchmarking is where the performances of institutions or individuals are compared using agreed indicators or standards. The rationale for benchmarking is that institutions will respond positively to being identified as a low outlier or desire to be or stay as a high performer, or both, and patients will be empowered to make choices to seek care at institutions that are high performers. Benchmarking often begins with a conceptual framework that is based on a logic model. Such a framework can drive the selection of indicators to measure performance, rather than their selection being based on what is easy to measure. A Donabedian range of indicators can be chosen, including structure, process and outcomes, created around multiple domains or specialties. Indicators based on continuous variables allow organizations to understand where their performance is within a population, and their interdependencies and associations can be understood. Benchmarking should optimally target providers, in order to drive them towards improvement. The DUQuA and DUQuE studies both incorporated some of these principles into their design, thereby creating a model of how to incorporate robust benchmarking into large-scale health services research.

scholarly journals Estudio de la enseñanza de ecosistemas amazónicos a través de la metodología de aprendizaje basada en la resolución de problemas (ABRP)

2018 ◽  
Vol 22 ◽  
pp. 9
Author(s):  
Carlos Henrique Nascimento ◽  
Ires Paula de Andrade Miranda
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Primary School ◽  
School Environment ◽  
Problem Based Learning ◽  
Problem Formulation ◽  
Teaching Methodology ◽  
Second Phase ◽  
Two Phases ◽  
Selection Of

The purpose was to analyze the Problem-based learning (PBL) as a methodological alternative for primary school that favor learning about Amazonian ecosystems. This research is descriptive with a qualitative-quantitative approach. The study was carried out with students from the 9th year of primary school. The teaching methodology based on the PBL was applied in two phases: In the first phase, a test of previous conceptions was carried out in order to know the perception of the students on topics related to some units of landscapes of the Amazonian ecosystems. The second phase consisted of the implementation of the learning methodology in the school environment. Four different phases were established in the application: i) selection of topics; ii) problem formulation; iii) problem solving; iv) synthesis and evaluation. The data collection instruments used were: preconceptions test and skills chart. The results showed that after the application of the ABRP methodology, the cognitive recognition of the Amazonian ecosystems can be perceived in the students, reaching additional goals that the PCN establish.

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