scholarly journals Problem reduction, renormalization, and memory

2006 ◽  
Vol 1 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Alexandre Chorin ◽  
Panagiotis Stinis
Keyword(s):  
Problem Reduction

Formal Solution of N-Type Taguchi Parameter Design Problems With Stochastic Noise Factors

1991 ◽  
Author(s):  
Nestor F. Michelena ◽  
Alice M. Agogino
Keyword(s):  
Performance Characteristic ◽  
Degrees Of Freedom ◽  
Formal Solution ◽  
Parameter Design ◽  
Absolute Deviation ◽  
Design Problems ◽  
Problem Reduction ◽  
Stochastic Parameters ◽  
Noise Factors ◽  
Monotonicity Analysis

Abstract The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The obtained design is robust, i.e., the least sensitive to variations on uncontrollable factors (noise). The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven, despite the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be employed, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multi-parametric case must take into account the characteristics of the probability space on which the random parameters are defined.

Modifying Transactional Databases to Hide Sensitive Association Rules

2021 ◽  
Author(s):  
Syam Menon ◽  
Abhijeet Ghoshal ◽  
Sumit Sarkar
Keyword(s):  
Supply Chain ◽  
Association Rules ◽  
Association Rule ◽  
Sensitive Information ◽  
Data Set ◽  
Problem Reduction ◽  
Transactional Databases ◽  
Potential Risks ◽  
Integer Formulations ◽  
Number Of Firms

Although firms recognize the value in sharing data with supply chain partners, many remain reluctant to share for fear of sensitive information potentially making its way to competitors. Approaches that can help hide sensitive information could alleviate such concerns and increase the number of firms that are willing to share. Sensitive information in transactional databases often manifests itself in the form of association rules. The sensitive association rules can be concealed by altering transactions so that they remain hidden when the data are mined by the partner. The problem of hiding these rules in the data are computationally difficult (NP-hard), and extant approaches are all heuristic in nature. To our knowledge, this is the first paper that introduces the problem as a nonlinear integer formulation to hide the sensitive association rule while minimizing the alterations needed in the data set. We apply transformations that linearize the constraints and derive various results that help reduce the size of the problem to be solved. Our results show that although the nonlinear integer formulations are not practical, the linearizations and problem-reduction steps make a significant impact on solvability and solution time. This approach mitigates potential risks associated with sharing and should increase data sharing among supply chain partners.

scholarly journals A Problem-Reduction Evolutionary Algorithm for Solving the Capacitated Vehicle Routing Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Wanfeng Liu ◽  
Xia Li
Keyword(s):  
Evolutionary Algorithm ◽  
Vehicle Routing ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Solution Quality ◽  
Routing Problem ◽  
Individual Solution ◽  
Problem Reduction ◽  
Evaluation Phase ◽  
Capacitated Vehicle

Assessment of the components of a solution helps provide useful information for an optimization problem. This paper presents a new population-based problem-reduction evolutionary algorithm (PREA) based on the solution components assessment. An individual solution is regarded as being constructed by basic elements, and the concept of acceptability is introduced to evaluate them. The PREA consists of a searching phase and an evaluation phase. The acceptability of basic elements is calculated in the evaluation phase and passed to the searching phase. In the searching phase, for each individual solution, the original optimization problem is reduced to a new smaller-size problem. With the evolution of the algorithm, the number of common basic elements in the population increases until all individual solutions are exactly the same which is supposed to be the near-optimal solution of the optimization problem. The new algorithm is applied to a large variety of capacitated vehicle routing problems (CVRP) with customers up to nearly 500. Experimental results show that the proposed algorithm has the advantages of fast convergence and robustness in solution quality over the comparative algorithms.

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