With the trend of multiple energies or flexible demand in power systems,binary variables appear in systemwide constraints,which are the foundation of marginal pricing currently in *** appropriate pricing method incent...
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With the trend of multiple energies or flexible demand in power systems,binary variables appear in systemwide constraints,which are the foundation of marginal pricing currently in *** appropriate pricing method incentivizes compliance of market participants;otherwise,compliance can be incentivized by paying discriminatory uplift payments which jeopardize transparency of *** paper proposes two theorems to examine whether the binary variables brought by multiple energies and flexible demand will impact compliance under marginal *** first theorem shows sufficient conditions with which marginal pricing with fixed binary variables incentivizes compliance,while the second theorem shows sufficient conditions to require uplift *** improve transparency by reducing uplift payments under cases which fall into the second theorem,this paper further proposes a pricing method by combining 1)designed constraints to price binary variables in system-wide constraints,and 2)convex hull pricing to price binary variables in private *** of the proposed theorems and pricing method is verified in an electricity-gas case(consisting of the IEEE 30-bus system and the NGS 10-node system)and the IEEE 118-bus test system.
This note proposes the use of a tuple encoding scheme to reduce the number of binary variables involved in trajectory optimization problems with inter-sample avoidance constraints. Copyright (c) 2016 John Wiley & ...
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This note proposes the use of a tuple encoding scheme to reduce the number of binary variables involved in trajectory optimization problems with inter-sample avoidance constraints. Copyright (c) 2016 John Wiley & Sons, Ltd.
This study proposes a deterministic model to solve the two-dimensional cutting stock problem (2DCSP) using a much smaller number of binary variables and thereby reducing the complexity of 2DCSP. Expressing a 2DCSP wit...
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This study proposes a deterministic model to solve the two-dimensional cutting stock problem (2DCSP) using a much smaller number of binary variables and thereby reducing the complexity of 2DCSP. Expressing a 2DCSP with stocks and cutting rectangles requires binary variables in the traditional model. In contrast, the proposed model uses binary variables to express the 2DCSP. Experimental results showed that the proposed model is more efficient than the existing model.
This paper presents a MATLAB code with the implementation of the Topology Optimization of binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49-61,2018). The TOBS i...
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This paper presents a MATLAB code with the implementation of the Topology Optimization of binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49-61,2018). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest.
This paper studies the classical task assignment problem (TAP) in which M unbreakable tasks are assigned to N agents with the objective to minimize the communication and process costs subject to each agent's capac...
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This paper studies the classical task assignment problem (TAP) in which M unbreakable tasks are assigned to N agents with the objective to minimize the communication and process costs subject to each agent's capacity constraint. Because a large-size TAP involves many binary variables, most, if not all, traditional methods experience the difficulty in solving the problem within a reasonable time period. Recent works present a logarithmic approach to reduce the number of binary variables in problems with mixed-integer variables. This study proposes a new logarithmic method that significantly reduces the numbers of binary variables and inequality constraints in solving task assignment problems. Our numerical experiments demonstrate that the proposed method is superior to other known methods of this kind for solving large-size TAPs.
We consider the problem of updating beliefs for binary random variables, when probability assessments are elicited for them based on information of varying quality. We propose the threshold model, a Bayesian updating ...
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We consider the problem of updating beliefs for binary random variables, when probability assessments are elicited for them based on information of varying quality. We propose the threshold model, a Bayesian updating procedure where only measures of location and correlation have to be specified before any updating is possible. The main aspect of this model is the use of Jeffrey's conditionalization. According to this rule, it is not necessary to model the assessments and how they relate to the quantities of interest in a fully parametric way. This paper is motivated by the practical issue where a large company needs to manage its assets and future expenditure. (c) 2004 Elsevier B.V. All rights reserved.
In this paper, we introduce a nonparametric mathematical programming (MP) approach for solving the binary variable classification problem. In practice, there exists a substantial interest in the binary variable classi...
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In this paper, we introduce a nonparametric mathematical programming (MP) approach for solving the binary variable classification problem. In practice, there exists a substantial interest in the binary variable classification problem. For instance, medical diagnoses are often based on the presence or absence of relevant symptoms, and binary variable classification has long been used as a means to predict (diagnose) the nature of the medical condition of patients. Our research is motivated by the fact that none of the existing statistical methods for binary variable classification, parametric and nonparametric alike, are fully satisfactory. The general class of MP classification methods facilitates a geometric interpretation, and MP-based classification rules have intuitive appeal because of their potentially robust properties. These intuitive arguments appear to have merit, and a number of research studies have confirmed that MP methods can indeed yield effective classification rules under certain non-normal data conditions, for instance if the data set is outlier-contaminated or highly skewed. However, the MP-based approach in general lacks a probabilistic foundation, necessitating an ad hoc assessment of its classification performance. Our proposed nonparametric mixed integer programming (MIP) formulation for the binary variable classification problem not only has a geometric interpretation, but also is Bayes inspired. Therefore, our proposed formulation possesses a strong probabilistic foundation. We also introduce a linear programming (LP) formulation which parallels the concepts underlying the MIP formulation, but does not possess the decision theoretic justification. An additional advantage of both our LP and MIP formulations is that, due to the fact that the attribute variables are binary, the training sample observations can be partitioned into multinomial cells, allowing for a substantial reduction in the number of binary and deviational variables, so that
In attempting to represent a multivariable system by a simpler one with only binary variables it is not always possible to achieve the required correlations. This paper explores the extra constraints on the pairwise c...
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In attempting to represent a multivariable system by a simpler one with only binary variables it is not always possible to achieve the required correlations. This paper explores the extra constraints on the pairwise correlations for two and three variables. For correlation specifications meeting the required inequalities, expressions are given for construction of a suitable probability model.
This article discusses measurement of socioeconomic inequalities in the prevalence of a health condition, in response to the recent exchange between Guido Erreygers and Adam Wagstaff, in which they discuss the merits ...
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This article discusses measurement of socioeconomic inequalities in the prevalence of a health condition, in response to the recent exchange between Guido Erreygers and Adam Wagstaff, in which they discuss the merits of their own corrections to the frequently used concentration index. We first reconcile their debate and discuss the value judgments implicit in their indices. Next, we provide a formal definition of the previously undefined value judgment in Wagstaff's correction. Finally, we show empirically that the choice of index matters, as illustrated by comparisons between countries using data from the European Survey of Health, Ageing and Retirement. (C) 2012 Elsevier B.V. All rights reserved.
In accordance with the regulation of the privatized English and Welsh water industry,. water companies are required to submit an asset management plan every few years. A requirement of South West Water's asset man...
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In accordance with the regulation of the privatized English and Welsh water industry,. water companies are required to submit an asset management plan every few years. A requirement of South West Water's asset management planning is to state the probability that some of its assets will need refurbishment or replacement within the following 5 years. Probability assessments are elicited for the company's assets based on information of varying quality. For the formulation and updating of beliefs we propose and employ the threshold model, a Bayesian updating procedure. The model's main aspect is Jeffrey's conditionalization. This is an updating rule based on a simple conditional independence assumption. According to this rule, it is not necessary to construct a fully specified joint density for the quantities of interest and the probability assessments.
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