Structural Learning of Boltzmann Machine: An Application

2015 ◽  
Vol 793 ◽  
pp. 657-662
Author(s):  
Shamshul Bahar Yaakob ◽  
Zamri Hassan ◽  
Syed Akhmal Syed Jamalil
Keyword(s):  
Variance Analysis ◽  
Mixed Integer ◽  
Structural Learning ◽  
Boltzmann Machine ◽  
Expected Return ◽  
Integer Quadratic Programming ◽  
Effective Selection ◽  
Mixed Integer Quadratic Programming ◽  
Mean Variance ◽  
Selection Of

In order to solve a problem efficiently, we propose the structural learning of Boltzmann machine. The proposed method enables us to solve the problem defined in terms of mixed integer quadratic programming. In this research, an analysis is performed by using the concepts of the reliability and risks of units evaluated using a variance-covariance matrix and also the effect and expanses of replacement are measured. Mean-variance analysis is formulated as a mathematical programming with two objectives to minimize the risk and maximize the expected return. Finally, we employ a Boltzmann machine to solve the mean-variance analysis efficiently. At the end, the result of our method was exemplified. This method enables us to obtain a more effective selection of results and enhanced the effectiveness of the decision making process.

Structural Learning of Boltzmann Machine and its Application

2015 ◽  
Vol 785 ◽  
pp. 63-67
Author(s):  
Shamshul Bahar Yaakob ◽  
Mohd Zamri Hasan ◽  
Amran Ahmed
Keyword(s):  
Life Cycle Management ◽  
Mixed Integer ◽  
Structural Learning ◽  
Boltzmann Machine ◽  
Expected Return ◽  
Integer Quadratic Programming ◽  
Effective Selection ◽  
Mixed Integer Quadratic Programming ◽  
Mean Variance ◽  
Selection Of

This study proposed a way to solve problem efficiently which is through structural learning of Boltzmann machine. This method used mixed integer quadratic programming to solve the problem. An analysis is conducted by using the ideas of the reliability and risks of units assessed using a variance-covariance matrix and the effect and expanses of replacement are determined. In this study, the mean-variance analysis is formulated as a mathematical program with two objectives: (1) minimization of risk and (2) maximization of expected return. Lastly, the effectiveness of proposed method is illustrated by way of a life cycle management example. The result of this suggested method was demonstrated at the end. By using this method, more effective selection of results is gathered. Thus, this prove that the effectiveness of the decision making process can be reinforced.

scholarly journals Review on Reformulation of the Mean-Variance Model with Real-life Trading Restrictions

2017 ◽  
Vol 14 (1) ◽  
pp. 40
Author(s):  
Feng Li
Keyword(s):  
Computing Time ◽  
Real Life ◽  
Mixed Integer ◽  
Variance Model ◽  
Integer Quadratic Programming ◽  
Continuous Relaxation ◽  
Perspective Reformulation ◽  
Mixed Integer Quadratic Programming ◽  
Trading Restrictions ◽  
Mean Variance

In this paper, we consider a class of portfolio selection problems with cardinality and minimum buy-in threshold constraints in real-life which can be formulated as mixed-integer quadratic programming (MIQP). Two reformulation methods that generate the same tight continuous relaxation of original problem are compared in the context under the branch-and-bound algorithm, one is the Perspective Reformulation and another is the Lift-and-Convexification Reformulation (LCR). Computational results show that the (PC) is more competitive than the (LCR) method in terms of computing time and nodes in MIQP solver CPLEX 12.7, what's more, this outperformance becomes more obvious as the size of instances grows.

scholarly journals Combinatorial Optimization of Service Order and Overtaking for Demand-Oriented Timetabling in a Single Railway Line

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Dewei Li ◽  
Shishun Ding ◽  
Yizhen Wang
Keyword(s):  
Travel Time ◽  
High Speed ◽  
Cost Benefit ◽  
Theory And Practice ◽  
Mixed Integer ◽  
High Speed Rail ◽  
Railway Line ◽  
Integer Quadratic Programming ◽  
Total Travel Time ◽  
Mixed Integer Quadratic Programming

Train timetabling is crucial for passenger railway operation. Demand-oriented train timetable optimization by minimizing travel time plays an important role in both theory and practice. Most of the current researches of demand-oriented timetable models assume an idealized situation in which the service order is fixed and in which zero overtaking exists between trains. In order to extend the literature, this paper discusses the combinatorial effect of service order and overtaking by developing four mixed-integer quadratic programming timetabling models with different service order as well as overtaking conditions. With the objective of minimizing passengers’ waiting time and in-vehicle time, the models take five aspects as constraints, namely dwell time, running time, safety interval, overtaking, and capacity. All four models are solved by ILOG CPLEX; and the results, which are based on Shanghai-Hangzhou intercity high-speed rail data, show that either allowing overtaking or changing service order can effectively optimize the quality of timetable with respect to reducing the total passengers’ travel time. Although optimizing train overtaking and service order simultaneously can optimize the timetable more significantly, compared to overtaking, allowing the change of service order can help passengers save total travel time without extending the train travel time. Moreover, considering the computation effort, satisfying both of the conditions in the meantime, when optimizing timetable has not got a good cost benefit.

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