Stochastic level-value approximation for quadratic integer convex programming

We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.

Deleting Outliers in Robust Regression with Mixed Integer Programming

In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.

Optimal layout model of feeder automation equipment oriented to the type of fault detection and local action

In feeder automation transformation there are difficulties in equipment and location selection.To help with this,an optimal layout model of feeder automation equipment oriented to the type of fault detection and local action is pro-posed.It analyzes the coordination relationship of the three most common types of automation equipment,i.e.,fault indicator,over-current trip switch and non-voltage trip switch in the fault handling process,and the explicit expres-sions of power outage time caused by a fault on different layouts of the above three types of equipment are given.Given constraints of power supply reliability and the goal of minimizing the sum of equipment-related capital invest-ment and power interruption cost,a mixed-integer quadratic programming model for optimal layout is established,in which the functional failure probability of equipment is linearized using the 3δprinciple in statistics.Finally,the basic characteristics of the proposed model are illustrated by different scenarios on the IEEE RBTS-BUS6 system.It can not only take into account fault location and fault isolation to enhance user power consumption perception,but also can guide precise investment to improve the operational quality and efficiency of a power company.