Expected Value Of Cost Research Articles

Characterizing local noise in QAOA circuits

Recently Xue et al (2019 arXiv:1909.02196) demonstrated numerically that QAOA performance varies as a power law in the amount of noise under certain physical noise models. In this short note, we provide a deeper analysis of the origin of this behavior. In particular, we provide an approximate closed form equation for the fidelity and expected cost in terms of the noise rate, system size, and circuit depth. As an application, we show these equations accurately model the trade off between larger circuits which attain better expected cost values, at the expense of greater degradation due to noise.

Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers

This paper discusses about Markovian (s,Q) inventory-queueing system with server interruptions of two heterogeneous servers. Matrix method is applied to obtain the steady state joint probability distribution of customers level in the queue, retrial group, status of the servers and stock level of heterogeneous system. This paper studies the significant effect of heterogeneous system (each server work with different service rate) as compared with homogeneous system (all servers work with same service rate). Performance measures are derived for heterogeneous system and homogeneous system. Appropriate cost functions for both models are defined. Numerical examples are used to compare the total expected cost rates of both systems. Heterogeneous system yields the minimum total expected cost value and therefore the heterogeneous system is effective.

Optimization models for siting water quality monitoring stations in a catchment

A water quality monitoring network (WQMN) must be designed so as to adequately protect the water quality in a catchment. Although a simulated annealing (SA) method was previously applied to design a WQMN, the SA method cannot ensure the solution it obtained is the global optimum. Therefore, two new linear optimization models are proposed in this study to minimize the deviation of the cost values expected to identify the possible pollution sources based on uniform cost (UC) and coverage elimination uniform cost (CEUC) schemes. The UC model determines the expected cost values by considering each sub-catchment being covered by which station, while the CEUC model determines the coverage of each station by eliminating the area covered by any upstream station. The proposed models are applied to the Derchi reservoir catchment in Taiwan. Results show that the global optimal WQMN can be effectively determined by using the UC or CEUC model, for which both results are better than those from the SA method, especially when the number of stations becomes large.

Economic analysis of risky projects by ANNs

Multilayer perceptron (MLP) and radial basis function (RBF) artificial neural networks (ANN) are used to model economic analysis of risky projects and are presented in this paper. Analytical models of risky projects are investigated and neural network function approximation results are compared. A general, problem independent ANNs are developed for the normalized input values for risky projects. The expected cost value and variance are the outputs of the ANNs. The simulation results of RBF and MLP with respect to a mathematical model are shown and concluded.

Optimization of nuclear reactor strategies under uncertainty

Operations research is applied to analysing uncertainties in the selection of nuclear reactor types. Dynamic programming methods have been extended to account for uncertain decision factors by including in the objective function a variance-related uncertainty factor as well as expected cost values. A technique is also described for obtaining total cost probability distributions. A case study is presented which uses the method to analyze a long-term planning problem for a given electric utility system. This problem is also solved by using fuzzy programming methods.

Optimal Engineering Design Under Uncertainty by Geometric Programming

This paper presents an application of stochastic (posynomial) geometric programming to an optimal engineering design problem. A theory developed by Avriel and Wilde for calculating and bounding the expected value of the objective function is summarized. Moreover, a method known as the statistical error propagation method is used to calculate approximate confidence intervals for the cost function. Stochastic geometric programming is applied to the design of a conventional “once-through” condensing system for a steam power plant in the presence of uncertainty (e.g., fuel costs can vary with market conditions). It is shown how the design engineer can extract a considerable amount of information from the solution of merely one small optimization problem. If tighter bounds on the expected cost value are desired, knowledge of discrete probability distributions for the individual random parameters is required and additional optimization problems must be solved.

Power System Production Cost Calculations - Sample Studies Recognition Forced Outages

The purpose of this paper is to present results of energy production cost calculations made for three sample power systems using a new, probabilistic technique which computes the statistical, expected value of the energy cost. These results demonstrate the importance of the effect of forced outages on expected, future power system energy costs. Unscheduled unit outages may increase calculated production costs by 2 to 5 percent. The calculations yield both expected cost values and loss-of-energy power system reliability measures and will provide information on the energy and power demand expected to be required for emergencies. These data are useful for system design. The paper illustrates the effect of the size of the available generating reserve on the system's probable loss-of-energy and expected production costs.