Role of Examples and Interpretation of Results in Developing Multi-Objective Optimization Techniques

The paper evaluates the suitability of examples used in developing averaging techniques of multi-objective optimization (MOO). Most of the examples used for proposing these techniques were not suitable. The results of these examples have also not been interpreted correctly. An appropriate example has also been solved with existing and improved averaging techniques of multi-objective optimization.

Optimal Model Average Prediction in Orthogonal Kriging Models

The main objective of this paper is to consider model averaging methods for kriging models.This paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square error.Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its superiority.The authors also analyse a real dataset for an illustration.

Statistical Procedures for Estimating and Detecting Climate Changes

This paper provides a concise description of the philosophy, mathematics, and algorithms for estimating, detecting, and attributing climate changes. The estimation follows the spectral method by using empirical orthogonal functions, also called the method of reduced space optimal averaging. The detection follows the linear regression method, which can be found in most textbooks about multivariate statistical techniques. The detection algorithms are described by using the space-time approach to avoid the non-stationarity problem. The paper includes （1） the optimal averaging method for minimizing the uncertainties of the global change estimate, （2） the weighted least square detection of both single and multiple signals, （3） numerical examples, and （4） the limitations of the linear optimal averaging and detection methods.

Average Sample-path Optimality for Continuous-time Markov Decision Processes in Polish Spaces

In this paper we study the average sample-path cost （ASPC） problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of （ε〉 0）-ASPC optimal stationary policies based on two different approaches： one is the ＂optimality equation＂ approach and the other is the ＂two optimality inequalities＂ approach.

Inspection strategies for quality products withrewards in a multi-stage production

In a multi-stage manufacturing system,defective components are generated due to deteriorating machine parts and failure to install the feed load.In these circumstances,the system requires inspection counters to distinguish imperfect items and takes a few discreet decisions to produce impeccable items.Whereas the prioritisation of employee appreciation and working on reward is one of the important policies to improve productivity.Here we look at the multistage manufacturing system as an M/PH/1 queue model and rewards are given for using certain inspection strategies to produce the quality items.A matrix analytical method is proposed to explain a continuous-time Markov process in which the reward points are given to the strategy of inspection in each state of the system.By constructing the value functions of this dynamic programming model,we derive the optimal policy and the optimal average reward of the entire system in the long run.In addition,we obtain the percentage of time spent on each system state for the probability of conformity and non-conformity of the product over the long term.The results of our computational experiments and case study suggest that the average reward increases due to the actions are taken at each decision epoch for rework and disposal of the non-conformity items.

STRONG N-DISCOUNT AND FINITE-HORIZON OPTIMALITY FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES

This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.

THE OPTIMAL REPLACEMENT FOR ADDITIVE DAMAGE MODELS IN DISCRETE SETTING

A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another. The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold. Upon failure the system must be replaced by a new and identical one and a cost is incurred. If the system is replaced before failure, a lower cost is incurred.On the basis of some assumptions, we specify a replacement rule which minimizes the longrun (expected) average cost per unit time and possesses the control limit property, Finally, an algorithm is discussed in a special case.