Performance sensitivities for parameterized Markov systems

It is known that the performance potentials (or equivalently, perturbation realization factors) can be used as building blocks for performance sensitivities of Markov systems. In parameterized systerns, the changes in parameters may only affect some states, and the explicit transition probability matrix may not be known. In this paper, we use an example to show that we can use potentials to construct performance sensitivities m a more flexible way; only the potentials at the affected states need to be estimated, and the transition probability matrix need not be known. Policy iteration algorithms, which are simpler than the standard one, can be established.     

A time aggregation approach to Markov decision processes

We propose a time aggregation approach for the solution of infinite horizon average cost Markov decision processes via policy iteration. In this approach, policy update is only carried out when the process visits a subset of the state space. As in state aggregation, this approach leads to a reduced state space, which may lead to a substantial reduction in computational and storage requirements, especially for problems with certain structural properties. However, in contrast to state aggregation, which generally results in an approximate model due to the loss of Markov property, time aggregation suffers no loss of accuracy, because the Markov property is preserved. Single sample path-based estimation algorithms are developed that allow the time aggregation approach to be implemented on-line for practical systems. Some numerical and simulation examples are presented to illustrate the ideas and potential computational savings.     

Optimally solving Markov decision processes with total expected discounted reward function: Linear programming revisited

We compare the computational performance of linear programming (LP) and the policy iteration algorithm (PIA) for solving discrete-time infinite-horizon Markov decision process (MDP) models with total expected discounted reward. We use randomly generated test problems as well as a real-life health-care problem to empirically show that, unlike previously reported, barrier methods for LP provide a viable tool for optimally solving such MDPs. The dimensions of comparison include transition probability matrix structure, state and action size, and the LP solution method.     

Stochastic learning and optimization—A sensitivity-based approach

We introduce a sensitivity-based view to the area of learning and optimization of stochastic dynamic systems. We show that this sensitivity-based view provides a unified framework for many different disciplines in this area, including perturbation analysis, Markov decision processes, reinforcement learning, identification and adaptive control, and singular stochastic control; and that this unified framework applies to both the discrete event dynamic systems and continuous-time continuous-state systems. Many results in these disciplines can be simply derived and intuitively explained by using two performance sensitivity formulas. In addition, we show that this sensitivity-based view leads to new results and opens up new directions for future research. For example, the n th bias optimality of Markov processes has been established and the event-based optimization may be developed; this approach has computational and other advantages over the state-based approaches.     

From screening to quantitative sensitivity analysis. A unified approach

The present work is a sequel to a recent one published on this journal where the superiority of ‘radial design’ to compute the ‘total sensitivity index’ was ascertained. Both concepts belong to sensitivity analysis of model output. A radial design is the one whereby starting from a random point in the hyperspace of the input factors one step in turn is taken for each factor. The procedure is iterated a number of times with a different starting random point as to collect a sample of elementary shifts for each factor. The total sensitivity index is a powerful sensitivity measure which can be estimated based on such a sample. Given the similarity between the total sensitivity index and a screening test known as method of the elementary effects (or method of Morris), we test the radial design on this method. Both methods are best practices: the total sensitivity index in the class of the quantitative measures and the elementary effects in that of the screening methods. We find that the radial design is indeed superior even for the computation of the elementary effects method. This opens the door to a sensitivity analysis strategy whereby the analyst can start with a small number of points (screening-wise) and then – depending on the results – possibly increase the numeral of points up to compute a fully quantitative measure. Also of interest to practitioners is that a radial design is nothing else than an iterated ‘One factor At a Time’ (OAT) approach. OAT is a radial design of size one. While OAT is not a good practice, modelers in all domains keep using it for sensitivity analysis for reasons discussed elsewhere (Saltelli and Annoni, 2010) [23]. With the present approach modelers are offered a straightforward and economic upgrade of their OAT which maintain OAT's appeal of having just one factor moved at each step.     

A note on the vanishing interest rate approach in average Markov decision chains with continuous and bounded costs

This work considers denumerable state Markov decision processes with discrete time parameter. The performance of a control policy is measured by the (lim sup) expected average cost criterion, the action sets are compact metric and the cost function is continuous and bounded. Within this framework, necessary and sufficient conditions are given so that the vanishing interest rate (VIR) method — also known as the vanishing discount effect approach — yields an average optimal stationary policy.     

A machine learning approach to assess price sensitivity with application to automobile loan segmentation

Price sensitivity is an outstanding business issue in companies and organizations that aim to undertake optimal managerial decisions for increasing sales and / or revenue. Hence, price sensitivity assessment has become an in fashion problem that has attracted the attention of a wide variety of actors and business units within the organizations. In this paper we propose a machine learning approach to assess price sensitivity for an automobile loan portfolio in order to get a segmentation revealing the existence of groups with differential price sensitivity, defined by their differential purchase responses against changes in the loan interest rate. The proposed method combines the power of conditional inference trees, random forests and model based recursive partitioning algorithms to implement a process for price group finding, variable selection and price sensitivity segmentation in order uncover such differential groups and characterize them by asset and product characteristics and by customer attributes as well. The resulting segmentation will define high sensitivity groups, where interest rate reductions can be recommended in order to increase sales, as well as nearly insensitive groups for which a price strategy that increases the interest rate is expected to have slight impact on loan disbursements.     

Multiple criteria decision analysis under complex uncertainty: A Pearson-like correlation-based Pythagorean fuzzy compromise approach

The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson-like correlation-based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval-valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real-life decision-making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well-known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson-like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation-based closeness coefficients to simultaneously measure the relative closeness to the positive-ideal PF/IVPF solutions and the relative remoteness from the negative-ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson-like correlation-based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.     

Using modified IPA to evaluate supplier’s performance: Multiple regression analysis and DEMATEL approach

This paper provides a methodology of Supplier Quality Performance Assessment (SQPA) for the industrial computer industry that introduces modified Importance-Performance Analysis (IPA) which uses the multiple regression analysis and Decision Making Trial and Evaluation Laboratory (DEMATEL) techniques, and creates value for all members through optimizing order-winners and qualifiers to promote supplier quality improvement and solve complex problems using the cause-effect relation. The techniques used in SQPA activities are easily understood. A case involving an industrial computer manufacturer is illustrated to show the benefits of our model.     

Integrating preventive and predictive maintenance policies with system dynamics: A decision table approach

A decision table is a practical tool that helps systems planners to make operational decisions, especially when they are under stress. With the effect of recent trends, such as the use of machine learning, data mining, and reinforcement learning methods, the maintenance decision has been a dynamic issue depending on system conditions. An expert may execute the maintenance or wait for the next periodic maintenance due to lack of maintenance workers, tools or budget, resources, etc., although the intelligent method predicts a failure approaching. Even sometimes, he/she may ignore the current periodic maintenance. Our method allows making some changes in the maintenance plan systematically. It integrates the results of preventive and predictive maintenance policies, and as different from the literature, it allows ignoring some maintenance actions depending on the maintenance resource levels in a decision table. Such a strategy helps to allocate limited resources to maintenance actions reasonably. We conducted an extensive simulation study on a real-life dataset. The preventive maintenance period is determined using classical approaches such as Weibull analysis. A machine learning algorithm is utilized to predict the type of failure. We have analyzed the performance of the proposed decision table approach under a variety of scenarios and with different parameter settings. We also showed the effect of parameter settings and the marginal utility of each maintenance policy. In addition, the approach provides several choices for planners. As a result, the proposed approach improves the system’s sustainability compared to traditional policies.     

VIRTUE: A visual tool for information retrieval performance evaluation and failure analysis

Objective: Information Retrieval (IR) is strongly rooted in experimentation where new and better ways to measure and interpret the behavior of a system are key to scientific advancement. This paper presents an innovative visualization environment: Visual Information Retrieval Tool for Upfront Evaluation (VIRTUE), which eases and makes more effective the experimental evaluation process.Methods: VIRTUE supports and improves performance analysis and failure analysis.Performance analysis: VIRTUE offers interactive visualizations based on well-known IR metrics allowing us to explore system performances and to easily grasp the main problems of the system.Failure analysis: VIRTUE develops visual features and interaction, allowing researchers and developers to easily spot critical regions of a ranking and grasp possible causes of a failure.Results: VIRTUE was validated through a user study involving IR experts. The study reports on (a) the scientific relevance and innovation and (b) the comprehensibility and efficacy of the visualizations.Conclusion: VIRTUE eases the interaction with experimental results, supports users in the evaluation process and reduces the user effort.Practice: VIRTUE will be used by IR analysts to analyze and understand experimental results.Implications: VIRTUE improves the state-of-the-art in the evaluation practice and integrates visualization and IR research fields in an innovative way.     

A hybrid data envelopment analysis and multi-attribute decision making approach to sustainability assessment

The concept of sustainability consists of three main dimensions: environmental, techno-economic, and social. Measuring the sustainability status of a system or technology is a significant challenge, especially when it needs to consider a large number of attributes in each dimension of sustainability. In this study, we first propose a hybrid approach, involving data envelopment analysis (DEA) and a multi-attribute decision making (MADM) methodologies, for computing an index for each dimension of sustainability, and then we define the overall sustainability index as the mean of the three measured indexes. Towards this end, we define new concepts of efficiency and cross-efficiency of order (p, q) where p and q are the number of inputs and outputs, respectively. For a given (p, q) , we address the problem of finding efficiency of order (p, q) by developing a novel DEA-based selecting method. Finally, we define the sustainability index as a weighted sum of all possible cross-efficiencies of order (p, q) . Form a computational viewpoint, the proposed selecting model significantly decreases the computational burden in comparison with the successive solving of traditional DEA models. A case study of the electricity-generation technologies in the United Kingdom is taken as a real-world example to illustrate the potential application of our method.     

A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.     

A simulated annealing-based permutation method and experimental analysis for multiple criteria decision analysis with interval type-2 fuzzy sets

The aim of this paper is to develop a simulated annealing-based permutation method for multiple criteria decision analysis within the environment of interval type-2 fuzzy sets. The outranking methodology constitutes one of the most fruitful approaches in multiple criteria decision making and has been applied in numerous real-world problems. The permutation method is a classical outranking model, which generalizes Jacquet–Lagreze's permutation method and is based on a pairwise criterion comparison of the alternatives. Because modeling of the uncertainty in the decision-making process becomes increasingly important, an extension to the interval type-2 fuzzy environment is a useful generalization of the permutation method and is appropriate for handling uncertain and imprecise information in practical decision-making situations. This paper produces a signed-distance-based comparison among the comprehensive rankings of alternatives for concordance and discordance analyses. An integrated nonlinear programming model is constructed for estimation of the criterion weights and the optimal ranking order of the alternatives under incomplete preference information. To enhance the implementation efficiency, a simulated annealing-based permutation method and its meta-heuristic algorithm are developed to produce a polynomial time solution for the total completion time problem. Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result.     

An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis

This paper presents an interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions for managing multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. First, certain likelihood-based preference functions are proposed using the likelihoods of interval-valued intuitionistic fuzzy preference relationships. Next, selected practical indices of concordance/discordance are established to evaluate all possible permutations of the alternatives. The optimal priority order of the alternatives is determined by comparing all comprehensive concordance/discordance values based on score functions. Furthermore, this paper considers various preference types and develops another interval-valued intuitionistic fuzzy permutation method using programming models to address multiple criteria decision-making problems with incomplete preference information. The feasibility and applicability of the proposed methods are illustrated in the problem of selecting a suitable bridge construction method. Moreover, certain comparative analyses are conducted to verify the advantages of the proposed methods compared with those of other decision-making methods. Finally, the practical effectiveness of the proposed methods is validated with a risk assessment problem in new product development.     

Aeroelastic modeling and stability analysis: A robust approach to the flutter problem

In this paper, a general approach to address modeling of aeroelastic systems, with the final goal to apply μ analysis, is discussed. The chosen test bed is the typical section with unsteady aerodynamic loads, which enables basic modeling features to be captured and so extend the gained knowledge to practical problems treated with modern techniques. The aerodynamic operator has a nonrational dependence on the Laplace variable s, and hence, 2 formulations for the problem are available: frequency domain or state‐space (adopting rational approximations). The study attempts to draw a parallel between the 2 consequent linear fractional transformation modeling processes, emphasizing critical differences and their effect on the predictions obtained with μ analysis. A peculiarity of this twofold formulation is that aerodynamic uncertainties are inherently treated differently and therefore the families of plants originated by the possible linear fractional transformation definitions are investigated. One of the main results of the paper is to propose a unified framework to address the robust modeling task, which enables the advantages of both the approaches to be retained. On the analysis side, the application of μ analysis to the different models is shown, emphasizing its capability to gain insight into the problem.     

On the variable structure control approach with sliding modes to robust finite-time consensus problems: A methodological overview based on nonsmooth analysis

When controlling cyber–physical systems via consensus algorithms, the robustness issue is of paramount importance because of model mismatching and/or disturbances that generally modify the Laplacian flow dynamics associated to the overall network, compromising the possibility to achieve any expected, orchestrated emergent behavior. To face this issue, the Variable Structure Control (VSC) approach has recently been shown to be an effective tool in designing control protocols over networks, providing robustness and often yielding finite-time convergence. Moreover, VSC further enables the decoupling of simultaneous control objectives where reaching a consensus state is only part of a more complex task, for instance as it happens in distributed optimization. Thus motivated, this paper overviews, from a tutorial perspective, some selected recent advances in the application of VSC with Sliding Modes to design robust consensus controllers in both the leader-less and the leader-following settings. Efforts are also made to unify the notation and to discuss the theoretical foundations of the nonsmooth analysis tools at the basis of their design for a wide readership unfamiliar with these problems and formal tools. To this aim, examples supporting the treatment, and numerical simulations, are given and discussed in detail. Finally, hints for future investigations along with some current open problems are provided.