Large-scale functional network time series model solved with mathematical programming approach

Development of statistical model for cancer incidence trend predictions can provide a sound and accurate foundation for planning a comprehensive national strategy for optimal partitioning of research resources. Several studies in the past showed that that there are racial/ethnic disparities exist between breast cancer incidence rates among black and white women in the United States. Some of the studies also showed that the disparity in breast cancer incidence rates among white and black US women is widening, with relatively higher incidence rates among black women. In this paper, we apply functional time series (FTS) models on the age-specific breast cancer incidence rates for these two major groups of women in US, and forecast their age-incidence curves. The data are obtained from the Surveillance, Epidemiology and End Results (SEER) program of the United States. We use annual unadjusted breast cancer incidence rates from 1973 to 2013 in 5-year agegroups (15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45–49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79, 80–84 and 85+). Age-specific cancer incidence curves are obtained using nonparametric smoothing methods. The curves are then decomposed using functional data paradigm and we fit functional time series (FTS) models for each population of women separately. The smoothed incidence curves are then forecasted and prediction intervals are calculated. Fifteen-year forecasts indicate an overall increase in future breast cancer incidence rates for both groups of women. This increase appears to be faster among black women and relatively slower among the whites. The projections suggest a need for equal delivery of quality care to eliminate breast cancer disparities among the two major groups of women in US.

This paper aims to develop a suitable restoration method by a joint usage of an Expert system (ES) and a Mathematical Programming (MP) approach. Under this devise, the optimal target system for storation is formulated as an MP problem and solved efficiently by the decomposition-coordination strategy; that is a whole problem is decomposed into subproblems according to the generic knowledge of experts. The introduction of a new concept ?>restorative operation cost ?> that reflects the various restoration strategies has decreased the number of rules in the knowledge-base to one third that of typical existing ES's. The validity and effectiveness of the combined method have been demonstrated by applying it to a practical size restoration problem.

This paper proposes a new mathematical programming approach to represent the dimensions of the discriminant space for the multiple-group classification problem. Few papers have investigated generalizations of two-group mathematical programming approaches for the classification of multiple groups. While several papers have proposed mathematical programming models for separating groups of observations, the issue of considering the classification problem by finding discriminant linear functions to describe the groups in fewer dimensions has not been addressed. The new mathematical programming approach proposed in this paper first solves the multiple-group problem using a single discriminant function, which essentially represents the separation of the groups in one dimension. Then the multiple-group problem is successively solved using single discriminant functions with the requirement that successive linear discriminant functions have a sample covariance equal to zero. An algorithm is proposed to classify observations from multiple groups using the linear discriminant functions from the mathematical programming approach in a reduced number of dimensions.

The air temperature (AT) is a significant factor in the environmental processes, human health, agriculture, and energy systems, so correct forecasting is very important. This paper explores the prediction of AT in a functional time series (FTS) model that models the high-frequency temperature data as smooth curves over the day that can model both deterministic seasonal cycles and other stochastic dynamics. Smoothing splines and Fourier-based functional representations are used to model and predict short-term variations in temperature by a functional autoregressive model, FAR(1). The performance of FAR(1) is systematically contrasted to those of classical statistical models such as ARIMA and VAR and machine-learning-based ones such as artificial neural networks (ANN) and autoregressive neural networks (ARNN). Accuracy of an error forecast is measured in terms of mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE). Empirical findings show the FAR(1) model records reduced forecasting errors and increased predictive stability both in months and in hours than the competition methods. Such results outline the utility of functional data analysis to utilize the smooth and periodic organization of temperature data. The research offers a practical and holistic model of predicting high-frequency AT, and it can be employed in the better decision-making in agricultural, energy and safety management among the population that operate during the climate variability.

Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

Incidence and mortality rates are considered as a guideline for planning public health strategies and allocating resources. We apply functional data analysis techniques to model age-specific brain cancer mortality trend and forecast entire age-specific functions using exponential smoothing state-space models. The age-specific mortality curves are decomposed using principal component analysis and fit functional time series model with basis functions. Nonparametric smoothing methods are used to mitigate the existing randomness in the observed data. We use functional time series model on age-specific brain cancer mortality rates and forecast mortality curves with prediction intervals using exponential smoothing state-space model. We also present a disparity of brain cancer mortality rates among the age groups together with the rate of change of mortality rates. The data were obtained from the Surveillance, Epidemiology and End Results (SEER) program of the United States. The brain cancer mortality rates, classified under International Classification Disease code ICD-O-3, were extracted from SEER*Stat software.

Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variance-covariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decision-makers to choose the most appropriate model for their decision-making situation.

As oil resources are being depleted and energy demand is rising, optimal well placement is becoming a more and more critical decision for reservoir management team with huge techno-economical impacts. This study focuses on modeling this problem and proposing a potential rigorous solution approach for that. We use mathematical programming approach, which previously has been largely ignored in this field, and model the problem using big-M formulation and dynamic model of multiphase flow. Moreover, to solve this model, we modify the “Outer Approximation with Equality Relaxation and Augmented Penalty” approach. It decomposes the well placement problem into a “fixed well location-production optimization” which is “integer free but nonlinear” and “linearized-well dependent optimization” which is “linear but integer dependent” models. We solve the production optimization part sequentially. The results show that the algorithm can efficiently find an improving direction to locate the new sites for drilling new wells. Since, well placement is a non-convex problem new sites are potentially local optimums. To our best knowledge, this is the first contribution that captures the dynamic feature of hydrocarbon production while locating the drilling sites for new wells using “mathematical programming approach”.

In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed in a decision support approach for schedule planning in cargo airlines. We think that using the same concept for planning and revenue management is essential for consistency of planning and operation. To meet the real-time requirements of revenue management special computational strategies for solving the large models are necessary.

Renewable energy forecasting services comprise various modules for intra-day and day-ahead forecasts. This work specifically addresses day-ahead forecasts, utilizing specifications based on endogenous, historical measurements. These specifications are designed to be computationally efficient, requiring fewer input variables and less training data. Such weather-independent specifications serve as benchmarks against the more computationally demanding forecasts based on numerical weather predictions. A series of experiments, designed to simulate the real-world application of an online system, were conducted on sliding windows of back-contact photovoltaic (installed at KAUST, Saudi Arabia) output series, solar irradiance recorded in Hawaii, and simulated data. Our analysis evaluated 24 specifications, which are variants of (i) functional time series models (including two novel shrinkage procedures); (ii) time series nearest neighbor schemes; (iii) exponential smoothing procedures; (iv) autoregressive integrated moving average processes; (v) automatic techniques based on time series decomposition; and (vi) the persistence model. In addition to employing outlier-robust accuracy metrics, such as mean absolute error, our evaluation also prioritized prediction-interval accuracy, quantified by the mean scaled interval score. Our findings suggest that practitioners can achieve significant improvements over the persistence model by forecasting daily profiles using adaptive nonparametric or functional data analysis-based procedures. Moreover, applying shrinkage to nearest neighbor (NN) forecasts toward smooth, average daily profiles significantly enhances NN performance. Conversely, some popular, computationally intensive models fail to perform adequately to justify their additional cost.

Presently, the number, types, and distribution of resources in a resource allocation system (RAS), may change frequently and dynamically due to fluctuant customer demands. Such changes in a resource allocation (RA) specification mean different production or service behaviors yielded by the providers. This new situation gives rise to a challenging problem, namely, how to switch smoothly the provider systems to support different production. This paper tries to address this problem from the viewpoint of discrete event system (DES) supervisory control. A Petri net (PN) controller of an RAS can be designed from a resource allocation specification using P-invariant. Once the RA specification is changed, the controller is updated following it. Moreover, if the changed specification is unreasonable, the whole control system, are reconfigured to reach a legal system state and a newly reasonable resource allocation solution is re-calculated. Specifically, the paper proposed a reconfiguration method of a PN control system that is transformed into PN reachability analysis problem using a mathematic programming approach. In our method, not only the transition firing costs but also the steps of concurrent firing are taken into account to achieve an optimal reconfiguration solution. Finally, an example is provided for illustrating the application of the mentioned methods.

In this chapter, a formulation for applying Ant Colony Optimization (ACO) to power plant maintenance scheduling optimization (PPMSO) has been developed and successfully tested using four case studies (original and modified versions of two benchmark case studies from the literature). In particular, the performance of the heuristic formulation developed, the two local search algorithms introduced and the overall utility of the ACO-PPMSO formulation were investigated. The results obtained have shown that the heuristic formulation improves the performance of the ACO-PPMSO algorithm significantly when applied to the four case studies investigated. It was found that while the PPMSO-2-opt local search operator seems to work well for unconstrained problems, it is not suitable for highlyconstrained PPMSO problems. Lastly, the results obtained by ACO-PPMSO for the two original case studies were better than those obtained by other optimisation methods, such as various genetic algorithm (GAs) formulations and simulated annealing (SA). For the 21-unit and 22-unit case studies, a new optimal solution has been found by the ACO-PPMSO

We propose a nonlinear prediction (NOP) method for functional time series. Conventional methods for functional time series are mainly based on functional principal component analysis or functional regression models. These approaches rely on the stationary or linear assumption of the functional time series. However, real data sets are often nonstationary, and the temporal dependence between trajectories cannot be captured by linear models. Conventional methods are also hard to analyze multivariate functional time series. To tackle these challenges, the NOP method employs a nonlinear mapping for functional data that can be directly applied to multivariate functions without any preprocessing step. The NOP method constructs feature space with forecast information, hence it provides a better ground for predicting future trajectories. The NOP method avoids calculating covariance functions and enables online estimation and prediction. We examine the finite sample performance of the NOP method with simulation studies that consider linear, nonlinear and nonstationary functional time series. The NOP method shows superior prediction performances in comparison with the conventional methods. Three real applications demonstrate the advantages of the NOP method model in predicting air quality, electricity price and mortality rate.

Forecasting future productivity is a critical task to every organization. However, the existing methods for productivity forecasting have two problems. First, the logarithmic or log-sigmoid value, rather than the original value, of productivity is dealt with. Second, the objective functions are not consistent with those adopted in practice. To address these problems, a fuzzy polynomial fitting and mathematical programming (FPF-MP) approach are proposed in this study. The FPF-MP approach solves two polynomial programming problems, based on the original value of productivity, in two steps to optimize accuracy and precision of forecasting future productivity, respectively. A real case was adopted to validate the effectiveness of the proposed methodology. According to the experimental results, the proposed FPF-MP approach outperformed six existing methods in improving the forecasting accuracy and precision.

Aggregating classifiers with mathematical programming