Fixed Time Horizon Research Articles

Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes

In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes.

Pressure-Driven Batch Distillation Optimal Control for Acetone-Methanol Separation

Over the last fifteen years, immense progress has been made in the research of pressure-swing batch distillation. The challenge lies in the fact that certain pressure-sensitive azeotropic mixtures cannot be separated in a regular open batch mode with an acceptable outcome. Throughout most of this text, findings contradict previously established facts. The separation of acetone-methanol by pressure-swing batch distillation in a mixed double system, consisting of a regular and inverted column, is the process under investigation. In this work, a comprehensive global solution to the optimal control problem is derived in the form of a sequential synthesis of controlled trajectories. A thorough analysis of the control variables, with and without parametric sensitivity of manipulated variables, on the optimal control pattern with variable reflux is presented. Most authors did not achieve significant results by simultaneously optimizing reflux and liquid division ratios or by using a "variable pressure gap." This study challenges previous findings, emphasizing the importance of simultaneous optimization of all three factors mentioned. During this study, the optimal reflux strategy through cyclic operation was extended to optimize energy expenditure over a fixed time horizon. Moreover, the proposed scheme offers a high level of operational flexibility, allowing units to be operated independently or as a system. Additionally, the facility of connecting additional devices is highlighted by the significant difference in output temperatures and the potential for using evaporated fluids consecutively. Lastly, the research provides a solid basis for future investigations into internal and external heat integration, potentially leading to conclusions about expanding the network using well-known heat cycles.

Online Conversion with Switching Costs: Robust and Learning-Augmented Algorithms

We introduce and study online conversion with switching costs, a family of online problems that capture emerging problems at the intersection of energy and sustainability. In this problem, an online player attempts to purchase (alternatively, sell) fractional shares of an asset during a fixed time horizon with length T. At each time step, a cost function (alternatively, price function) is revealed, and the player must irrevocably decide an amount of asset to convert. The player also incurs a switching cost whenever their decision changes in consecutive time steps, i.e., when they increase or decrease their purchasing amount. We introduce competitive (robust) threshold-based algorithms for both the minimization and maximization variants of this problem, and show they are optimal among deterministic online algorithms. We then propose learning-augmented algorithms that take advantage of untrusted black-box advice (such as predictions from a machine learning model) to achieve significantly better average-case performance without sacrificing worst-case competitive guarantees. Finally, we empirically evaluate our proposed algorithms using a carbon-aware EV charging case study, showing that our algorithms substantially improve on baseline methods for this problem.

A Predictive Energy Management Strategy for Heavy Hybrid Electric Vehicles Based on Adaptive Network-Based Fuzzy Inference System-Optimized Time Horizon

Energy management strategies play a crucial role in enhancing the fuel efficiency of hybrid electric vehicles (HEVs) and mitigating greenhouse gas emissions. For the current commonly used time horizon optimization methods that only target the trend curve of the optimal battery state of charge (SOC) trajectory obtained offline, which are only suitable for buses with known future driving conditions, this paper proposed an energy management strategy based on an adaptive network-based fuzzy inference system (ANFIS) that optimizes the time horizon length and enhances adaptability to driving conditions by integrating historical vehicle velocity, accelerations, and battery SOC trajectory. First, the vehicle velocity prediction model based on the radial basis function (RBF) neural network is used to predict the future velocity sequence. After that, ANFIS was used to optimize and update the length of the forecast time horizon based on the historical vehicle velocity sequence. Finally, compared with the fixed time horizon energy management strategy, which is based on model predictive control (MPC), the average calculation time of the energy management strategy is reduced by about 23.5%, and the fuel consumption per 100 km is reduced by about 6.12%.

Linear quadratic optimal control turnpike in finite and infinite dimension: Two-term expansion of the value function

In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in this expansion, proportional to T, corresponds to the optimal value attained through the classical turnpike theory in the associated static problem. The remaining terms are associated with optimal stabilization problems towards the turnpike.

Load Scheduling of Smart Net-Zero Residential Buildings Based on Pandemic Situation

Load scheduling is an effective way of utilizing loads of smart residential buildings according to the preferences of the inhabitants or grid demands, while reducing the cost of energy. This work proposes objective functions for load scheduling to confine the cost of energy within the consumers’ preference range while keeping the load consumption closer to the load demand as possible, to minimize system loss during normal and pandemic condition such as COVID-19 periods, fulfilling the unique features of a net-zero energy building. The proposed objective function is implemented by considering the realistic grid power cost, levelized cost of renewable sources, battery, and incentives offered by the utility system existing in California, USA. In addition to three different types of days such as normal working days, weekends and pandemic situations, brown out power outages are considered as operating conditions. Particle swarm optimization (PSO) is utilized in all considered operating conditions. Two terms that account for the total energy cost savings and the total delayed/scheduled load over a fixed time horizon are formulated as performance indices to illustrate the effectiveness of the proposed objective functions for load scheduling. All of the cases are optimized by the Paticle Swarm Optimization (PSO) and non-optimized systems are simulated in the MATLAB environment. It is evident from the simulation results that the proposed objective function is very efficient in tackling the energy resources, loads and grid power to maximize cost savings and minimize shifting of loads for later hours for normal and pandemic situations in net-zero energy buildings. Moreover, it is equally effective in responding to any emergency situations such as brown out energy crisis situations, which are not considered in the literature so far. In all cases, the performance index also validates the effectiveness of the proposed objective function-based scheduling system for net-zero energy buildings.

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Fuzzy clustering of the healthy life expectancy decomposition: A multi-population analysis

This work analyses healthy life expectancy, which combines information on the period life table with the age-specific disability prevalence data in a single indicator. We quantify how much mortality and disability contributed to changes in healthy life expectancy over a fixed time horizon by age group and population to understand if life expectancy is increasing faster than the decline of disability. The prominent heterogeneity in mortality and health worldwide calls for a cross-country comparative analysis. The methodology used is decomposition, which splits the difference between two times of an aggregate index by assigning the difference to its components. Besides, through a cluster analysis, we categorize countries according to the age-specific contributions of mortality and disability simultaneously, using the healthy life expectancy decomposition results. This allows us to ease the interpretation and better outline the outcomes. Since health is increasingly considered a crucial aspect of economic growth, monitoring health expectancies is essential to assess the financial sustainability of the health and social security system. Some policy implications are finally discussed.

Across-time risk-aware strategies for outperforming a benchmark

We propose a novel objective function for constructing dynamic investment strategies with the goal of outperforming an investment benchmark at multiple points of evaluation during the investment time horizon. The proposed objective is intuitive, easy to parameterize, and directly targets a favorable tracking difference of the actively managed portfolio relative to the benchmark. Under stylized assumptions, we derive closed-form optimal investment strategies to guide the intuition in more realistic settings. In the case of discrete rebalancing with investment constraints, optimal strategies are obtained using a neural network-based numerical approach that does not rely on dynamic programming techniques. Compared to the targeting of a favorable tracking difference relative to the benchmark only at some fixed time horizon, our results show that the proposed objective offers a number of advantages: (i) The associated optimal strategies exhibit potentially more attractive asset allocation profiles, in that less extreme positions in individual assets are taken early in the investment time horizon, while achieving a similar terminal terminal wealth distribution. (ii) Across-time risk awareness leads to more robust performance and a higher probability of benchmark outperformance during the investment horizon in out-of-sample testing. The resulting strategies therefore exhibit desirable characteristics for active portfolio managers with periodic reporting requirements.

A Fuzzy Inventory Replenishment Model for Deteriorating and Ameliorating Items under Linear Trend in Demand and Partial Backlogging.

This research paper deals with an inventory replenishment model for both deteriorating and ameliorating items under linear trend in demand over a fixed time horizon. This paper aimed to develop the model with shortages which are partially backlogged. The model is developed under the fuzzy environment. Optimal technique is used to solve the model considering Signed Distance Method (SD). The ordering cost, purchase cost, holding cost, deteriorating cost, ameliorating cost, shortage cost and opportunity cost are all considered as fuzzy cost parameters. Finally the fuzzy model is illustrated with the help of a numerical example and a sensitivity of the optimal solution towards the changes in the values of all fuzzy cost parameters is also furnished, and a concluding remark is given expressing the model development and also future research works in consequence of the present.

Heuristic Rules for the Dynamic Pricing Problem

This paper is devoted to the development of heuristics for the dynamic pricing problem. A discrete time model of dynamic pricing on the fixed time horizon is proposed. It is applicable to products that satisfy two properties: 1) product value expires at a certain predetermined date, and 2) consumers demand at most a single unit of the product. This type of demand structure allows deriving a simple system of recursive equations for optimal prices using dynamic programming techniques. Optimal pricing policy is expressed as a function of time to expiration and inventory levels of unsold products. An analytical solution to this problem was obtained for special cases, while for the general case, a numerical algorithm has been developed. Qualitative characteristics of the optimal pricing policy are established, and their implications for dynamics of inventories and prices are discussed. Based on these observations, a simple heuristic rule for dynamic price adjustments is proposed. Performance of this heuristic is evaluated against the optimal dynamic and fixed-price policies using Monte-Carlo experiments. Results demonstrate high efficiency of the proposed heuristic strategy and its even simpler derivatives. Heuristics’ adaptability and ease of implementation should make it suitable and attractive for small and medium businesses.

Optimal and politically opportune language policies for the vitality of minority languages

Language policies for the purpose of (re)vitalizing a minority language are analyzed as a dynamic cost-effectiveness problem. We focus on policy measures with two types of cost structures: costs largely proportional to the number of beneficiaries (a rival measure) and costs independent of the number of beneficiaries (a non-rival measure). An example of the former is home nursing in the minority language and an example of the latter is street signs in the minority language. Both types of measures are assumed to contribute positively to the vitality of the minority language. We stylize the analysis, letting the rival measure have an immediate direct effect on the vitality and the non-rival one a protracted indirect effect on the language’s status. Two problems are addressed. Firstly, we study how the optimal combination of the two types of measure changes as the policy is implemented and the vitality of the minority language increases and show that a policy with fixed budget shares as a rule is sub-optimal. Secondly, we compare the opportune policy of a policy maker planning with a fixed time horizon with the optimal policy as the time horizon approaches infinity. The policy maker has incentives to plan for a sub-optimal policy with a reduction in the protracted measure for the whole planning period and making it equal to zero at the time horizon. All effects are illustrated in numeric examples.

Fully-coupled mean-field FBSDE and maximum principle for related optimal control problem

In this paper, motivated by the study of Stackelberg differential game of McKean–Vlasov type, we first investigate the solvability for the mean-field forward–backward stochastic differential equation (MF-FBSDE), which involves one McKean–Vlasov stochastic differential equation (SDE) and one mean-field type backward stochastic differential equation (BSDE). Under some weakly coupled conditions, we use a purely probabilistic approach to prove the well-posedness of such MF-FBSDE with arbitrary fixed time horizon. Then we consider a mean-field control problem, where the state dynamic is given by controlled MF-FBSDE. We establish the stochastic maximum principle and verification theorem for this optimal control problem. We mention that our weakly coupled conditions introduced in studying the solvability for the MF-FBSDE can be applied to simultaneously guarantee the well-posedness of variational equation and adjoint equation which are both fully-coupled MF-FBSDE. As an application, we consider a Stackelberg differential game whose system is described by a McKean–Vlasov SDE. We give a necessary condition for the existence of Stackelberg solutions.

Number of life-years lost at the time of diagnosis and several years post-diagnosis in patients with solid malignancies: a population-based study in the Netherlands, 1989-2019.

Loss of life expectancy (LOLE) may provide more intuitive information on the impact of cancer than relative survival over a fixed time horizon (e.g., 5-year relative survival). We aimed to assess the evolution of the LOLE using a nationwide, population-based cohort including patients diagnosed with one of 17 most frequent solid malignancies. From the Netherlands Cancer Registry, we selected adult patients diagnosed with one of the 17 most frequent solid malignancies in the Netherlands during 1989-2019, with survival follow-up until 2022. We used flexible parametric survival models to estimate the LOLE at diagnosis and the LOLE after surviving several years post-diagnosis (conditional LOLE; CLOLE) by cancer type, calendar year, age, sex, and disease stage. For all cancers combined, the LOLE consistently decreased from 1989 to 2019. This decrease was most pronounced for males with prostate cancer (e.g., from 6.9 [95% confidence interval [CI], 6.7-7.1] to 2.7 [95% CI, 2.5-3.0] for 65-year-olds) and females with breast cancer (e.g., from 6.6 [95% CI, 6.4-6.7] to 1.9 [95% CI, 1.8-2.0] for 65-year-olds). The LOLE among patients with cancers of the head and neck or the central nervous system remained constant over time. Overall, the CLOLE showed that the life years lost among patients with cancer decreased with each additional year survived post-diagnosis. For example, the LOLE at diagnosis for 65-year-old females diagnosed with breast cancer in 2019 was 1.9 [95% CI, 1.8-2.0] compared with 1.7 [95% CI, 1.6-1.8], 1.0 [95% CI, 0.9-1.1], and 0.5 [95% CI, 0.5-0.6] when surviving one, five, and ten years post-diagnosis, respectively. Estimates for other combinations of patient and tumour characteristics are available in a publicly available web-based application. Our findings suggested that the evolution of LOLE substantially varies across cancer type, age, and disease stage. LOLE estimates help patients better understand the impact of their specific cancer diagnosis on their life expectancy. None.

A Stochastic Formulation to Evaluate the Sustainability of Structural Systems

During their life cycle, engineering systems typically suffer from deterioration due to aging and exposure to extreme events and harsh environmental conditions. As a result, regular or exceptional recovery strategies can be required to restore the system to a target structural performance level. This paper proposes a novel stochastic formulation for evaluating the sustainability of engineering systems as a function of their structural performance over a fixed time horizon. The life-cycle sustainability of the system is evaluated in terms of its cost and environmental impact, which includes the impact of the construction and possible recovery strategies. The formulation integrates state-dependent stochastic models that sequentially capture the effects of gradual and shock deterioration processes and the subsequent recovery processes on the system’s sustainability. Moreover, the formulation accounts for the relevant uncertainties, such as those in the external conditions (e.g., environmental exposure and potential hazards) and those in the environmental emissions associated with the materials and energy used throughout the system life cycle. The formulation uses the Renewal Theory-based Life-Cycle Analysis (RTLCA) formulation for a more computationally efficient evaluation of sustainability measures. As an illustration, the proposed analysis was used to evaluate the life-cycle sustainability of a typical reinforced concrete (RC) bridge.

On Data Collection in SIC-Capable Space–Air–Ground Integrated IoT Networks

This article considers routing and uplinks scheduling in space–air–ground integrated networks. Specifically, it considers a successive interference cancellation-capable unmanned aerial vehicle (UAV) that collects data from ground devices operating in an Internet of Things network. Its objective is to maximize the minimum flow rate to a terrestrial gateway over a fixed time horizon. It outlines a mixed integer linear program (MILP) to optimize in each time slot: the routing from the UAV to the gateway, the set of links from ground devices to the UAV, and the flow rate over links. It also proposes a novel algorithm, called iterative flow and path reservation (IFPR), for use by the UAV to select paths. Further, IFPR uses two methods to schedule communications between ground devices and the UAV. The first method, called simplified MILP (SMILP), aims to maximize the sum rate from ground devices. The second method, called less data schedule first, prioritizes ground devices that have uploaded the least amount of data to the gateway. Numerical results show satellite links help the UAV collects 61% more data from ground devices. Moreover, as compared to the MILP, IFPR collects 23% less data. Further, for both MILP and IFPR, their Jain’s fairness index reaches around one when the number of time slots is sufficiently large. Finally, when IFPR uses SMILP, the gateway collects more data but at the expense of fairness.

An application of optimal control in medical systems: optimal investment strategy in doctors.

Health care is ever more important with the aging population and with the increased awareness of the importance of the medical systems due to the corona crisis that showed the capacity of the health care infrastructure, especially in terms of numbers of health care personnel such as doctors, was not sufficient. Assuming that the number of doctors per patient is one of the determinants of patient satisfaction, optimal investments in new doctors, specialist doctors and foreign doctors are analyzed. Optimal Control Theory is employed to determine the optimal investment strategy for new doctors (new graduates), specialists and foreign doctors to maximize the net (of costs) patient satisfaction over a fixed time horizon. It is found that a nation with an insufficient number of total doctors and specialist doctors at the beginning of the planning horizon should increase the investment in new doctors as a quadratic function of time, increase the local specialist doctors linearly, while employing foreign doctors as to equate their cost to the marginal satisfaction of patients.

Cleaning Schedule Optimization of Heat Exchanger Network Using Moving Window Decision-Making Algorithm

A moving window decision-making algorithm is proposed for the cleaning schedule optimization of heat exchanger network system subject to fouling in refinery crude preheat train. This algorithm is designed by incorporating the moving window scheme into a conventional multi-period optimal control problem (OCP) framework and has a distinct feature that it can efficiently handle a complex problem where a long-time horizon is considered. When compared with the conventional multi-period OCP method using fixed time horizon, our algorithm always shows an excellent performance regarding the computational time, still finding a compatible optimal solution. In our moving window decision-making algorithm, it is important to determine the optimal moving window size for the given time horizon as it significantly influences the optimization performance.

Asymptotics of a time bounded cylinder model

AbstractOne way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb {R}^d$ and a random direction movement scheme. Given a fixed time horizon $T>0$, we model these movements via cylinders in $\mathbb {R}^d \times [0,T]$. In this work, we derive central limit theorems for functionals of the union of these cylinders. The volume and the number of isolated cylinders and the Euler characteristic of the random set are considered and give an answer to the achievable throughput, the availability of nodes, and the topological structure of the network.

Assessing Performance and Clinical Usefulness in Prediction Models With Survival Outcomes: Practical Guidance for Cox Proportional Hazards Models.

Risk prediction models need thorough validation to assess their performance. Validation of models for survival outcomes poses challenges due to the censoring of observations and the varying time horizon at which predictions can be made. This article describes measures to evaluate predictions and the potential improvement in decision making from survival models based on Cox proportional hazards regression. As a motivating case study, the authors consider the prediction of the composite outcome of recurrence or death (the "event") in patients with breast cancer after surgery. They developed a simple Cox regression model with 3 predictors, as in the Nottingham Prognostic Index, in 2982 women (1275 events over 5 years of follow-up) and externally validated this model in 686 women (285 events over 5 years). Improvement in performance was assessed after the addition of progesterone receptor as a prognostic biomarker. The model predictions can be evaluated across the full range of observed follow-up times or for the event occurring by the end of a fixed time horizon of interest. The authors first discuss recommended statistical measures that evaluate model performance in terms of discrimination, calibration, or overall performance. Further, they evaluate the potential clinical utility of the model to support clinical decision making according to a net benefit measure. They provide SAS and R code to illustrate internal and external validation. The authors recommend the proposed set of performance measures for transparent reporting of the validity of predictions from survival models.