Robust Design Optimization via Failure Domain Bounding

[1] The objective of the least cost design problem of a water distribution system is to find its minimum cost with discrete diameters as decision variables and hydraulic controls as constraints. The goal of a robust least cost design is to find solutions which guarantee its feasibility independent of the data (i.e., under model uncertainty). A robust counterpart approach for linear uncertain problems is adopted in this study, which represents the uncertain stochastic problem as its deterministic equivalent. Robustness is controlled by a single parameter providing a trade-off between the probability of constraint violation and the objective cost. Two principal models are developed: uncorrelated uncertainty model with implicit design reliability, and correlated uncertainty model with explicit design reliability. The models are tested on three example applications and compared for uncertainty in consumers' demands. The main contribution of this study is the inclusion of the ability to explicitly account for different correlations between water distribution system demand nodes. In particular, it is shown that including correlation information in the design phase has a substantial advantage in seeking more efficient robust solutions.

In this paper, a new strategy for modeling uncertainties in the substructures and interfaces of a dynamical system is presented. This strategy is based on (1) the reduction in the dynamical model of each substructure using the Craig–Bampton method and (2) the use of the nonparametric probabilistic approach for the global modeling of uncertainties in each substructure. As an improvement with respect to existing nonparametric methods, the methodology proposed here constructs separated models of uncertainties for the inner and interface degrees of freedom, which allows to control separately the levels of fluctuation induced by these two sources of uncertainties. This methodology is applied for the analysis of the random vibration of a drill-string. Three strategies are compared: (1) a full nonparametric probabilistic approach on all the system, (2) the existing nonparametric probabilistic approach together with the Craig–Bampton substructuring method, and (3) the new nonparametric probabilistic approach proposed here with the separation of the inner and interface degrees of freedom uncertainties. It turns out that, for the same level of uncertainty, the three approaches give similar results, but the new approach gives more flexibility for the control of the probabilistic model.

Variable fidelity robust optimization of pulsed laser orbital debris removal under epistemic uncertainty

The current energy transition and the underlying growth in variable and uncertain renewable-based energy generation challenge the proper operation of power systems. Classical probabilistic uncertainty models, e.g., stochastic programming or robust optimisation, have been used widely to solve problems such as the day-ahead energy and reserve dispatch problem to enhance the day-ahead decisions with a probabilistic insight of renewable energy generation in real-time. By doing so, the scheduling of the power system becomes, production and consumption of electric power, more reliable (i.e., more robust because of potential deviations) while minimising the social costs given potential balancing actions. Nevertheless, these classical models are not valid when the uncertainty is imprecise, meaning that the system operator may not rely on a unique distribution function to describe the uncertainty. Given the Distributionally Robust Optimisation method, our approach can be implemented for any non-probabilistic, e.g., interval models rather than only sets of distribution functions (ambiguity set of probability distributions). In this paper, the aim is to apply two advanced non-probabilistic uncertainty models: Interval and ϵ-contamination, where the imprecision and in-determinism in the uncertainty (uncertain parameters) are considered. We propose two kinds of theoretical solutions under two decision criteria—Maximinity and Maximality. For an illustration of our solutions, we apply our proposed approach to a case study inspired by the 24-node IEEE reliability test system.

We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and provide novel learnability conditions for the underlying algorithms. We then consider different constrained optimization problems affected by uncertainty represented by means of scenarios. We show that the compression learning perspective provides a unifying framework for scenario based optimization, since the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that satisfies some consistency assumption. To illustrate this, we revisit the scenario approach within the developed context. Moreover, using the compression learning machinery we provide novel results on the probability of constraint violation for the class of cascading optimization problems.

We consider the sensor deployment problem in the context of distance uncertainty. It is characterized by differentiated arrangement of specific detection probability thresholds at different locations. The problem is formulated as an integer linear programming (ILP) model firstly, aiming at optimizing the number of sensors and their locations. Based on the robust discrete optimization methodology, the uncertain model is transformed into an equivalent ILP problem considering distance uncertainty. The proposed approach can control the tradeoff between optimality and robustness by varying the parameters named protection levels. Uniform and non-uniform event detection probabiliy distributions are considered in the experiment. The results show that, as the distance uncertainty increases, the constraint violation can be avoided in the robust model and the robust solution can provide a significant improvement at the expense of a small loss in optimality when compared to the optimal solution of a deterministic scenario.

Integrated energy system (IES) is considered as an effective system to integrate high penetration of intermittent renewable generation and achieve China’s national goal of reaching peak carbon emission by 2030 and carbon neutrality by 2060. As a result, there have been significant advancements over the recent years in IES modeling, planning, and operation, especially the treatment of uncertainty factors. This paper reviews the development of IES planning approaches focusing on modeling of uncertainty factors. Firstly, coordinated IES planning frameworks, processes and techniques are surveyed and categorized including their application scenarios, advantages and disadvantages, they are then compared with traditional grid planning. Secondly, the modeling of uncertainty factors was systematically reviewed and summarized. IES planning methods under uncertainty are further divided into a number of categories, such as probability optimization, stochastic optimization, robust optimization, possibility and mixed probability-possibility optimization. The uncertainty modeling methodologies are summarized and compared, including applications of uncertainty models in different situations. Finally, discussions on development trends, challenges and research directions in uncertainty modeling for IES planning are presented and recommendations are made.

An evidence-based robust optimization method for pulsed laser orbital debris removal (LODR) is presented. Epistemic type uncertainties due to limited knowledge are considered. The objective of the design optimization is set to minimize the debris lifetime while at the same time maximizing the corresponding belief value. The Dempster–Shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used to model and compute the uncertainty impacts. A Kriging based surrogate is used to reduce the cost due to the expensive numerical life prediction model. Effectiveness of the proposed method is illustrated by a set of benchmark problems. Based on the method, a numerical simulation of the removal of Iridium 33 with pulsed lasers is presented, and the most robust solutions with minimum lifetime under uncertainty are identified using the proposed method.

A probabilistic model and software tool for evaluating the long-term performance of landfill covers

A novel two stage robust optimization model is presented in this research paper for scheduling of multi-energy Combined Cooling, Heating, and Power (CCHP) microgrid. This model will effectively address uncertainties in renewable energy source (RES) generation. The approach presented employs a twostage framework that integrates Maximum Entropy Ellipsoid (MEE) uncertainty modelling, the Big-M method, and the Column and Constraint Generation (C&CG) algorithm. The MEE set look after realistic uncertainties by accounting for correlations between RES sources, like wind turbine (WT) or photovoltaic (PV). These RES are often influenced by shared environmental factors. The Big-M method guarantees efficient handling of conditional constraints within the optimization, especially critical in scenarios. C&CG method is used to solve the Two Stage Robust Optimization model, which utilizes worst-case scenarios under MEE balancing both robust feasibility and computational efficiency. Through this robust optimization approach, the study aims to minimize operational costs, reduce CO2 emissions, and improve the overall reliability of energy supply. Special attention is given to managing demand-side responses and incorporating real-time energy consumption patterns, ultimately leading to a more sustainable and cost-effective energy solution for CCHP microgrids in the face of volatile renewable energy conditions.

In this paper, we consider chance-constrained Stochastic Model Predictive Control problems for uncertain linear systems subject to additive disturbance. A popular method for solving the associated chance-constrained optimization problem is by means of randomization, in which the chance constraints are replaced by a finite number of sampled constraints, each corresponding to a disturbance realization. Earlier approaches in this direction lead to computationally expensive problems, whose solutions are typically very conservative both in terms of cost and violation probabilities. One way of overcoming this conservatism is to use piecewise affine (PWA) policies, which offer more flexibility than conventional open-loop and affine policies. Unfortunately, the straight-forward application of randomized methods towards PWA policies will lead to computationally demanding problems, that can only be solved for problems of small sizes. To address this issue, we propose an alternative method based on a combination of randomized and robust optimization. We show that the resulting approximation can greatly reduce conservatism of the solution while exhibiting favorable scaling properties with respect to the prediction horizon.

For decades now, the notion of "performance" has been synonymous with "speed" (as measured in FLOPS, short for floating-point operations per second). Unfortunately, this particular focus has led to the emergence of supercomputers that consume egregious amounts of electrical power and produce so much heat that extravagant cooling facilities must be constructed to ensure proper operation. In addition, the emphasis on speed as the performance metric has caused other performance metrics to be largely ignored, e.g., reliability, availability, and usability. As a consequence, all of the above has led to an extraordinary increase in the total cost of ownership (TCO) of a supercomputer. Despite the importance of the TOP500 List, we argue that the list makes it much more difficult for the high-performance computing (UPC) community to focus on performance metrics other than speed. Therefore, to raise awareness to other performance metrics of interest, e.g., energy efficiency for improved reliability, we propose a Green500 List and discuss the potential metrics that would be used to rank supercomputing systems on such a list.

Interval‐based multi‐objective robust optimization aims to achieve high‐performance solutions insensitive to uncertainty, has garnered significant attention. However, efficiently analyzing the maximum fluctuations of solutions in both objective and constraint functions to assess their robustness remains challenging. To address this issue, this article proposes an adaptive coevolution method, which can evaluate the maximum fluctuations of multiple candidate solutions with respect to a function in a single run. This method is integrated with the multi‐objective evolutionary algorithm (MOEA) to develop a framework termed adaptive coevolution‐based multi‐objective robust optimization (AC‐MORO) for solving multi‐objective robust optimization problems. To evaluate the performance of AC‐MORO, it is compared with MODE‐RO on a set of benchmark problems; meanwhile, a performance metric is proposed to test the accuracy of the adaptive coevolution method in analyzing the robustness of solutions. The impact of various parameter settings on the efficiency of the proposed method is also investigated. Subsequently, a variant of the adaptive coevolution method is explored to further enhance the performance of AC‐MORO. Finally, AC‐MORO is applied to address robust optimization problems in practical engineering.

This work proposes a novel data-driven robust model predictive control (DDRMPC) framework for automatic control of greenhouse in-door climate. The framework integrates dynamic control models of greenhouse temperature, humidity, and CO₂ concentration level with data-driven robust optimization models that accurately and rigorously capture uncertainty in weather forecast error. Data-driven uncertainty sets for ambient temperature, solar radiation, and humidity are constructed from historical data by leveraging a machine learning approach, namely, support vector clustering with weighted generalized intersection kernel. A training-calibration procedure that tunes the size of uncertainty sets is implemented to ensure that data-driven uncertainty sets attain an appropriate performance guarantee. In order to solve the optimization problem in DDRMPC, an affine disturbance feedback policy is utilized to obtain tractable approximations of optimal control. A case study of controlling temperature, humidity, and CO₂ concentration of a semiclosed greenhouse in New York City is presented. The results show that the DDRMPC approach ends up with 14% and 4% lower total cost than rule-based control and robust model predictive control with L₁-norm-based uncertainty set, respectively. The constraint violation probability, which is the percentage of time that the greenhouse system states violate the constraint throughout the whole growing period, for DDRMPC is only 0.39%. Hence, the proposed DDRMPC framework can prevent the greenhouse climate from becoming harmful to plants and fruits. In conclusion, the proposed DDRMPC approach can improve the greenhouse climate control performance and reduce cost compared with other control strategies.

Abstract: Effective stochastic and robust optimisation in cloud and network operations depends critically on the realism of the underlying uncertainty models. Many existing studies rely on simplistic independent and identically distributed assumptions or coarse aggregate demand profiles, which fail to represent temporal patterns, correlations, and extreme events. This study develops a stochastic modelling and scenario generation framework tailored to cloud workload and network traffic inputs for operations research models. Using data produced by CloudSim and NS-3, as well as representative trace datasets, large volumes of time series are preprocessed with Hadoop and Apache Spark. Statistical and econometric models, including ARIMA, vector autoregression, and panel data formulations, are estimated in R, statsmodels, Stata, SPSS, and EViews to capture temporal dynamics and cross-sectional dependencies. Scenario generation procedures derive multi-period demand and traffic paths consistent with these models, with calibration and validation performed via distributional tests and forecast error metrics. Numerical illustrations demonstrate that stochastic optimisation models fed by the proposed scenario sets yield decisions that are more robust to demand spikes and structural changes than models using naive or static assumptions. The framework provides a systematic bridge between data-driven uncertainty modelling and scenario-based optimisation in digital infrastructure. Keywords: stochastic modeling, scenario generation, cloud computing, network traffic, time-series analysis, econometric modeling, stochastic programming, demand uncertain