Robust Optimization Framework Research Articles

Variational quantum circuit learning-enabled robust optimization for AI data center energy control and decarbonization

As the demand for artificial intelligence (AI) models and applications continues to grow, data centers that handle AI workloads are experiencing a rise in energy consumption and associated carbon footprint. This work proposes a variational quantum computing-based robust optimization (VQC-RO) framework for control and energy management in large-scale data centers to address the computational challenges and overcome limitations of conventional model-based and model-free strategies. The VQC-RO framework integrates variational quantum circuits (VQCs) with classical optimization to enable efficient and uncertainty-aware control of energy systems in AI data centers. Quantum algorithms executed on noisy intermediate-scale quantum (NISQ) devices are used for value function estimation trained with Q-learning, leading to the formulation of a robust optimization problem with uncertain coefficients. The quantum computing-based robust control strategy is designed to address uncertainties associated with weather conditions and renewable energy generation while optimizing energy consumption in AI data centers. This work also outlines the computational experiments conducted at various AI data center locations in the United States to analyze the reduction in power consumption and carbon emission levels associated with the proposed quantum computing-based robust control framework. This work contributes a novel approach to energy-efficient and sustainable data center operation, promising to reduce carbon emissions and energy consumption in large-scale data centers handling AI workloads by 9.8 % and 12.5 %, respectively.

Robust Design Optimization of Electric Machines with Isogeometric Analysis

In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.

Rank-1 transition uncertainties in constrained Markov decision processes

We consider an infinite-horizon discounted constrained Markov decision process (CMDP) with uncertain transition probabilities. We assume that the uncertainty in transition probabilities has a rank-1 matrix structure and the underlying uncertain parameters belong to a polytope. We formulate the uncertain CMDP problem using a robust optimization framework. To derive reformulation of the robust CMDP problem, we restrict to the class of stationary policies and show that it is equivalent to a bilinear programming problem. We provide a simple example where a Markov policy performs better than the optimal policy in the class of stationary policies, implying that, unlike in classical CMDP problem, an optimal policy of the robust CMDP problem need not be present in the class of stationary policies. For the case of a single uncertain parameter, we propose sufficient conditions under which an optimal policy of the restricted robust CMDP problem is unaffected by uncertainty. The numerical experiments are performed on randomly generated instances of a machine replacement problem and a well-known class of problems called Garnets.

Integrated optimisation of strategic planning and service operations for urban air mobility systems

With the rapid development of novel vehicle technologies, electric vertical take-off and landing (eVTOL) vehicles are becoming a new transport servicing model to achieve better urban air mobility (UAM) systems. The UAM systems can efficiently utilise low-altitude airspace resources, providing a solution to alleviate congestion in urban ground traffic. This paper delves into an integrated optimisation problem aimed at addressing decision-making processes related to the strategic planning and service operation of UAM systems, considering both demand uncertainty and spatial equity. The problem encompasses various decision components, including parking stand numbers at vertiports and vertistops, eVTOL fleet sizing as well as eVTOL fleet allocation and operations. Additionally, we introduce a spatial equity metric and establish a bi-objective optimisation model to balance the trade-off between service profitability and spatial equity considerations. We transform the bi-objective optimisation model to a tractable single-objective formulation using ε-constraint approach and linearisation technique. In this paper, we employ a scenario-based robust optimisation framework that incorporates the interval robust method to capture the demand uncertainty, enhancing resilience against uncertain factors. We evaluate the model performance using a small-scale example and further validate the proposed model through a real-world case study. Numerical analysis results demonstrate that the scenario-based robust optimisation framework can ensure the robustness of decision-making against the effect of uncertain conditions. Furthermore, numerical experiments reveal a trade-off between profitability and spatial equity, potentially requiring a partial sacrifice of profit to attain a desired equity level. Finally, we propose valuable policy recommendations to guide the decision-making processes of UAM service providers.

An ADMM-enabled robust optimization framework for self-healing scheduling of smart grids integrated with smart prosumers

Enhancing the reliability of energy networks and minimizing downtime is crucial, making self-healing smart grids indispensable for ensuring a continuous power supply and fortifying resilience. As smart grids increasingly incorporate decentralized prosumers, innovative coordination strategies are essential to fully exploit their potential and improve system self-healing capabilities. To address this need, this paper presents a novel bi-level strategy for managing the self-healing process within a smart grid influenced by Hydrogen Refueling Stations (HRSs), Electric Vehicle Charging Stations (EVCSs), and energy hubs. This approach taps into the combined potential of these prosumers to boost system self-healing speed and reliability. In the initial stage, the Smart Grid Operator (SGO) conducts self-healing planning during emergencies, communicating required nodal capacities to prevent forced load shedding and outlining incentives for smart prosumers. Subsequently, prosumers schedule their activities and contribute flexible capacities to the SGO. Bridging the first and second stages, an adaptive Alternating Direction Method of Multipliers (ADMM) algorithm ensures convergence between the SGO and prosumer schedules within a decentralized framework. This strategy underwent implementation on a 118-node distribution system using GAMS. Results demonstrate that the proposed concept reduces Forced Load Shedding (FLS) by 32.04% and self-healing costs by 17.48% through effective utilization of smart prosumers' flexible capacities. Furthermore, outcomes indicate that the SGO reduces FLS by 6.69% by deploying Mobile Electrical Energy Storages (MEESs) and Mobile Fuel Cell Trucks (MFCTs) to critical nodes.

An efficient and robust shape optimization framework for gridshell designs based on node shifting method

In this paper, a novel and efficient shape optimization framework for freeform gridshell designs, especially for cantilevering structures, is proposed based on the node shifting method. The nodal coordinates are directly chosen as the design variables without any extra parameterization, and are iteratively updated to minimize the structural compliance. The distributed load filter is introduced for a smoother and more efficient shape updating scheme, where the negative sensitivity numbers are applied as the virtual external load for the shape updating analysis to guarantee both the smoothness of surfaces and the sustained reduction of structural compliance at each step. The penalized volume adjustment subroutine is then applied to satisfy the volume constraint and to improve the uniformity of grids. Compared to the conventional nodal shifting methods, it is observed that a much more stable and faster convergence is achieved. A variety of examples are presented to demonstrate the improved effectiveness and the efficiency of the proposed algorithm.

Iterative learning robust optimization - with application to medium optimization of CHO cell cultivation in continuous monoclonal antibody production

In the presence of uncertainty, the optimum obtained based on a nominal identified model can neither provide any performance guarantee nor ensure that critical constraints are satisfied, which is crucial for e.g., bioprocess applications characterized by a high degree of complexity combined with costly experiments. Hence, uncertainty should be considered in the optimization and, furthermore, experiments designed to reduce the uncertainty most important for optimization. Herein, we propose a general framework that combines model-based robust optimization with optimal experiment design. The proposed framework can take advantage of prior knowledge in the form of a mechanistic model structure, and the importance of this is demonstrated by comparing it to more standard black-box models typically employed in learning. Through optimal experiment design, we repeatedly reduce the uncertainty most relevant for optimization so as to maximize the potential for improving the worst-case performance by balancing between exploration and exploitation. This makes the proposed method an efficient model-based robust optimization framework, especially in cases with limited experimental resources. The main part of the paper focuses on the case with modeling uncertainty that can be reduced with the availability of more experimental data. Towards the end of the paper, we consider extending the method to also include inherent uncertainty, such as input uncertainty and unmeasured disturbances. The effectiveness of the method is illustrated through a realistic simulation case study of medium optimization of Chinese hamster ovary cell cultivation in continuous monoclonal antibody production, where the metabolic network consists of 23 extracellular metabolites and 126 reactions.

Distributed robust scheduling optimization for energy system of steel industry considering prediction uncertainties

Predictive scheduling is commonly deployed for the energy systems in the steel industry, while the uncertainties caused by the predictions can lead to under-optimization or over-adjustment. In order to solve this problem, a novel distributed robust optimization framework is proposed in this study. A Robust Optimization (RO) model is established at first to mathematically address the prediction uncertainties, where the gas, steam, and electricity networks are considered as distributed participants, with their operating costs and CO2 emissions costs as the objectives for minimization. Then the vanilla 2-block Alternating Direction Multiplier Method (ADMM) is extended to a 3-block structure in this study for solving the established RO model in a distributed manner. Considering the superiority on efficiency, the Column-and-Constraint Generation (C&CG) algorithm is deployed for each block. To ensure convergence considering the extensive interaction between the updated dual and coupling variables in each iteration of the overall ADMM and each C&CG, an adaptive bridging method is developed in this study. Finally, experiments using real data from a steel plant in China demonstrate that the proposed framework has a deviation of less than 1.33 % while with higher efficiency and better robustness compared to other algorithms.

Multidisciplinary Robust Design Optimization Incorporating Extreme Scenario in Sparse Samples

Abstract Robust design optimization (RDO) is a potent methodology that ensures stable performance in designed products during their operational phase. However, there remains a scarcity of robust design optimization methods that account for the intricacies of multidisciplinary coupling. In this article, we propose a multidisciplinary robust design optimization (MRDO) framework for physical systems under sparse samples containing the extreme scenario. The collaboration model is used to select samples that comply with multidisciplinary feasibility, avoiding time-consuming multidisciplinary decoupling analyses. To assess the robustness of sparse samples containing the extreme scenario, linear moment estimation is employed as the evaluation metric. The comparative analysis of MRDO results is conducted across various sample sizes, with and without the presence of the extreme scenario. The effectiveness and reliability of the proposed method are demonstrated through a mathematical case, a conceptual aircraft sizing design, and an energy efficiency optimization of a hobbing machine tool.

Advanced tree‐seed optimization based fractional‐order PID controller design for simplified decoupled industrial tank systems

AbstractControlling coupled tank systems is challenging due to interactions between tanks, nonlinear dynamics, time delays, uncertainties, and cross‐coupling effects. The design of effective control strategies to address these complexities while ensuring stability and robust performance is difficult. Hence, this study focuses on presenting an innovative approach to enhance level control in coupled tank systems by employing a fractional‐order proportional‐integral‐derivative (FOPID) controller. The FOPID controller is designed by imposing constraints on the performance metric and closed‐loop gain. Besides, the defined optimization problem is solved by employing a tree seed algorithm. Further, the stability is analyzed graphically using the singular value analysis. The inherent complexities of coupled tank systems are effectively addressed by designing decouplers. The unique characteristics of the tree seed algorithm to navigate complex solution spaces and its effective handling of constraints offer a robust optimization framework. The validity and efficiency of the proposed method are analyzed in a range of simulation experiments conducted on distinct interconnected tank systems. Besides, the stability is verified graphically. The analysis highlights the effectiveness of the control law in handling uncertainties and disturbances. Besides, the proposed method reduces the settling time to around . Through a systematic integration of optimization and comprehensive stability analysis, the study provides a holistic solution for optimizing level control in coupled tank systems.

An innovative method for building electricity energy management in smart homes based on electric vehicle energy capacity

The surging demand for electricity, fueled by environmental concerns, economic considerations, and the integration of distributed energy resources, underscores the need for innovative approaches to smart home energy management. This research introduces a novel optimization algorithm that leverages electric vehicles (EVs) as integral components, addressing the intricate dynamics of household load management. The study’s significance lies in optimizing energy consumption, reducing costs, and enhancing power grid reliability. Three distinct modes of smart home load management are investigated, ranging from no household load management to load outages, with a focus on the time-of-use (ToU) tariff impact, inclining block rate (IBR) pricing, and the combined effect of ToU and IBR on load management outcomes. The algorithm, a multi-objective approach, minimizes the peak demand and optimizes cost factors, resulting in a 7.9% reduction in integrated payment costs. Notably, EVs play a pivotal role in load planning, showcasing a 16.4% reduction in peak loads and a 7.9% decrease in payment expenses. Numerical results affirm the algorithm’s adaptability, even under load interruptions, preventing excessive increases in paid costs. Incorporating dynamic pricing structures like inclining block rates alongside the time of use reveals a 7.9% reduction in payment costs and a 16.4% decrease in peak loads. In conclusion, this research provides a robust optimization framework for smart home energy management, demonstrating economic benefits, peak load reduction potential, and enhanced reliability through strategic EV integration and dynamic pricing.

Managing Coins for Depository Institutions in Coin Supply Chains for Improved Circulation

We study the U.S. Coin Supply Chain from both the demand and supply side perspectives to improve coin circulation in the economy. More specifically, we provide an operating policy for Depository Institutions (DIs) to improve their efficiency in packaging, distributing, coordinating, and managing the inventory of coins. We further propose a new policy (via a Rewards Program) to increase coin circulation in the economy and optimally determine a reward price, which, if implemented by the Federal Reserve System (FRS), can incentivize DIs to process the coins themselves and/or frequently deposit excess coins at the FRS. We identify the structures of DIs’ best response to the reward price and FRS’s optimal pricing policy. The results and insights developed in this study can be beneficial to both the FRS and DIs in increasing the efficiency of the nation’s coin circulation and thereby reducing their operating costs. Additionally, to estimate the societal benefit from the Rewards Program, we formulate the coin flow for an entire FRS region as an optimization problem from the supply side perspective and quantify the societal costs (and benefits) with and without the reward. We show via numerical experiments that both the FRS and Dis reduce their operating costs as a result of the program and produce a surplus benefit for the society. The reward price that maximizes this surplus is determined optimally. We also propose a robust optimization framework to help DIs and the FRS to manage their inventory under uncertain demand while attaining their cost reduction goals.

A tri-level Typhoon-DAD robust optimization framework to enhance distribution network resilience

Extreme natural disasters such as typhoon often cause failures in distribution networks within a short time, and even lead to large area blackouts. We propose a tri-level robust optimization framework that combines pre-disaster, in-disaster and post-disaster strategy comprehensively to enhance distribution network resilience. The typhoons are regarded as attackers, and a tri-level Defender-Attacker-Defender model for typhoon disaster is used to integrate multiple resilience resources. In the first level, line hardening and distributed generation unit commitment are used to improve resilience in pre-disaster. The second level contains attack budget, attack time, hardening budget, repair time and load loss. It couples with the third level iteratively to generate the worst failure scenario under typhoon. In the third level, the Nested Column-and-Constraint Generation algorithm is used to solve distribution network reconfiguration and intentional islanding. Simulation time is spanned to the entire 24-hour disaster day. In the end, the proposed framework is tested through a case study using real data from super typhoon “Mangkhut” (2018) in Yangjiang, China. The result shows that it can effectively reduce load loss under the worst typhoon scenario and enhance distribution network resilience with limited resources.

Physics-informed machine learning for reservoir management of enhanced geothermal systems

With the energy demand arising globally, geothermal recovery by Enhanced Geothermal Systems (EGS) becomes a promising option to bring sustainable energy supply along with mitigating CO2 emission. However, reservoir management of EGS primarily relies on reservoir simulation, which is quite expensive due to the reservoir heterogeneity, the interaction of matrix and fractures, and the intrinsic multi-physics coupled nature. Therefore, a robust optimization framework is critical for the management of EGS. We develop a general Physics-Informed Machine Learning (PIML) framework for reservoir management with multiple optimization options. A robust forward surrogate model fl is developed based on a convolutional neural network, and it successfully learns the nonlinear relationship between input reservoir model parameters (e.g., fracture permeability field) and interested state variables (e.g., temperature field and produced fluid temperature). fl is trained using simulation data from the EGS coupled thermal-hydro simulation model by sampling reservoir model parameters. As fl is accurate, efficient and fully differentiable, EGS thermal efficiency can be optimized following two schemes: (1) training a control network fc to map reservoir geological parameters to reservoir decision parameters by coupling it with fl; (2) directly optimizing the reservoir decision parameters based on coupling the existing optimizers with fl. We evaluate the impact of reservoir model parameters on the thermal recovery based on simulation datasets through sensitivity analyses, and demonstrated that injection mass rate dominates thermal recovery. Further, the forward model fl performs accurate and stable predictions of evolving temperature fields (relative error 1.27 ± 0.89%) in EGS and the time series of produced fluid temperature (relative error 0.26 ± 0.46%), and its speedup to the counterpart high-fidelity simulator is 4564 times. When optimizing with fc, we achieve thermal recovery with a reasonable accuracy but significantly low CPU time during inference, 0.11 seconds/task. When optimizing with Adam optimizer, we achieve the objective perfectly with relatively high CPU time, 4.58 seconds/task. This is because the former optimization scheme requires a training stage for fc but its inference is non-iterative, while the latter scheme requires an iterative inference without training. We also investigate the option to use fc inference as an initial guess for Adam optimizer, which decreases Adam’s CPU time but achieves excellent convergence in the objective function. This is the highest recommended option among the three evaluated. The efficiency, scalability and accuracy observed in our reservoir management framework makes it highly applicable to near real-time reservoir management in EGS as well as other similar system management processes.

A robust optimal control framework for controlling aberrant RTK signaling pathways in esophageal cancer.

This study presents a new framework for obtaining personalized optimal treatment strategies targeting aberrant signaling pathways in esophageal cancer, such as the epidermal growth factor (EGF) and vascular endothelial growth factor (VEGF) signaling pathways. A new pharmacokinetic model is developed taking into account specific heterogeneities of these signaling mechanisms. The optimal therapies are designed to be obtained using a three step process. First, a finite-dimensional constrained optimization problem is solved to obtain the parameters of the pharmacokinetic model, using discrete patient data measurements. Next, a sensitivity analysis is carried out to determine which of the parameters are sensitive to the evolution of the variants of EGF receptors and VEGF receptors. Finally, a second optimal control problem is solved based on the sensitivity analysis results, using a modified pharmacokinetic model that incorporates two representative drugs Trastuzumab and Bevacizumab, targeting EGF and VEGF, respectively. Numerical results with the combination of the two drugs demonstrate the efficiency of the proposed framework.

Sosyal Medya Reklam Platformu Seçimi için Yeni Bir Dayanıklı Teorik Yaklaşım

Social media advertisement is one of the hottest topics of marketing. This study aims to investigate the selection of social media advertising platforms with a worst-case analysis. In this scope, we propose a novel fuzzy multi-criteria decision making (MCDM) approach based on the robust portfolio optimization framework. We call it the Robust Theoretical Fuzzy Evaluation System (R-FES). We use a case study in the literature to demonstrate R-FES and compare its results with Fuzzy VIKOR’s results. We find with R-FES that the social media advertisement budget should be allocated almost equally. We also find that Spearman’s rank correlation of Fuzzy VIKOR and R-FES results equals -0.5643. That is, they give very different rankings. We emphasize that these results are specific to the case study and thus can not be generalized.

SOLVING THE TASK OF LOCAL OPTIMA TRAPS IN DATA MINING APPLICATIONS THROUGH INTELLIGENT MULT-AGENT SWARM AND ORTHOPAIR FUZZY SETS

Local optima traps pose a significant challenge in optimizing complex problems, particularly in data mining applications, where traditional algorithms may get stuck in suboptimal solutions. This study addresses this issue by combining the power of intelligent multi-agent swarm algorithms and orthopair fuzzy sets to enhance optimization processes. We propose a novel approach that leverages the collective intelligence of a multi-agent swarm system, enabling effective exploration and exploitation of solution spaces. Additionally, orthopair fuzzy sets are introduced to model and represent uncertainties inherent in data mining tasks, providing a more robust optimization framework. Our work contributes to the advancement of optimization techniques in data mining by offering a synergistic solution to local optima traps. The integration of intelligent multi-agent swarms and orthopair fuzzy sets enhances the algorithm’s adaptability and resilience, leading to improved convergence and better solutions. Experimental results demonstrate the efficacy of our proposed approach in overcoming local optima traps, showcasing superior performance compared to traditional algorithms. The hybrid system exhibits increased convergence rates and consistently discovers more accurate and diverse solutions across various data mining scenarios.

Robust Ordering Policies with Limited Information on Stochastic Lead Time

Lead time is a rather uncertain factor in manufacturing and inventory systems. In fact, it is always difficult to know the full information of stochastic lead time distribution. So a problem arises how a decision maker decides its ordering policy including advance ordering time, based on historically limited information. In this paper, this problem is solved under a robust-optimization framework, and the minimax regret criterion is adopted. We first derive the decision maker’s robust ordering policies only with the range or the mean of stochastic lead time distribution respectively. The corresponding maximum regret, in other words, the value of full information is then derived. It is shown that when the decision maker uses the range to make decisions, this robust ordering policy exactly minimizes the realized costs if the average of the lower and higher limits of the range equals the realized lead time. When the decision maker uses the means to make decisions, the uncertainty of lead time distribution would lead the decision maker to place the order less in advance. Besides, this uncertainty would cause significant additional costs, especially when the mean is large.

Probabilistic Forecasting-Based Reserve Determination Considering Multi-Temporal Uncertainty of Renewable Energy Generation

Operating reserve, among the most important ancillary services, is a powerful prescription for mitigating increasing uncertainty of renewable generation. Traditional reserve determination neglects uncertainty of renewable generation variations within the dispatch interval, which cannot gurantee sufficient reserve deliverability in real-time operation. This paper proposes a probabilistic forecasting-based reserve determination method to efficiently deal with multi-temporal uncertainty of renewable energy in power systems. A novel probabilistic forecasting approach is proposed by integrating Dirichlet process Gaussian mixture model into bootstrap-based extreme learning machine. A unified uncertainty model is constructed for depicting both interval-averaged uncertainty and intra-interval uncertainty by combing the probabilistic forecasts and linearized Itô-process model. In current business practices of many independent system operators, the coordinated determination of two well-designed reserve products, including regulating reserve and ramp capability reserve, is formulated in a two-stage robust optimization framework. A Bernstein polynomial-based model reformulation approach is then employed to handle the existing heterogeneity in the sub-models of each stage. Consequently, the integrated reserve determination is embedded in a generic two-stage robust optimization problem, which can be efficiently solved by the adopted modified column-and-constraint generation method. Finally, numerical simulations are implemented to validate the effectiveness and profitability of the proposed approach.

Inventory planning for self-serve pharmacy kiosks: A fill rate maximization approach

In recent years, self-serve kiosks have become increasingly popular due to their 24/7 availability and lower setup and operational costs compared to traditional brick-and-mortar stores. However, the inventory planning for pharmacy kiosks is a challenge due to its limited capacity to store thousands of drugs ordered in various quantities, each with low and sporadic drug demand. In this work, we model the pharmacy kiosk inventory planning problem as a capacitated multiproduct newsvendor problem under fill rate maximization objective. We present a data-driven robust optimization framework where product demand lies within an uncertainty set generated from product clustering. A column-and-constraint generation based solution approach is proposed to solve industry scale instances. The proposed robust framework is tested on actual pharmacy sales data and randomly generated instances with 2000 products. The robust solutions outperform scenario-based stochastic solutions with an increase in out-of-sample fill rate of 5.8%, on average, and of up to 17%. Comparative analysis with profit objective reveals that the fill rate objective results in 17% higher out-of-sample fill rate by compromising 20% in profits, on average.