Robust Optimization Approach Research Articles

Robust global optimization of plasmonic filter based on Q factor analysis using graded index

Abstract To reduce the impact of uncertainties in various manufacturing processes while maintaining satisfactory performance level, we propose a robust global optimization approach for plasmonic filters based on extraordinary optical transmission by use of Q factor analysis with reasonable computational cost. The gradient index is employed as a metric for robustness, and the multiobjective genetic algorithm is selected as a global optimization tool. The figures of merit and gradient index are chosen as two objective functions with the design variables being the slit width, slit height, and period of the slit array, respectively. The finite element method is employed to investigate a variety of optical properties rigorously. The numerical optimization results demonstrate that the proposed approach provides improved effectiveness and efficiency in designing plasmonic filters under fabrication uncertainties by using Q factor analysis. The method proposed in this study enables systematic robust optimization while accounting for manufacturing uncertainties, which would be infeasible under typical time constraints. Specifically, within the proposed optimization framework, Q factor analysis can be employed due to a 20.60-times reduction in computational time. To the best of our knowledge, this represents the first robust optimization design for enhanced filter performance based on Q factor analysis in EOT, necessitating comprehensive spectrum calculations alongside fabrication tolerance considerations.

Enhancing Large-Diameter Tunnel Construction Safety with Robust Optimization and Machine Learning Integrated into BIM

Aim This study aims to enhance safety in large diameter tunnel construction by integrating robust optimization and machine learning (ML) techniques with Building Information Modeling (BIM). By acquiring and preprocessing various datasets, implementing feature engineering, and using algorithms like SVM, decision trees, ANN, and random forests, the study demonstrates the effectiveness of ML models in risk prediction and mitigation, ultimately advancing safety performance in civil engineering projects. Background Large diameter tunnel construction presents significant safety challenges. Traditional methods often fall short of effectively predicting and mitigating risks. This study addresses these gaps by integrating robust optimization and machine learning (ML) approaches with Building Information Modeling (BIM) technology. By acquiring and preprocessing diverse datasets, implementing feature engineering, and employing ML algorithms, the study aims to enhance risk prediction and safety measures in tunnel construction projects. Objective The objective of this study is to improve safety in large diameter tunnel construction by integrating robust optimization and machine learning (ML) techniques with Building Information Modeling (BIM). This involves acquiring and preprocessing diverse datasets, using feature engineering to extract key parameters, and applying ML algorithms like SVM, decision trees, ANN, and random forests to predict and mitigate risks, ultimately enhancing safety performance in civil engineering projects. Methods The study's methods include acquiring and preprocessing various datasets (geological, structural, environmental, operational, historical, and simulation). Feature engineering techniques are used to extract key safety parameters for tunnels. Machine learning algorithms, such as decision trees, support vector machines (SVM), artificial neural networks, and random forests, are employed to analyze the data and predict construction risks. The SVM algorithm, with a 98.76% accuracy, is the most reliable predictor. Results The study found that the Support Vector Machine (SVM) algorithm was the most accurate predictor of risks in large diameter tunnel construction, achieving a 98.76% accuracy rate. Other models, such as decision trees, artificial neural networks, and random forests, also performed well, validating the effectiveness of ML-based solutions for risk assessment and mitigation. These predictive models enable stakeholders to monitor construction, allocate resources, and implement preventative measures effectively. Conclusion The study concludes that integrating machine learning (ML) approaches with Building Information Modeling (BIM) significantly improves safety in large diameter tunnel construction. The Support Vector Machine (SVM) algorithm, with 98.76% accuracy, is the most reliable predictor of risks. Other models, like decision trees, artificial neural networks, and random forests, also perform well, validating ML-based solutions for risk assessment. Adopting these ML approaches enhances safety performance and resource management in civil engineering projects.

A robust optimization approach for designing multi-period airport hub network with uncertain capacity

A robust optimization approach for designing multi-period airport hub network with uncertain capacity

A distributionally robust optimization approach of multi-park integrated energy systems considering shared energy storage and Uncertainty of Demand Response

To enhance the economic efficiency and renewable energy integration capacity of multi-park integrated energy systems (MPIES) and address the issue of insufficient consideration of demand response uncertainty in existing studies, this paper proposes a distributionally robust optimization approach for multi-park integrated energy systems, considering shared energy storage and the uncertainty of demand response. First, models of the shared energy system and demand response are established. Based on these models, a deterministic optimization scheduling model for MPIES is developed, aiming to minimize system costs while considering constraints such as grid power balance. To address uncertainty in demand response, this paper employs Interval Type-2 Fuzzy Theory to construct uncertainty sets and considers system reliability constraints. The original optimization problem is then transformed into an equivalent robust counterpart model, and the optimal distributionally robust solution is obtained through parameter domain decomposition methods. Finally, the proposed method is validated using the IEEE 33-bus system. The results show that considering shared energy storage and demand response individually can reduce total system costs by 4.86 % and 26.46 %, respectively. After accounting for the uncertainty in demand response, the total system cost increases only slightly by 4.36 %, but this improves the system's robustness.

Adjustable robust optimization approach for SVM under uncertainty

The support vector machine (SVM) is one of the successful approaches to the classification problem. Since the values of features are typically affected by uncertainty, it is important to incorporate uncertainty into the SVM formulation. This paper focuses on developing a robust optimization (RO) model for SVM. A key distinction from existing literature lies in the timing of optimizing decision variables. To the best of our knowledge, in all existing RO models developed for SVM, a common assumption is that all decision variables are decided before the uncertainty realization, which leads to an overly conservative decision boundary. However, this paper adopts a different strategy by determining the variables that assess the misclassification error of data points or their fall within the margin post-realization, resulting in a less conservative model. The RO models where decisions are made in two stages (some before and the rest after the uncertainty resolution), are called adjustable RO models. This adjustment results in a three-level optimization model for which two decomposition-based algorithms are proposed. In these algorithms, after providing a bi-level reformulation, the model is divided into a master-problem (MP) and a sub-problem the interaction of which yields the optimal solution. Acceleration of algorithms via incorporating valid inequalities into MP is another novelty of this paper. Computational results over simulated and real-world datasets confirm the efficiency of the proposed model and algorithms.

Liner fleet deployment and empty container repositioning under demand uncertainty: A robust optimization approach

This paper investigates a robust optimization problem concerning the integration of fleet deployment and empty container repositioning in a shipping line network, where a fleet of vessels is dispatched to transport both laden and empty containers, aiming to fulfill a predetermined set of requests over a defined time horizon. The sizes of customer demands are uncertain and are characterized by a budgeted uncertainty set. This study aims to ascertain the vessel types assigned to each shipping route, the routing of laden containers, and the repositioning of empty containers in a manner that minimizes the total cost. Simultaneously, it ensures the feasibility of all transportation plans for any realization of demand within the uncertainty set. We introduce a path-based two-stage robust formulation for addressing the problem. In the first stage, the assignment of vessel types to each shipping route is determined, and the second stage focuses on establishing the routing of laden containers and repositioning of empty containers under a worst-case scenario. We propose the Column-and-Constraint Generation algorithm for solving the proposed robust formulation. To address large-scale size instances, we propose an acceleration technique, i.e., the piece-wise affine policy, which reduces the dimensions of the uncertainty set while maintaining a bounded compromise in solution quality. Comprehensive numerical experiments derived from real-world industries, such as the Shanghai port and CMA CGM, are conducted to validate the proposed formulation and solution methodologies.

Managing platelets supply chain under uncertainty: A two-stage collaborative robust programming approach

This study investigates the role of horizontal collaboration among blood centers in mitigating the negative impacts of fluctuations in blood platelet supply and demand during normal circumstances and after sudden-onset disasters. Specifically, four scenarios are studied: no collaboration, collaboration among blood centers, collaboration among hospitals, and collaboration among blood centers and hospitals. To formulate these scenarios, we propose a two-stage robust programming model that enables decision-makers to monitor the collaborative behavior of blood centers and hospitals before and after changes in supply and demand occur. In the first stage, a robust optimization approach is developed to cope with supply and demand uncertainties, where collaboration is limited to blood centers. In the second stage, the uncertain parameters (supply and demand) are treated as deterministic. The key decision is how to transfer platelets among hospitals located in a collaborative cluster. This research uses benchmark data from previous studies to test and validate the developed model and solution approach. Comparing the results obtained in different scenarios, we systematically select the most favorable scenario in terms of model performance under normal and emergency situations. The final results indicate that the network achieves the highest performance when blood centers and hospitals participate in the grand coalition.

Comprehensive stress-driven multi-material problem for heat-sinking heterogeneous structures

In the realm of designing thermoelastic structures, particularly within aerospace and broader engineering fields, complex challenges arise from the diverse behaviors of heterogeneous materials and the intricate requirements of stress-based systems in coupled thermomechanical considerations. This study addresses these challenges by proposing a comprehensive methodology with two main contributions: (i) the development of an effective unified solution for stress-driven designs that tackle heat-sinking problems by accommodating a wide range of materials, from homogeneous to heterogeneous and (ii) the introduction of a robust stress-based optimization approach for multi-material problems within coupled thermomechanical systems. The methodology employs the well-established P-norm approach to consolidate heterogeneous stresses into a unified global metric. Additionally, it integrates effective material interpolation with the generalized Solid Isotropic Material with Penalization (SIMP) framework, resulting in comprehensive multi-material models that include the constitutive matrix, thermal conductivity, thermal stress coefficient, and thermoelastic stress distributions. To further enhance adaptability and flexibility, the methodology incorporates a polygonal discretization technique. Detailed sensitivity analyses, using the adjoint variable technique, are conducted to improve computational efficiency in gradient-based mathematical programming algorithms. The efficiency, robustness, and practicality of the proposed methodology are validated through numerical examples, demonstrating its effectiveness and reliability in real-world applications.

Signal-devices management and data-driven evidential constraints based robust dispatch strategy of virtual power plant

Ensuring the safety and reliability of energy systems is very important in power grid operation. However, inherent intricacies and uncertainties of modern-day power systems, such as the mismatch between signal frequency and equipment response speed and the stochasticity associated with renewable energy and load forecasts, create significant challenges for generation dispatch planning. This study proposes a robust optimization approach with constraints based on signal-devices management and data-driven evidential distribution constraints. The first stage of this approach is to decompose and recombine the net power demand according to the Hilbert-Huang transform and device capability. The signal-device management constraints are then established based on this. The second stage formulates an evidential constraint based on data-driven evidential distribution and chance constraints in a distributionally robust optimization framework that caters to the stochasticity associated with renewable energy and load forecasts. The proposed model is validated on a virtual power plant to assess the approach’s efficacy for different dispatching scenarios. Penalty-based sensitivity analysis provides further insights into the proposed method’s performance for varying levels of CO2 emissions. Simulation results demonstrate that system flexibility becomes increasingly crucial for maintaining system stability and security as the penetration of renewable energy grows. Compared with chance constraint, the proposed data-driven evidential constraint effectively enables the optimization framework to handle stochasticity after sacrificing 0.62% more economic loss and 0.7% more environmental loss. Excessively high penalty parameters for CO2 do not promote economic development, resulting in 21.08% and 52.51% more economic and environmental losses without obvious environmental protection.

Net-Zero Scheduling of Multi-Energy Building Energy Systems: A Learning-Based Robust Optimization Approach With Statistical Guarantees

Net-Zero Scheduling of Multi-Energy Building Energy Systems: A Learning-Based Robust Optimization Approach With Statistical Guarantees

First-Order Algorithms for Robust Optimization Problems via Convex-Concave Saddle-Point Lagrangian Reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first-order approaches, based on online convex optimization, have been proposed as alternatives for the case of large-scale problems. However, existing first-order methods are either stochastic in nature or involve a binary search for the optimal value. We show that this problem can also be solved with deterministic first-order algorithms based on a saddle-point Lagrangian reformulation that avoid both of these issues. Our approach recovers the other approaches’ [Formula: see text] convergence rate in the general case and offers an improved [Formula: see text] rate for problems with constraints that are affine both in the decision and in the uncertainty. Experiment involving robust quadratic optimization demonstrates the numerical benefits of our approach. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Veni.191E.035] and the Israel Science Foundation [Grant 1460/19]. 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.2022.0200 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0200 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A novel set-induced robust optimization model under correlated uncertainty: a comparative theoretical and computational study

In practical scenarios, optimization problems frequently involve uncertain parameters that exhibit correlated fluctuations. The widely adopted set-induced robust optimization approach is employed to address correlated uncertainty in environments with limited data. This approach focuses on deriving a deterministic reformulation of the original uncertain optimization problem, ensuring that the constructed solution remains feasible for all potential realizations of input parameters within a predefined uncertainty set. However, this approach often yields overly conservative solutions. In this study, an innovative uncertainty set is developed to mitigate the over-conservatism associated with the set-induced robust optimization approach under correlated uncertainty. Moreover, from the proposed description of data uncertainty, a robust linear reformulation of the original uncertain optimization problem is established to strike a balance between conservativeness and optimality. Computational studies exploring production planning optimization programs demonstrate the superior performance of the proposed robust model over other alternatives, considering various levels of correlation among uncertain parameters.

Budget allocation problem for projects with considering risks, robustness, resiliency, and sustainability requirements

Budget Allocation Problem (BAP) for projects is considered one of the critical risks that necessitate the completion of projects in the shortest possible duration. This aspect is significant in extensive projects such as national endeavors directly impacting people's livelihoods. This research focuses on introducing Sustainable, Robust, Resilient, and Risk-averse Budget Allocation for Projects (S3RBAP). A hybrid robust stochastic optimization approach was employed, incorporating Weighted VaR (WVaR) and the minimum function as risk criteria to ensure the robustness of the objective function. This model is designed to minimize the weighted expected value, WVaR, and the minimum progress function, thereby promoting the 3R and sustainability framework to tackle budget fluctuations and enhance project viability. The case study revolves around the construction of national projects in Iran. Ultimately, the project's required budget was allocated within the budgetary constraints. Sensitivity analysis found that the integration of 3R and sustainability led to a 13.5 % reduction in the progress function compared to scenarios without these principles. Furthermore, increasing the conservatism coefficient to 20 % decreased the progress function to −0.58 %. Reducing the resiliency coefficient had an adverse effect by disrupting the budget allocation process. The computational time is increased gradually with the escalation of problem complexity, while the progress function decreases due to the increased number of projects. The findings demonstrate that using an exponential function promotes risk aversion, whereas a sine function encourages risk-seeking behaviour within this research context.

Integrating heterogenous robustness levels to the multi-objective target-oriented robust optimization of a microalgal biorefinery

Integrated biorefineries offer an efficient way to produce biofuels by enhancing profit through the generation of marketable by-products and by reducing environmental impact by reutilizing waste streams originating from different processes within the system. Employing a variety of conversion technologies, integrated biorefineries yield a wide range of products and byproducts, encompassing biofuels, biochemicals, and bioenergy, all derived from biomass feedstocks. Several mathematical methods have been developed in order to optimize the design of biorefineries with consideration for uncertainty, including the multi-objective target-oriented robust optimization (MOTORO) approach that enables target-seeking behavior while maximizing the tolerable deviation of parameters in the system. However, the phenomenon of heterogenous robustness levels that tradeoff risks with each other has not been investigated in both MOTORO and in wider robust optimization literature. The present study addresses this gap by applying multiple, potentially non-equal degrees of robustness to each customer's demand, allowing stakeholders to place unequal risks on each customer. As a result, limited resources may be more efficiently utilized in line with existing knowledge or preference regarding uncertainties. The proposed improvement was applied to an algal biorefinery system with two customers, where robustness successfully exhibited tradeoffs with each other while retaining inverse relationships with system underperformance and variation as evaluated from a Monte Carlo simulation.

Direct Mail or Bonded Warehouse? Logistics Mode Selection in Cross-Border E-Commerce under Exchange Rate Risk

The rapid development of cross-border e-commerce (CBEC) has enabled more suppliers to expand into overseas markets, meeting increasingly diverse consumer demands. Selecting an effective logistics mode is a crucial issue for suppliers, yet uncertainty in demand and exchange rate fluctuations make this problem challenging. This paper considers a supply chain consisting of a supplier and a CBEC platform. Using a distributionally robust optimization approach, we provide optimal overseas warehousing strategies and logistics mode selection for suppliers, given partial distribution information of market demand and exchange rate, such as means, variances, and covariances. It is found that when demand and exchange rate fluctuations are small, the supplier chooses the bonded warehouse logistics mode to reduce costs. Conversely, when demand and exchange rate fluctuations increase, the supplier opts for the direct mail mode to respond flexibly to market risk. The correlation between exchange rate and demand also affects the choice of logistics mode. Specifically, with low correlation, the preference is for the bonded warehouse mode, whereas high correlation leads suppliers to choose the direct mail mode. In addition, the impact of demand and exchange rate fluctuations on suppliers’ overseas warehousing volumes depends on the product’s profit margin. These findings provide guidance for the selection of CBEC logistics under exchange rate risk.

The Robust Optimization of Low-Carbon Economic Dispatching for Regional Integrated Energy Systems Considering Wind and Solar Uncertainty

In this paper, a two-stage robust optimization approach is employed to address the variability in renewable energy output by accounting for the uncertainties associated with wind and solar energy. The model aims to achieve a balanced system that is both low-carbon and economically efficient while also being resilient to uncertainties. Initially, a regional integrated energy system model is developed, integrating electricity, gas, and heat. The variability of wind and photovoltaic power outputs is represented using a modifiable uncertainty set. A resilient optimal scheduling model is formulated in two stages, with the objective of minimizing costs under worst-case scenarios. This model is solved iteratively through a column and constraint generation approach. Additionally, the scheduling model incorporates horizontal time shifts and vertical complementary substitutions for carbon trading costs and demand-side loads to avoid excessive conservatism and to manage carbon emissions and energy trading in the regional integrated energy system (RIES). Results show that the two-stage robust optimization approach significantly enhances the system’s resilience to risks and minimizes economic losses. The inclusion of carbon trading mechanisms and the demand response prevents the system from becoming overly robust, which could impede economic growth, while also reducing carbon emissions. The proposed method effectively achieves balanced optimal scheduling for a robust, economical, and low-carbon system.

Enhancing the Robustness of Rib-Groove Filling and Strain Homogeneity in the Isothermal Forging of Titanium Alloy Multi-Rib Components

Isothermal forging stands as an effective technology for the production of large-scale titanium alloy multi-rib components. However, challenges have persisted, including die underfilling and strain concentration due to the complex material flow and heterogeneous deformation within the forging die cavity. While approaches centered on optimized billet designs have mitigated these challenges, uncertainties in process parameters continue to introduce unacceptable variations in forming accuracy and stability. To tackle this issue, this study introduced a multi-objective robust optimization approach for billet design, accounting for the multi-rib eigenstructure and potential uncertainties. The approach includes finite element (FE) modeling for analyzing the die-filling and strain inhomogeneity within the multi-rib eigenstructure. Furthermore, it integrated image acquisition perception and feed back technologies (IAPF) for real-time monitoring of material flow and filling sequences within die rib-grooves, validating the accuracy of the FE modeling. By incorporating dimensional parameters of the billet and uncertainty factors, including friction, draft angle, forming temperature, speed, and deviations in billet and die, quantitative analyses on the rib-groove filling and strain inhomogeneity with fluctuation were conducted. Subsequently, a dual-response surface model was developed for statistical analysis of the cavity filling and strain homogeneity. Finally, the robust optimization was processed using a non-dominated sorting genetic algorithm II (NSGA-II) and validated using the IAPF technologies. The proposed approach enables robust design enhancements for rib-groove filling and strain homogeneity in titanium alloy multi-rib components.

An Adaptive Distributionally Robust Optimization Approach for Optimal Sizing of Hybrid Renewable Energy Systems

An Adaptive Distributionally Robust Optimization Approach for Optimal Sizing of Hybrid Renewable Energy Systems

An assessment methodology for the flexibility capacity of new power system based on two-stage robust optimization

The inherent variability in wind and solar power output presents a significant challenge to the flexibility balance of power systems. This paper introduces an innovative method for evaluating the flexibility capacity of a new power system, employing a two-stage robust optimization approach. Firstly, a power system flexibility supply and demand balance mechanism model is constructed and quantitatively characterized for the power system flexibility shortfalls set. Subsequently, taking into account timescale characteristics and directionality, the time series production simulation technique is applied to establish the effective ramping and flexibility supply distribution model of thermal power and energy storage units, enabling an analysis of the power system's supply regulation capabilities. On this basis, a power system flexibility capacity assessment method is proposed, which divides the system regulation resources into demand set and supply set, and constructs a power system flexibility capacity assessment model to ensure that the maximum system flexibility margin and the lowest operating cost are taken as the optimization objectives under the system security operation constraints. The column and constraint generation (C&CG) robust optimization algorithm is used to decompose the master problem and the max-min dual-layer subproblems for iterative solving, and the optimal capacity of each unit of the system in terms of output and flexibility is derived. Finally, the effectiveness and superiority of the proposed method is verified through case analysis, which shows that the method can improve the flexibility capacity by 14.9% and reduce the operating cost by 15.83% compared with the traditional proportional allocation method.

Nature-Based Secondary Resource Recovery under Climate Change Uncertainty: A Robust Multi-Objective Optimisation Methodology

The management of high-volume (HV) waste poses a persistent challenge in sustainable materials management and represents an untapped opportunity in circular economy models. This study proposes a conceptual decision-making framework to operationalise a novel circular economy strategy for HV waste, involving temporary storage to facilitate nature-based secondary resource recovery. Using an illustrative case study of a candidate HV waste (legacy mining waste), we apply a robust multi-objective spatial optimisation approach at a national scale, employing an exact solution approach. Our methodology integrates mixed-integer linear programming to evaluate the economic viability, social benefits, and impacts of climate change uncertainties on nature-based solutions (NbS) implementation across diverse scenarios. The results demonstrate that NbS can enhance economic feasibility by incorporating carbon sequestration and employment benefits while demonstrating resilience against climate change projections to ensure long-term sustainability. The findings suggest that although NbS can improve the circular economy of HV nationally, it is essential to assess additional ecosystem services and address multiple uncertainties for effective macro-level sustainability assessment of HV management. This study offers a robust decision-making framework for policymakers and stakeholders to plan and implement nature-based circular economy strategies for HV waste streams at a national level while effectively managing long-term planning uncertainties.