Robust Optimization Research Articles

Solving the waste bin location problem with uncertain waste generation rate: A bi-objective robust optimization approach.

An efficient municipal solid waste (MSW) system is critical to modern cities in order to enhance sustainability and liveability of urban life. With this aim, the planning phase of the MSW system should be carefully addressed by decision makers. However, planning success is dependent on many sources of uncertainty that can affect key parameters of the system, for example, the waste generation rate in an urban area. With this in mind, this article contributes with a robust optimization model to design the network of collection points (i.e. location and storage capacity), which are the first points of contact with the MSW system. A central feature of the model is a bi-objective function that aims at simultaneously minimizing the network costs of collection points and the required collection frequency to gather the accumulated waste (as a proxy of the collection cost). The value of the model is demonstrated by comparing its solutions with those obtained from its deterministic counterpart over a set of realistic instances considering different scenarios defined by different waste generation rates. The results show that the robust model finds competitive solutions in almost all cases investigated. An additional benefit of the model is that it allows the user to explore trade-offs between the two objectives.

Adjustable light robust optimization with second order stochastic dominance constraints

Robust optimization suffers from excessive conservatism and infeasibility due to stringent requirements on all constraints within the uncertainty set, rendering robust solutions impractical. The light robust approach has been proposed to mitigate these challenges. This method aims to identify a solution that minimizes the weighted sum of all constraint violations while adhering to a predetermined limit on the deterioration of expected return. Drawing inspiration from light robustness, our paper introduces the adjustable light robust optimization models with second-order stochastic dominance constraints. We empirically examine their feasibility, out-of-sample performance, and the dynamic trade-off between return and robustness.

Improved Multi-Strategy Sand Cat Swarm Optimization for Solving Global Optimization

The sand cat swarm optimization algorithm (SCSO) is a novel metaheuristic algorithm that has been proposed in recent years. The algorithm optimizes the search ability of individuals by mimicking the hunting behavior of sand cat groups in nature, thereby achieving robust optimization performance. It is characterized by few control parameters and simple operation. However, due to the lack of population diversity, SCSO is less efficient in solving complex problems and is prone to fall into local optimization. To address these shortcomings and refine the algorithm’s efficacy, an improved multi-strategy sand cat optimization algorithm (IMSCSO) is proposed in this paper. In IMSCSO, a roulette fitness–distance balancing strategy is used to select codes to replace random agents in the exploration phase and enhance the convergence performance of the algorithm. To bolster population diversity, a novel population perturbation strategy is introduced, aiming to facilitate the algorithm’s escape from local optima. Finally, a best–worst perturbation strategy is developed. The approach not only maintains diversity throughout the optimization process but also enhances the algorithm’s exploitation capabilities. To evaluate the performance of the proposed IMSCSO, we conducted experiments in the CEC 2017 test suite and compared IMSCSO with seven other algorithms. The results show that the IMSCSO proposed in this paper has better optimization performance.

Enhancing the design of a two-stage CMOS operational amplifier utilising the Bat Algorithm

ABSTRACT The increasing demand for high-performance two-stage CMOS Op-Amps in electronic, communications, and biomedical applications necessitates their operation with wide bandwidth, high voltage gain, and low power consumption. By leveraging the Bat Algorithm global search and local exploration capabilities, the study demonstrates a significant improvement in the amplifier’s overall performance. This design of a two-stage CMOS Op-Amp using 0.18 µm TSMC technology, powered by a ± 1.8 V supply voltage. The simulation outcomes were gathered using the PSPICE software (version 17.4). These design strategies prove highly efficient, achieving high gain, high frequency, and low power consumption. Additionally, the paper showcases the execution and simulation results of a two-stage CMOS Op-Amp based on the Bat Algorithm, utilising MATLAB for this purpose. The employment of the BA results in substantial enhancements in performance metrics. Specifically, the Unity Gain Bandwidth sees a doubling in its value, the voltage gain rises by 20%, power consumption falls by 39.1%, and the Common Mode Rejection Ratio improves by 20% compared to a two-stage CMOS Op-Amp designed without the BA. The findings underscore the BA potency as a robust optimisation method for boosting the performance of a two-stage CMOS Op-Amp.

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

A risk-averse distributionally robust optimisation approach for drone-supported relief facility location problem

Drone-supported last-mile humanitarian logistics applications play a crucial role in the rapid and efficient delivery of essential relief items, such as medicine, blood, and vaccines, during disaster and emergency situations. This paper explores a novel drone-supported relief facility location problem (DSRFLP) aimed at establishing an effective drone-supported last-mile humanitarian logistics system. The problem involves making joint decisions for both pre-disaster and post-disaster phases while considering the characteristics of drone-based delivery operations and uncertain demands. In the pre-disaster phase, we make the decisions regarding the locations of drone-supported relief facilities, inventory prepositioning of relief items, assignment of drones to the opened facilities, and allocation of drones to disaster demand sites. In the post-disaster phase, we make decisions related to delivery quantities. To tackle the challenge of incomplete demand distribution information in chaotic disaster environments, we establish a distributionally robust optimisation (DRO) model to handle the uncertainty of demands. This model adopts worst-case mean Conditional Value-at-Risk as the risk measurement, reflecting the risk-averse attitude of humanitarian organisers. In this paper, three ambiguity sets (box, ellipsoidal, and polyhedral) are considered to describe the ambiguity distributions of demands. To overcome the computational challenge, we reformulate the DRO model under three ambiguity sets into two mixed-integer linear programming models and one second-order cone programming model, which can be efficiently solved by off-the-shelf solvers. Furthermore, we validate our proposed DRO model through a small-scale example and a large-scale case study based on the Lushan earthquake in China. The computational outcomes underscore the superior performance of the proposed DRO model to mitigate the impact arising from incomplete probability distributions. We propose managerial implications and insights to support the decision-making of humanitarian organisations based on the experimental results. Finally, we propose two extended models to incorporate multiple relief items and equity constraints in priority settings and conduct numerical experiments to adapt to various real-world disaster scenarios.

Data-driven Wasserstein distributionally robust dual-sourcing inventory model under uncertain demand

Dual-sourcing inventory management, which is aimed at replenishing inventory through two supply sources, has been extensively incorporated across various industries as it can mitigate supply chain related operational risks. Given the practical relevance of this framework, many dual-sourcing inventory models based on stochastic and robust optimization approaches have been developed. However, these approaches encounter challenges such as the curse of dimensionality or solution conservativeness. In this study, we developed a data-driven distributionally robust optimization model for dual-sourcing inventory management under uncertain demand conditions, in which partial information regarding the distribution of the uncertain demand is available. A tractable model was constructed to solve the problem, and an optimal solution was derived in a closed-form expression. Numerical experiments were conducted to evaluate the performance of the proposed model in comparison with benchmark models in terms of the order-, stock-, and rolling-horizon-related parameters and demand distributions. The results demonstrated the benefit of adopting the dual-sourcing strategy in inventory management based on the distributionally robust optimization approach. In addition, the proposed model outperformed the benchmark models in terms of mitigating the bullwhip effect.

Multi-time-scale voltage control of the distribution network with energy storage equipped soft open points

The integration of distributed generation (DG) units into distribution networks (DNs) has brought about several operational challenges, including voltage issues and increased power loss. Energy storage equipped soft open points (E-SOPs) can accurately and flexibly control active and reactive power flows to address these problems. Additionally, the photovoltaic (PV) inverter and the network reconfiguration (NR) play a significant role in voltage control by adjusting the reactive power and the topology of the DN, respectively. However, due to differences in response times, there is a lack of systematic coordination between NR and the inverters of the E-SOP and PV. This paper proposes a multi-time-scale voltage control model that includes day-ahead NR scheduling, inter-day droop control optimization of the PV and E-SOP, and real-time local droop control. Considering the uncertainties of renewable DG outputs and loads, a robust optimization method is used in the day-ahead stage to obtain a reliable network structure. Then, with more accurate intra-day predictions, a stochastic optimization method is used to obtain the optimal state-of-charge interval, aiming to provide a flexible regulation range for battery energy storage to cope with the power fluctuations during the real-time stage. In addition, to address the intra-day voltage control model with bilinear constraints of the droop control function, a particle swarm optimization method is used. The results are verified on a 33-bus DN system through comparative analyses, showing effective performance.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

Robust maximum fairness consensus models with aggregation operator based on data-driven method

In group decision-making (GDM), when decision-makers (DMs) feel it is unfair, they may take uncooperative measures to disrupt the consensus-reaching process (CRP). On the other hand, it is difficult for the moderator to objectively determine each DM’s unit consensus cost and weight in CRP. Hence, this paper proposes data-driven robust maximum fairness consensus models (RMFCMs) to address these. First, this paper uses the robust optimization method to construct multiple uncertainty sets to describe the uncertainty of the DMs’ unit adjustment cost and proposes the RMFCMs. Subsequently, based on the DMs’ historical data, the DMs’ weights in the CRP are determined by a data-driven method based on the kernel density estimation (KDE) method. Finally, this paper also applies the proposed models to the carbon emission reduction negotiation process between governments and enterprises, and the experimental results verify the rationality and robustness of the proposed consensus model.

Modeling a robust 2-service community healthcare network design problem with central hospital congestion

We address a more realistic variant of the community healthcare network design problem, considering a 2-service network framework and hospital congestion structures. Our objective is to minimise the total expected cost through strategic location of central hospitals and allocation of community health stations. Notably, each community health station is allocated to exactly two central hospitals. We also account for uncertainties in resident medical demands, which are challenging to predict accurately due to their volatility. To tackle this, we propose an adaptive distributionally robust optimisation approach that confines uncertain variables to an ambiguity set reflecting demand distribution characteristics. To enhance tractability, we reformulate the distributionally robust model as a mixed-integer linear programme within the specified ambiguity set. Numerical experiments on a real case demonstrate the validity and superiority of the proposed model. Finally, the impact of uncertainty is discussed in depth and some managerial insights for healthcare managers are summarised.

A novel metaheuristic based on object-oriented programming concepts for engineering optimization

This paper presents a novel, robust, efficient, and simple optimization algorithm called the Object-Oriented Programming Optimization Algorithm (OOPOA) for tackling constrained and unconstrained optimization problems. The algorithm is inspired by the inheritance concept of Object-Oriented programming languages, where the features of a class are classified into three types according to inheritance probability: public, private, and protected. The object-oriented programming inheritance concept is implemented in the algorithm to update the population for the next generations. The proposed algorithm ensures exploitation by selecting the solution with the highest fitness to be inherited in each iteration. It ensures exploration by applying a mutation process that helps explore wide regions in the search space. The performance of this technique is demonstrated by solving 34 different optimization tasks, including 20 standard benchmark problems, ten IEEE Congress of Evolutionary Computation benchmark test functions, and four constrained real-world engineering design problems.

A robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets

In order to better describe the uncertainty of renewable energy output, this paper proposed a novel robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets. First, an ellipsoidal uncertainty set was established using historical data on renewable energy output, and a data-driven convex hull polyhedral set was established by connecting high-dimensional ellipsoidal vertices; on this basis, an adaptive data-driven polyhedral set model was established to address the problem of high conservatism in the scaling process of convex hull polyhedral sets. Furthermore, a novel adaptive data-driven robust scheduling model for new distribution systems was established, and a column-and-constraint generation (C&CG) algorithm was used to solve the robust scheduling model. Finally, the improved IEEE-33 bus system simulation verification shows that the robust scheduling model for new distribution systems based on adaptive data-driven polyhedral sets can reduce conservatism and improve the robustness of optimization results.

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.

Steam generator efficiency optimization under uncertainty through multi-fidelity modeling

The steam generator is an essential equipment in power plants, and understanding its behavior with the aid of mathematical models allows for improved decision-making aiming toward better efficiency. Well-calibrated models can help identify new operating conditions that lead to efficiency enhancement. Unfortunately, due to the complexity of steam generators, computationally efficient models based solely on energy-mass balance usually present limiting simplifications. Alternatively, computational fluid dynamics can solve reacting flow phenomena but require a great amount of computational time. Purely data-driven models often extrapolate poorly as they do not necessarily contain the physical equations that drive the system’s behavior. In this scenario, the multi-fidelity approach is an attractive solution because it combines physics-grounded representation with a low computational footprint and allows for mapping the efficiency of the steam generator considering uncertainty propagation. This paper presents a multi-fidelity model that simulates the efficiency of a steam generator from the PECÉM power plant. The model is assembled by the sum of two Gaussian processes, trained using one high-fidelity and one low-fidelity dataset. The high-fidelity dataset is formed by the observed operation of the actual power plant at varying operating conditions. These same operating parameters are the input for the energy-mass balance model built using the EBSILON software to generate the low-fidelity dataset. The observed efficiency of the PECÉM power plant ranged from 82.89% to 84.37%, with a mean value of 83.58%. The resulting multi-fidelity model presents a root mean square error of 0.19%, which is six times lower than the error obtained by the energy-mass balance model. This model is then used for global sensitivity analysis and robust optimization. A Pareto front mapping expected efficiency and its confidence level is built by exploring not yet experimented operational points. Finally, data clustering allowed the identification of efficiencies around 86%, which adds 1.63% to the power plant’s maximum level.

AI‐Based Ensemble Flood Forecasts and Its Implementation in Multi‐Objective Robust Optimization Operation for Reservoir Flood Control

AbstractInforming reservoirs with forecasts is highly important for real‐time flood control. This study proposed a forecast‐informed methodology framework for reservoir flood control operation under uncertainty. A new combination of two post‐processing methods, that is, the Cloud model and error‐based copula functions, were developed to merge individual AI‐based forecasts to ensemble flood forecasts, so called stochastic errors‐based Cloud (SE‐Cloud). A multi‐objective robust optimization model (MRO) integrating the risk, resilience, and vulnerability was then proposed to tackle flood control problems under ensemble forecasts; for comparison, a two‐objective stochastic optimization model (TSO) was developed to minimize the expected highest reservoir level and peak release. The proposed methodology was applied to the Lishimen reservoir in the Shifeng River subbasin, China, aiming to comprehensively verify the relationships among deterministic forecasts, ensemble forecasts, and flood control performance. Results showed that the Cloud model could effectively integrate different models and improve forecast accuracy. But a higher deterministic forecast quality did not consistently result in improved flood control performance. SE‐Cloud could capture the peak flow and effectively characterize forecast uncertainties and increased hypervolume values by 13.14%–39.65% compared to the Cloud model, indicating the superiority of ensemble forecasts in generating robust solutions over individual deterministic forecasts. MRO released more inflow than TSO, decreasing the expected highest water level by 0.05 m and incrementing the expected peak release by 4.29%. However, with downstream resilience value remaining at zero, it is demonstrated that MRO improving upstream vulnerability did not necessarily diminish resilience. The enhanced robustness highlights the potential of AI‐based ensemble forecasts in flood control.

Multi-objective robust optimization of staff scheduling for emergency under stochastic demand

Large-scale centralized emergency rescue staff scheduling under emergencies has always been a challenge. With a specific focus on nucleic acid testing amid the COVID-19 pandemic, this study introduces a model that considers dynamic changes in staff supply at rescue points, the varying demand at sampling points over time, and their impact on the spread of the epidemic. We quantified the emergency weight of sampling points by the demand and the regional risk degree and adopted robust optimization with base constraint. With the objectives of minimum comprehensive service distance, maximum weighted value of demand satisfaction rate, and minimum loss caused by unmet demand, a multi-stage, multi-medical rescue point medical staff scheduling model for nucleic acid sampling points with the influence caused by uncertain demand disturbance was built, and an improved NSGA-II-HC algorithm was designed to solve the optimization problem under the influence of demand disturbances. The testing results proved that the NSGA-II-HC algorithm can tackle the issue of insufficient uniformity and diversity in the solution set of NSGA-II while Multi-Objective Particle Swarm Optimization (MOPSO) failed to do so. Taking the epidemic data of Guangzhou city in May 2021 as a case study, our model and algorithm are verified to be feasible. We offer a scheme selection strategy according to the loss degree of two conflicting objectives, the comprehensive service distance and shortage loss. The results suggest that, compared with the demand deterministic model, the decision mechanism under the robust model can reduce the deviation from the optimization objective due to the demand disruption

6σ Robust Lightweight Design of the GIL/GIS Bus Based on Co‐Simulation of Insulation, Current Flow, and Mechanical Stress

6<i>σ</i> Robust Lightweight Design of the GIL/GIS Bus Based on Co‐Simulation of Insulation, Current Flow, and Mechanical Stress

Robust topology optimization for multi-material structures considering material uncertainties

Multi-material structures have attracted more and more attention from scholars and engineers, because they usually have good composite performance. Uncertainty factors are ubiquitous in practice, especially for material uncertainties. Multi-material structures contain many materials with different properties, material uncertainties will affect the allocation of material usage, thereby affecting structural performance. Therefore, it is crucial to consider material uncertainties in the design of multi-material structures. This paper detailedly explores the impacts of elastic modulus uncertainty and Poisson's ratio uncertainty on the design of multi-material structures. The topology optimization is to minimize the compliance subjected to a mass constraint, where multiple materials can be freely allocated during the optimization. Floating projection topology optimization is adopted to search for the structural topologies, and robust sensitivity information is derived. For the quantification of material uncertainties, this paper introduces a non-intrusive polynomial chaos expansion (PCE) method to implicitly quantify them, the computational efficiency and accuracy in PCE is compared with the classical Monte Carlo method. Finally, topology optimization examples are provided to demonstrate the effects of elastic modulus uncertainty, Poisson's ratio uncertainty and hybrid uncertainty on the design of multi-material structures.

A data-driven distributionally robust optimization approach for the core acquisition problem

Reusing electric vehicles (EV) batteries that reach the end of their useful first life is an environmental and cost-competitive option; however, the process of recycling EV batteries is not yet mature. Due to complex electrochemical reactions and physical conditions, the quality of used EV batteries (cores) is highly uncertain. The remanufacturer needs to make the acquisition decision under quality distributional ambiguity. Perfect quality distribution of cores cannot be known to the remanufacturer in practice. We develop distributionally robust optimization models based on phi-divergence measures and the imprecise Dirichlet model (DRO-IDM) to derive robust decisions. First, we find that the bounds of quality probability intervals are identified solely based on the collected data by introducing the imprecise Dirichlet model. The derived finite-sample boundary can reduce the scope of the uncertainty set and avoid the no-direction search issue. Second, our models can hedge against distributional uncertainty, reduce the probability of a robust solution that deviates from the optimal solution, and correct bias in decision making. Third, we extend the DRO-IDM to develop data-driven models, that can reassess the value of multisource quality information to improve the estimation accuracy of core quality and maximize the remanufacturer’s profit. Our study provides new insights for remanufacturers: the new remanufacturing process proposed in our work can assist remanufacturers in utilizing the values of cores without disassembly; the information-aware algorithm can offer the remanufacturing sector a valuable tool for efficiently filtering out invalid information in optimizing acquisition decisions; this capability empowers decision-makers to leverage multiple sources of information and expedite the process of digital transformation in remanufacturing; our approach can also provide a manner of integrating information fusion and distribution learning into remanufacturing.