Active Robust Optimization: Optimizing for Robustness of Changeable Products

The coupling of finite element simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a generally applicable strategy for modeling and efficiently solving robust optimization problems based on time consuming simulations. Noise variables and their effect on the responses are taken into account explicitly. The robust optimization strategy consists of four main stages: modeling, sensitivity analysis, robust optimization and sequential robust optimization. Use is made of a metamodel-based optimization approach to couple the computationally expensive finite element simulations with the robust optimization procedure. The initial metamodel approximation will only serve to find a first estimate of the robust optimum. Sequential optimization steps are subsequently applied to efficiently increase the accuracy of the response prediction at regions of interest containing the optimal robust design. The applicability of the proposed robust optimization strategy is demonstrated by the sequential robust optimization of an analytical test function and an industrial V-bending process. For the industrial application, several production trial runs have been performed to investigate and validate the robustness of the production process. For both applications, it is shown that the robust optimization strategy accounts for the effect of different sources of uncertainty onto the process responses in a very efficient manner. Moreover, application of the methodology to the industrial V-bending process results in valuable process insights and an improved robust process design.

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

An accurate estimation of range uncertainties is essential to exploit the potential of proton therapy. According to Paganetti's study, a value of 2.4% (1.5 standard deviation) is currently recommended for planning robust treatments with Monte Carlo dose engines. This number is based on a dominant contribution from the mean excitation energy of tissues. However, it was recently shown that expressing tissues as a mixture of water and "dry" material in the CT calibration process allowed for a significant reduction of this uncertainty. We thus propose an adapted framework for pencil beam scanning robust optimization. First, we move towards a spot-specific range uncertainty (SSRU) determination. Second, we use the water-based formalism to reduce range uncertainties and, potentially, to spare better the organs atrisk. The stoichiometric calibration was adapted to provide a molecular decomposition (including water) of each voxel of the CT. The SSRU calculation was implemented in MCsquare, a fast Monte Carlo dose engine dedicated to proton therapy. For each spot, a ray-tracing method was used to propagate molecular I-values uncertainties and obtain the corresponding effective range uncertainty. These were then combined with other sources of range uncertainties, according to Paganetti's study of 2012. The method was then assessed on three head-and-neck patients. Two plans were optimized for each patient: the first one with the classical 2.4% flat range uncertainty (FRU), the second one with the variable range uncertainty. Both plans were then compared in terms of target coverage and OAR mean dose reduction. Robustness evaluations were also performed, using the SSRU for both plans in order to simulate errors as realistically aspossible. For patient 1, it was found that the median SSRU was 1.04% (1.5 standard deviation), yielding, therefore, a very large reduction from the 2.4% FRU. All three SSRU plans were found to have a very good robustness level at a 90% confidence interval while sparing OAR better than the classical plan. For instance, in nominal cases, average reductions in the mean dose of 15.7, 8.4, and 13.2% were observed in the left parotid, right parotid, and pharyngeal constrictor muscle, respectively. As expected, the classical plans showed a higher but unnecessary level ofrobustness. Promising results of the SSRU framework were observed on three head-and-neck cases, and more patients should now be considered. The method could also benefit to other tumor sites and, in the long run, the variable part of the range uncertainty could be generalized to other sources of uncertainty in order to move towards more and more patient-specifictreatments.

Robust optimization of a marine current turbine using a novel robustness criterion

This paper proposes a framework for solving high-dimensional robust multi-objective optimization problems. A decision variable classification-based framework is developed to search for robust Pareto-optimal solutions. The decision variables are classified as highly and weakly robustness-related variables based on their contributions to the robustness of candidate solutions. In the case study, an order scheduling problem in the apparel industry is investigated via the proposed framework. The experimental results reveal that the performance of robust evolutionary optimization can be greatly improved via analyzing the properties of decision variables and then decomposing the high-dimensional robust multi-objective optimization problem.

Seismic fragility analysis is a complex process involving different sources of uncertainties. In this paper, an alternative procedure for seismic fragility analysis based on the uniform design method (UD) is proposed. UD is used to generate a reasonable sample to build probabilistic seismic demand models (PSDMs), which are used to generate the fragility curves of a cable-stayed bridge. Sensitivity analyses of different uncertainties are carried out by comparison of the fragility curves for different components. It is concluded that (1) the UD method can consider different sources of uncertainties in fragility analysis with reasonable accuracy; (2) the bridge system is more fragile than any component of bridges; and (3) the damage probability of fragility considering uncertainty in the ground motion, geometry, and material is larger than that considering only the uncertainty in the ground motion.

Following substantial advancements in stochastic classes of decision-making optimization problems, scenario-based stochastic optimization, distributionally robust optimization, and chance-constrained optimization have recently gained an increasing attention. Despite the remarkable developments in probabilistic forecast of uncertainties (e.g., in renewable energies), most approaches are still being employed in a univariate framework which fails to unlock a full understanding on the underlying interdependence among uncertain variables of interest. In order to yield cost-optimal solutions with predefined probabilistic guarantees, conditional and dynamic interdependence in uncertainty forecasts should be accommodated in power systems decision-making. This becomes even more important during the emergencies where high-impact low-probability (HILP) disasters result in remarkable fluctuations in the uncertain variables. In order to model the interdependence correlation structure between different sources of uncertainty in power systems during both normal and emergency operating conditions, this paper aims to bridge the gap between the probabilistic forecasting methods and advanced optimization paradigms; in particular, perdition regions are generated in the form of ellipsoids with probabilistic guarantees. We employ a modified Khachiyan’s algorithm to compute the minimum volume enclosing ellipsoids (MVEE). Application results based on two datasets on wind and photovoltaic power are used to verify the efficiency of the proposed framework.

This research aims to adopt two robust optimisation approaches for a real-world flow shop manufacturing system with batch processing machines, where the processing time and size of job are non-deterministic and uncertain. Each machine can process multiple jobs simultaneously as long as the machine capacity is not exceeded. Two important decisions are required: (1) grouping jobs into batches and (2) scheduling the established batches on machines. A mathematical optimisation model is presented, and then two famous robust optimisation approaches are adopted for the purpose of converting the deterministic model to the robust one. An efficient particle swarm optimisation (PSO) algorithm is developed to solve the problem in a reasonable time. In order to verify the developed model and evaluate the performance of our proposed algorithm, a set of small to large test problems are generated, and a simulation approach and a commercial optimisation solver are used to solve these problems. Analysis of the implementation of two independent robust optimisation methods is performed by the paired t-test on all of the test problems. Furthermore, the Taguchi method, as a statistical optimisation technique, is employed to investigate the appropriate level of PSO parameters.

Incorporate robust optimization and demand defense for optimal planning of shared rental energy storage in multi-user industrial park

Purpose This study aims to investigate how different sources of uncertainty hinder the measurement and reporting of greenhouse gas (GHG) emissions in the steel supply chain (SC). It also examines how information processing mechanisms can support SC planning and help organizations manage these uncertainties. Design/methodology/approach A qualitative approach is used, based on semi-structured interviews with 16 informants from 12 European companies operating at different positions in the steel SC, including raw material producers, manufacturers, logistics providers, wholesalers and service partners. Grounded in the organizational information processing theory, the study analyzes how uncertainty affects emissions-related information processing and planning decisions. Findings The study identifies six key sources of uncertainty that hinder emissions measurement and reporting in the steel SC. These uncertainties manifest differently across procurement, production, distribution and sales planning stages. The findings illustrate how organizations can respond through information processing mechanisms that support emissions-related planning tasks and help integrate decarbonization goals into SC decision-making. In this study, procurement planning emerged as a particularly critical stage, where targeted information processing mechanisms can help mitigate emissions-related uncertainties. Research limitations/implications This study contributes to research on sustainable SC management and SC planning by identifying key factors that generate emissions-related uncertainty and highlighting how information processing can support decarbonization efforts. Practical implications Organizations can benefit from understanding how uncertainties related to GHG emissions measurement and reporting emerge and intensify. The study suggests several information processing mechanisms that can help organizations mitigate these challenges through SC planning and inform policymaking for better carbon management. Originality/value This research contributes to the understanding of how different sources of uncertainty emerge and complicate GHG emissions measurement and reporting in the steel SC.

One of the main focuses for network planning is on the optimization of network resources required to build a network under certain traffic demand projection. Traditionally, the inputs to this type of network planning problems are treated as deterministic. In reality, the varying traffic requirements and fluctuations in network resources can cause uncertainties in the decision models. The failure to include the uncertainties in the network design process can severely affect the feasibility and economics of the network. Therefore, it is essential to find a solution that can be insensitive to the uncertain conditions during the network planning process. As early as in the 1960's, a network planning problem with varying traffic requirements over time had been studied. Up to now, this kind of network planning problems is still being active researched, especially for the VPN network design. Another kind of network planning problems under uncertainties that has been studied actively in the past decade addresses the fluctuations in network resources. One such hotly pursued research topic is survivable network planning. It considers the design of a network under uncertainties brought by the fluctuations in topology to meet the requirement that the network remains intact up to a certain number of faults occurring anywhere in the network. Recently, the authors proposed a new planning methodology called Generalized Survivable Network that tackles the network design problem under both varying traffic requirements and fluctuations of topology. Although all the above network planning problems handle various kinds of uncertainties, it is hard to find a generic framework under more general uncertainty conditions that allows a more systematic way to solve the problems. With a unified framework, the seemingly diverse models and algorithms can be intimately related and possibly more insights and improvements can be brought out for solving the problem. This motivates us to seek a generic framework for solving the network planning problem under uncertainties. In addition to reviewing the various network planning problems involving uncertainties, we also propose that a unified framework based on robust optimization can be used to solve a rather large segment of network planning problem under uncertainties. Robust optimization is first introduced in the operations research literature and is a framework that incorporates information about the uncertainty sets for the parameters in the optimization model. Even though robust optimization is originated from tackling the uncertainty in the optimization process, it can serve as a comprehensive and suitable framework for tackling generic network planning problems under uncertainties. In this paper, we begin by explaining the main ideas behind the robust optimization approach. Then we demonstrate the capabilities of the proposed framework by giving out some examples of how the robust optimization framework can be applied to the current common network planning problems under uncertain environments. Next, we list some practical considerations for solving the network planning problem under uncertainties with the proposed framework. Finally, we conclude this article with some thoughts on the future directions for applying this framework to solve other network planning problems.

Fine-tuned robust optimization: Attaining robustness and targeting ideality

A robust optimization framework for energy management of CCHP users with integrated demand response in electricity market

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.

Assessment of uncertainties and variations in PV modules degradation rates and lifetime predictions using physical models