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Control inputs of fully constrained cable-driven parallel robots (CDPRs) are constrained by the positiveness of the cables tension, as cables merely apply tensile forces. The positive tension distribution (PTD) in CDPRs is usually guaranteed with iterative optimization techniques, utilizing the redundant actuation of the CDPR. The iterative nature of the conventional PTD limits their real-time application since the worst-case computation time of the iterative methods is not predictable. In addition, optimization methods are prone to model uncertainties. This article addresses the PTD problem in the fully constrained CDPRs with a control viewpoint. In the proposed approach, the PTD algorithm is an integral part of the controller, which explicitly generates positive values for the cables tension. To this aim, a saturation-type function is coupled with the controller, and its effect is compensated using a nonlinear disturbance observer. The stability of the proposed control scheme is also investigated in detail through Lyapunov’s second method, considering a nonsingular terminal sliding mode controller. Furthermore, the performance of the proposed methodology is compared with the conventional method for a six-degrees-of-freedom CDPR, in the presence of uncertainties. Finally, the effectiveness of the proposed control scheme is investigated through experiments. [ABSTRACT FROM AUTHOR]

In remanufacturing research, most researchers predominantly emphasised on the recovery of whole product (core) rather than at the component level due to its complexity. In contrast, this paper addresses the challenges to focus on remanufacturing through component recovery, so as to solve production planning problems of hybrid remanufacturing and manufacturing systems. To deal with the uncertainties of quality and quantity of product returns, the processing time of remanufacturing, remanufacturing costs, as well as market demands, a robust optimisation model was developed in this research and a case study was used to evaluate its effectiveness and efficiency. To strengthen this research, a sensitivity analysis of the uncertain parameters and the original equipment manufacturer’s (OEM’s) pricing strategy was also conducted. The research finding shows that the market demand volatility leads to a significant increase in the under fulfilment and a reduction in OEM’s profit. On the other hand, recovery cost reduction, as endogenous cost saving, encourages the OEM to produce more remanufactured products with the increase in market demand. Furthermore, the OEM may risk profit loss if they raise the price of new products, and inversely, they could gain more if the price of remanufactured products is raised. [ABSTRACT FROM PUBLISHER]

This article presents a systematic robust current control design approach for three-phase voltage-source converters. Robustness is guaranteed by combining intrinsic passive properties of the impedance uncertainty at the point of common coupling together with stability results from a passivity-based control theory. This approach ensures stability against typical uncertainty sources at mid and high frequencies, such as cable resonances or other converters interaction, with significant less conservative performances than the obtained with the traditional robust control theory. The approach uses multiobjective controller synthesis formulation that allows us to logically combine robustness requirements with performance objectives avoiding heuristic iteration over the control structure and parameters. The controller synthesis is performed by means of a nonsmooth $\mathcal {H}_{\infty }$ optimization technique that tunes all free parameters of a vector-based controller function, which constraints its structure. This results in a synthesized controller with lower order than those obtained with convex optimization definitions of the $\mathcal {H}_{\infty }$ control problem. The design methodology is validated in time and frequency domain by means of theoretical analysis and experimental results with three usual grid filters: L, LCL, and LLCL. [ABSTRACT FROM AUTHOR]

In recent years, remarkable advancements have been achieved in quantitative analysis methods for supply chain design (SCD). Typically, cost or service level optimisation has been included in the objective functions. At the same time, supply chain managers face the ripple effect that arises from vulnerability, instability and disruptions in supply chains. This research aimed to quantify the ripple effect in the supply chain from the structural perspective. The research agenda of this study includes issues of integrating operability objectives as new key performance indicators, e.g. resilience, stability, robustness into SCD decisions. The research is based on a simultaneous consideration of both static structural properties of SCD and execution dynamics subject to uncertainty and disruptions. Due to high dimensionality of real SCD problems, such integration can hardly be implemented in only one model. In this study, an original two-model multi-criteria approach is proposed in order to assess the potential ability of an SCD to remain stable and resilient. This modelling approach is based on a combined application of a static and a dynamic model. A multi-criteria approach relies on the analytic hierarchy process method. The results of this research can be used as an additional quantitative analysis tool in order to select an SCD. An additional application of the developed method is that it can be used at the control stage in order to adapt supply chain execution subject to the achievement of desired economic performance. [ABSTRACT FROM AUTHOR]

• A novel concept of power-to-gas (P2G)-based virtual power plant (GVPP) is designed. • Power-gas-power effect of GVPP brought by P2G and gas storage tank is discussed. • A multi-objective flexible risk aversion model for GVPP operation is proposed. • Payoff table of optimization model is applied for multiple iterative weighting method. • Different operation cases for verifying the proposed operation strategy are defined. Power-to-gas (P2G) provides a new means for accommodating abandoned new energy that will support the optimal operation of virtual power plants (VPPs) in the future. In this study, a novel structure of a P2G-based virtual power plant (GVPP) is designed. A flexible risk aversion model for GVPP operation is proposed with two objectives—maximum operation profit and minimum operation risk. In the model, the conditional value at risk method and robust optimization theory are utilized to reflect uncertainty risks. To solve the multi-objective model, a solution algorithm was constructed for iteratively obtaining the optimal weight coefficient for transforming the multi-objective model into a single-objective model based on a payoff table and a rough set method. Four simulation cases were set for comparative analysis based on a nine-node energy hub system. The results show the following outcomes: (1) GVPP realizes the complementary utilization of distributed energy and forms a power-gas-power recycling mode, (2) the proposed model can provide an effective decision-making tool for different risk-attitude decision makers by setting a reasonable confidence level and robust coefficient, (3) P2G and price-based demand response (PBDR) improve the grid-connected space of clean energy, in particular, PBDR improves the flexibility of system operation and reduces operation risk, and (4) if the maximum emission trade allowance (META) is considered, P2G preferentially converts carbon dioxide into methane when the META is lower, while clean energy is preferentially used to satisfy load demand and the methane produced by P2G can be sold to the natural gas network when the META is higher. Overall, the proposed optimal decision model achieves the maximum utilization of clean energy to obtain higher economic benefits while rationally controlling operation risks; hence, providing reliable support for decision makers. [ABSTRACT FROM AUTHOR]

The position control and vibration suppression problems of the flexible solar array drive system containing uncertainty are considered in this paper. The uncertainty in system may be due to unknown parameters and external disturbance. The uncertainty bound can be described via a fuzzy set. In addition, there exists the flexible vibration in the system. A new optimal robust control approach with input shaping is proposed for the flexible solar array drive system. By designing the position command trajectory, the input shaper is proposed to suppress the flexible vibration. To enhance the position control performance, the optimal robust control is proposed by fuzzy description of the uncertainty bound. Neither the system nor the control is fuzzy if–then rule based. The global solution to this optimal design problem is demonstrated to be always existent and unique. The resulting control is able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while minimizing a fuzzy-based performance index associated with both the fuzzy performance and the control cost. In addition, the flexible vibration can be effectively suppressed. The novelty of this research is a systematic control approach by blending input shaping technology, control theory, fuzzy set theory, and optimization theory into an integrated framework, for solving the position control and vibration suppression problems of flexible solar array drive system with mismatched conditions. [ABSTRACT FROM AUTHOR]

To achieve the state estimation of uncertain nonlinear systems, this paper proposes a novel optimal robust observer via the fuzzy bound information of the uncertainty. A robust observer scheme is first proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the state estimation system regardless of the actual value of the uncertainty. To optimize the observer gain, a fuzzy set-theoretic-based optimal approach is then proposed by utilizing the fuzzy information of the uncertainty bound. The optimization problem is completely solved in analytic form. The resulting observer is able to guarantee the robustness of the state estimation system to the uncertainty, while minimizing an optimization index related to the state estimation performance and the observer cost. The novelty of this research is a creative optimal robust observer design by blending state estimation theory, fuzzy set theory, and optimization theory into an integrated framework. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A preventive crude oil scheduling method to handle ±10% demand fluctuation is developed. • The scheduling is performed to maximize the profit in single objective optimization. • Inter-period fluctuations in feed rate of crude distillation unit is additionally minimized in multi-objective optimization. • Four industrial-scale examples with time horizon of 3, 7, 14 and 20 days are solved. Abstract Crude oil supply about 33% of the total energy consumption worldwide and is predominantly (>50%) processed in marine access refineries. Therefore, crude oil scheduling which enables the efficient processing of the crude to increase the profitability is an important problem. It often becomes challenging due to the presence of combinatorial constraints, discrete variables and uncertainties. This study addresses the crude oil scheduling under commonly present demand uncertainty. A proactive two-stage approach has been developed to solve such optimization problems. A discrete-time model is used with structure adapted genetic algorithm (SAGA) for solving single- and multi-objective scheduling optimizations. In the first stage, an initial schedule is generated with the nominal parameters provided a priory. The same schedule is then checked and accepted in the second stage only if it is robust with respect to demand uncertainty. This method is applied to four different industrial size problems with scheduling horizon of 3, 7, 14 and 20 days. The objective function in the single objective formulation is the maximization of profit. However, in multi-objective optimization, an additional objective of minimization of fluctuation in crude oil supply to crude distillation units is used as it provides a better control and operability of the plant. The proposed method is successfully implemented for the above four different crude oil scheduling problems to generate the robust schedule. [ABSTRACT FROM AUTHOR]

Abstract We address the problem of designing as well as redesigning a relief network over multiple periods as a strategic decision which plays a critical role in the post-disaster management. Design of the relief network has a significant impact on the effective performance of disaster response operations. For considering both the uncertainty and dynamism of the decision-making environment, a comprehensive scenario-based robust approach embedded in the rolling horizon framework is proposed. The proposed mixed-integer linear programming model is inspired by a real case study of a disaster management in Iran, which aims to minimize the total cost of network management. Furthermore, restorative strategies are considered to increase the efficiency and robustness of the proposed relief network under disaster. To tackle the proposed optimization model, a heuristic solution algorithm is adopted. The results indicate that the proposed robust relief network provides an affordable access to its demand points in a sustainable manner under disaster. In addition, extensive computational results illustrate the efficiency of the proposed model in dealing with the considered disaster management issues. Highlights • A comprehensive scenario-based robust approach embedded in the rolling horizon framework. • Multi-objective mixed-integer linear programming model is inspired by a real case study of a disaster management in Iran. • Restorative strategies to increase the efficiency and robustness of the relief network under disaster. • An efficient solution algorithm for the two-phase rolling horizon robust optimization approach. [ABSTRACT FROM AUTHOR]

Robust fuzzy model predictive control of discrete nonlinear systems is investigated in this paper. A recently developed Takagi–Sugeno (T–S) fuzzy approach which uses nonlinear local models is adopted to approximate the nonlinear systems. A critical issue that restricts the practical application of classical model predictive control is the online computational cost. For model predictive control of T–S fuzzy systems, the online computational burden is even worse. Especially for complex systems with severe nonlinearities, parametric uncertainties, and disturbances, existing model predictive control of T–S fuzzy systems usually leads to a very conservative solution or even no solution in some occasions. However, more relaxed results can be achieved by the proposed fuzzy model predictive control approach which adopts T–S systems with nonlinear local models. Another advantage is that online computational cost of the optimization problem through solving matrix inequalities can be significantly reduced at the same time. Simulations on a numerical example and a two-tank system are presented to verify the effectiveness and advantages of the proposed method. Comparisons among several T–S fuzzy approaches are illustrated and show that the best settling time is achieved via the proposed method. [ABSTRACT FROM AUTHOR]

Summary: A new robust controller design method that satisfies the H∞ criterion is developed for linear time‐invariant single‐input single‐output (SISO) systems. A data‐driven approach is implemented in order to avoid the unmodeled dynamics associated with parametric models. This data‐driven method uses fixed‐order controllers to satisfy the H∞ criterion in the frequency domain. The necessary and sufficient conditions for the existence of such controllers are presented by a set of convex constraints. These conditions are also extended to systems with frequency‐domain uncertainties in polytopic form. It is shown that the upper bound on the weighted infinity norm of the sensitivity function converges monotonically to the optimal value, when the controller order increases. Additionally, the practical issues involved in computing fixed‐order rational H∞ controllers in discrete‐time or continuous‐time by convex optimization techniques are addressed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Independent operation of single microgrids (MGs) faces problems such as low self-consumption of local renewable energy, high operation cost and frequent power exchange with the grid. Interconnecting multiple MGs as a multi-microgrid (MMG) is an effective way to improve operational and economic performance. However, ensuring the optimal collaborative operation of a MMG is a challenging problem, especially under disturbances of intermittent renewable energy. In this paper, the economic and collaborative operation of MMGs is formulated as a unit commitment problem to describe the discrete characteristics of energy transaction combinations among MGs. A two-stage adaptive robust optimization based collaborative operation approach for a residential MMG is constructed to derive the scheduling scheme which minimizes the MMG operating cost under the worst realization of uncertain PV output. Transformed by its KKT optimality conditions, the reformulated model is efficiently solved by a column-and-constraint generation (C&CG) method. Case studies verify the effectiveness of the proposed model and evaluate the benefits of energy transactions in MMGs. The results show that the developed MMG operation approach is able to minimize the daily MMG operating cost while mitigating the disturbances of uncertainty in renewable energy sources. Compared to the non-interactive model, the proposed model can not only reduce the MMG operating cost but also mitigate the frequent energy interaction between the MMG and the grid. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles are famous for their wide range of applications. In D3 (Dirty-Dull-Dangerous) UAV applications flight conditions may vary on large scale. External disturbances like atmospheric turbulences and gusts may be subjected to UAV, and as a result, UAV flight mission might be conducted with high level of the degradation of the accuracy. Sensor noises are also present, and theirs negligence might lead to improper dynamic performances of the closed loop control systems. Uncertainties of the control systems being structured or unstructured may tend the closed loop control system to stability bounds. In worst case, uncertainties may destabilize closed loop control systems. The purpose of the author is to present a robust controller design method called H2-optimal design ensuring stability of the closed loop control systems with simultaneous dynamic performances predefined for the closed loop control system. [ABSTRACT FROM AUTHOR]

Summary: This study is concerned with the rigorous solution of worst‐case robust optimal control problems having bounded time‐varying uncertainty and nonlinear dynamics with affine uncertainty dependence. We propose an algorithm that combines existing uncertainty set‐propagation and moment‐expansion approaches. Specifically, we consider a high‐order moment expansion of the time‐varying uncertainty, and we bound the effect of the infinite‐dimensional remainder term on the system state, in a rigorous manner, using ellipsoidal calculus. We prove that the error introduced by the expansion converges to zero as more moments are added. Moreover, we describe a methodology to construct a conservative, yet more computationally tractable, robust optimization problem, whose solution values are also shown to converge to those of the original robust optimal control problem. We illustrate the applicability and accuracy of this approach with the robust time‐optimal control of a motorized robot arm. [ABSTRACT FROM AUTHOR]

The use of weights in multi-objective problems is one of the simplest ways to include multiple criteria in optimization models, in what is known as a weighted-sum approach. However, the solution to these models is highly dependent on the value of the weights, which is difficult to determine accurately. In this paper, we consider that the weights are defined as intervals of possible values rather than point estimates, and formulate a robust version of the traditional multi-objective optimization model. We explore, through a computational experiment, the effect that the uncertainty in the weights has on the optimal decisions and the levels obtained of the different objectives. Robust solutions favor decisions that produce similar levels of the different objectives and produce more of those objectives for which the weights are more certain. We apply this model to a lumber production problem where, in practice, more than a single performance indicator is pursued, but there is no clear preference relationship among them. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for the offering strategy of a virtual power plant that participates in the day-ahead and the real-time energy markets. The virtual power plant comprises a conventional power plant, a wind-power unit, a storage facility, and flexible demands, which participate in the day-ahead and the real-time markets as a single entity in order to optimize their energy resources. We model the uncertainty in the wind-power production and in the market prices using confidence bounds and scenarios, respectively, which allows us to formul-ate the strategic offering problem as a stochastic adaptive robust optimization model. Results of a case study are provided to show the applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

Modern Robust Control has had two distinct lines of development: (a) Robustness through quadratic optimization and (b) Robustness under parametric uncertainty. The first approach consists of Kalman’s Linear Quadratic Regulator and H ∞ optimal control. The second approach is the focus of this overview paper. It provides an account of both analysis as well as synthesis based results. This line of results was sparked by the appearance of Kharitonov’s Theorem in the early1980s. This result was rapidly followed by further results on the stability of polytopes of polynomials such as the Edge Theorem and the Generalized Kharitonov Theorem, stability of systems under norm bounded perturbations and the computation of parametric stability margins. Many of these analysis results established extremal testing sets where stability or performance would breakdown. Starting in 1997, when it was established that high order controllers were fragile, attention turned to the synthesis and design of the parameters of low order controllers such as three term controllers and more particularly Proportional-Integral-Derivative (PID) controllers. An extensive theory of design of such systems has developed in the last twenty years. We provide a summary without proofs, of many of these results. [ABSTRACT FROM AUTHOR]

Since their first appearance in the 1970's, industrial robotic manipulators have considerably extended their application fields, allowing end-users to adopt this technology in previously unexplored scenarios. Correspondingly, the way robot motion can be specified has become more and more complex, requiring new capabilities to the robot, such as reactivity and adaptability. For an even enhanced and widespread use of industrial manipulators, including the newly introduced collaborative robots, it is necessary to simplify robot programming, thus allowing this activity to be handled by non-expert users. Next generation robot controllers should intelligently and autonomously interpret production constraints, specified by an application expert, and transform them into motion commands only at a lower and real-time level, where updated sensor information or other kind of events can be handled consistently with the higher level specifications. The availability of several execution strategies could be then effectively exploited in order to further enhance the flexibility of the resulting robot motion, especially during collaboration with humans. This paper presents a novel methodology for motion specification and robust reactive execution. Traditional trajectory generation techniques and optimisation-based control strategies are merged into a unified framework for simultaneous motion planning and control. An experimental case study demonstrates the effectiveness and the robustness of this approach, as applied to an image-guided grasping task. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive robust network-constrained AC unit commitment (AC-UC) model. This model is formulated as a min–max–min optimization problem, which allows representing the uncertain nature of wind power productions in terms of bounded intervals. A tri-level decomposition algorithm using primal and dual cutting planes is introduced to solve this AC-UC problem and to find a robust commitment schedule withstanding the worst realizations of uncertain wind power. To reduce the computation burden and to obtain a tractable formulation, the AC power flow equations are convexified using a Signomial transformation. The proposed AC-UC model is illustrated using the IEEE 24-bus reliability test system. Simulation results demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Uncertainty analysis of an industrial grinding optimization process involving various sources of uncertainties and multiple numbers of objective functions has been studied in this work. Two primary sources of uncertainties, e.g . (1) operational parameters such as feed size distributions that are subjected to uncertainty due to varied range of feed sources that the industrial grinding process handles, and (2) model parameters that are obtained by the regression analysis of experimental data and subjected to regression and experimental errors, have been considered. Moreover, obtaining statistical distributions for these uncertain parameters are practically challenging. Hence, these parameters are considered as fuzzy numbers and the embedded uncertain multi-objective optimization problem has been analyzed using credibility based fuzzy robust optimization (FRO) technique. This technique helps in converting the uncertain fuzzy optimization formulation into a deterministic equivalent form, which can be further utilized to obtain the Pareto solutions by well-developed evolutionary algorithms. Initially, PO solutions are obtained by considering the uncertainty in different sets of uncertain parameters separately. This is followed by the study of amalgamated effect of uncertain parameters on PO solutions. Along with this, different fuzzy measures e.g . credibility, possibility, necessity etc . are utilized to observe their effects on final solutions. PO solutions obtained from possibility and necessity based FRO show the optimistic and pessimistic attitudes of risk, respectively. This provides a key to a decision maker to select any point based on the existing risk appetite. As compared to the deterministic results, the robust Pareto solutions show potential improvements of 26% and 16% in throughput and mid-size fractions, respectively. This generic approach not only provides the solution for robust range of operation based on the risk appetite of the enterprise, but also helps a decision maker to decide which parameters, amidst the set of uncertain parameters, are more sensitive to the results utilizing various fuzzy measures such as credibility, possibility and necessity. Along with this, the PO solutions obtained with robust optimization are compared with the solutions obtained by Expected Value Model (EVM). [ABSTRACT FROM AUTHOR]

In this work, we consider the problem of daily production optimization in the upstream oil and gas domain. The objective is to find the optimal decision variables that utilize the production systems efficiently and maximize the revenue. Typically, mathematical models are used to find the optimal operation in such processes. However, such prediction models are subject to uncertainty that has been often overlooked, and the optimal solution based on nominal models can thus render the solution useless and may lead to infeasibility when implemented. To ensure robust feasibility, worst case optimization may be employed; however, the solution may be rather conservative. Alternatively, we propose the use of scenario-based optimization to reduce the conservativeness. The results of the nominal, worst case and scenario-based optimization are compared and discussed. [ABSTRACT FROM AUTHOR]

One of the major challenges of today's world is the energy crisis, which has significant impact on other issues, such as world economy or the environment. Due to its vital role in manufacturing, energy saving should be considered as an important element of production planning, especially for energy intensive manufacturing plants. In this paper, an aggregate planning model is developed to consider energy planning, demand and production capacity simultaneously. The model happens to be a linear program with three objective functions, which minimize the operational cost, the energy cost and carbon emission. The proposed model is solved as a single-objective model applying a goal attainment technique. To overcome the effects of uncertain input data, we apply the robust optimization approach to this model. The practicality of the proposed approach is illustrated by applying it to a smelting manufacturer, which produces a wide range of products such as aluminum, copper and lead. Considering uncertainty in objective function parameters, we provide some insights into the relationship between the budgets of uncertainty and optimal values. Moreover, regarding uncertainty in product demands, we generate the robust solutions which have a better performance than the deterministic solutions; also we test “ Aggregate constraints approach ” to the maximum production capacity parameters successfully. The sensitivity of different uncertain parameters is also analyzed. [ABSTRACT FROM AUTHOR]

Task-space inverse dynamics (TSID) is a well-known optimization-based technique for the control of highly redundant mechanical systems, such as humanoid robots. One of its main flaws is that it does not take into account any of the uncertainties affecting these systems: poor torque tracking, sensor noises, delays, and model uncertainties. As a consequence, the resulting control-state trajectories may be feasible for the ideal system, but not for the real one. We propose to improve the robustness of TSID by modeling uncertainties in the joint torques, either as Gaussian random variables or as bounded deterministic variables. Then we try to immunize the constraints of the system to any—or at least most—of the realizations of these uncertainties. When the resulting optimization problem is computationally too expensive for online control, we propose ways to approximate it that lead to computation times below 1 ms. Extensive simulations in a realistic environment show that the proposed robust controllers greatly outperform the classic one, even when other unmodeled uncertainties affect the system (e.g., errors in the inertial parameters, delays in the velocity estimates). [ABSTRACT FROM AUTHOR]

The active distribution network is a new solution to the flexible utilization of distributed energy resources to suit the characteristics of the distribution network. Advanced “active” network management is to coordinate “generation, network, load” optimization and achieve the right balance between operational expenditure (OPEX) and capital expenditure (CAPEX). To demonstrate the advancement from introducing an active distribution network, the key features of distribution network planning mainly including traditional models is first introduced. Extensive literature in generic planning is then summarized and categorized in terms of objective functions, system modeling, solution algorithms, and tools. This is followed by an extended review and in-depth discussion of concepts and representative topic developments in optimal active distribution network planning. In contrast to traditional planning, it takes into account the effects from a range of active network interventions that are exercised at differing time scales while capturing the intrinsically stochastic behavior of renewable generation or demand response to produce strategic plans that are robust against a highly uncertain energy future. Finally, a multi-dimensional framework for optimal active distribution network planning is proposed to overcome the limitations of the current state of the art, and the challenges in each stage are also highlighted. [ABSTRACT FROM AUTHOR]

This paper presents new results on linear transceiver designs in a multiple-input–multiple-output (MIMO) link. By considering the minimal total mean-square error (MSE) criterion, we prove that the robust optimal linear transceiver design has a channel-diagonalizing structure, which verifies the conjecture in the previous work. Based on this property, the original design problem can be transformed into a scalar problem, whose global optimal solution is first obtained in this work. Simulation results show the performance advantages of our solution over the existing schemes. [ABSTRACT FROM AUTHOR]

To consider the interval uncertainty in a practical optimal design problem, a new methodology for efficient robust optimizations is proposed. The proposed methodology uses a constrained formulation for robust performances not only in alleviating the inefficiency of the existing approaches in modeling interval uncertainties but also in avoiding the deficiency in the biasing force selection. The gradient information is used as both a trigger to activate the uncertain quantification procedure and the steepest increment direction to develop a fast searching phase. The stochastic approximation method is employed to minimize the computational burdens in computing the gradients. The numerical results on a case study are reported to validate the proposed methodology. [ABSTRACT FROM AUTHOR]

Solving optimization problems under hybrid uncertainty bears a heavy computational burden. In this study, we propose a unified structured optimization approach, termed robust granular optimization (RGO), to tackle the optimization problems under hybrid manifold uncertainties in a computationally tractable manner. Essentially, the RGO can be regarded as a complementary fusion of granular computing and robust optimization techniques. The paradigm of RGO consists of three core phases: 1) uncertainty identification, 2) information granulation in which basic granular units (BGUs) are formed, and 3) robust optimization realized over the BGUs. Following the proposed paradigm, we develop two classes of RGO models for general single-stage and two-stage optimization problems with separable and higher order hybrid uncertainties, respectively. It is shown that both types RGO models can be equivalently transformed into linear programs or mixed integer linear programs that can be handled efficiently by off-the-shelf solvers. Furthermore, a target-based tradeoff model is developed to enhance the flexibility of the RGO models in balancing the granularity level (or robustness level) and the solution conservativeness. The tradeoff model can also be efficiently solved by a binary search algorithm. Finally, sufficient computational studies are presented, and comparisons with the existing approaches show that the RGO models can bring much higher computational efficiency and scalability without losing much optimality, and the RGO solutions exhibit a stronger resistance to the uncertainty. [ABSTRACT FROM PUBLISHER]

Robust design optimization aims to find solutions that are competent and reliable under given uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this paper focuses on problems where uncertainties emanate from design variables. In commercial designs, being reliable is often of more practical value than being globally best (but unreliable). Robust optimization poses three key challenges: 1) appropriate formulation of the problem ; 2) accurate estimation of the “robustness” measure; and 3) efficient means to identify the set of tradeoff robust solutions with an affordable computational cost. In this paper, four different problem formulations for robust optimization are presented and analyzed. The proposed formulations offer a set of tradeoff solutions with robustness from two perspectives—feasibility robustness, i.e., robustness against failure and performance robustness, i.e., robustness assuring good performance. The approach also provides means to identify critical constraints or performance functions that affect the overall robustness. The problem is posed as a many-objective optimization problem and a decomposition-based evolutionary approach is used for solving it. The performance of the proposed approach and the consequences of using different formulations are illustrated using two numerical examples and four engineering problems. [ABSTRACT FROM PUBLISHER]

Flooding is one of the leading causes of loss due to natural catastrophes, and at least one third of all losses due to natural forces can be attributed to flooding. Flood management systems involve a variety of complexities, such as multiple uncertainties, dynamic variations, and policy implications. This paper presents an inexact probabilistic–possibilistic programming with fuzzy random coefficients (IPP-FRC) model for flood management in a hybrid uncertain environment. IPP-FRC is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi-region, multi-flood-level, and multi-option context. The possibility and necessity measures used in IPP-FRC are suitable for risk-seeking and risk-averse decision making, respectively. A case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management. The results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence, implying a potential tradeoff between fulfillment of objectives and associated risks. A number of decision alternatives can be obtained under different policy scenarios. They are helpful for decision makers to formulate the appropriate flood management policy according to practical situations. The performance of IPP-FRC is analyzed and compared with a possibility-based fractile model. [ABSTRACT FROM AUTHOR]

Developing long term operation rules for multi-reservoir systems is complicated due to the number of decision variables, the non-linearity of system dynamics and the hydrological uncertainty. This uncertainty can be addressed by coupling simulation models with multi-objective optimisation algorithms driven by stochastically generated hydrological timeseries but the computational effort required imposes barriers to the exploration of the solution space. The paper addresses this by (a) employing a parsimonious multi-objective parameterization-simulation-optimization (PSO) framework, which incorporates hydrological uncertainty through stochastic simulation and allows the use of probabilistic objective functions and (b) by investigating the potential of multi-objective surrogate based optimisation (MOSBO) to significantly reduce the resulting computational effort. Three MOSBO algorithms are compared against two multi-objective evolutionary algorithms. Results suggest that MOSBOs are indeed able to provide robust, uncertainty-aware operation rules much faster, without significant loss of neither the generality of evolutionary algorithms nor of the knowledge embedded in domain-specific models. [ABSTRACT FROM AUTHOR]

Uncertainty can be defined as the probability of difference between the forecasted value and the real value. As this probability is small, the operation cost of the power system will be less. This purpose necessitates modeling of system random variables (such as the output power of renewable resources and the load demand) with appropriate and practicable methods. In this paper, an adequate procedure is proposed in order to do an optimal energy management on a typical micro-grid with regard to the relevant uncertainties. The point estimate method is applied for modeling the wind power and solar power uncertainties, and robust optimization technique is utilized to model load demand uncertainty. Finally, a comparison is done between deterministic and probabilistic management in different scenarios and their results are analyzed and evaluated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a model to optimization of milk run system that is one of VRP problem with time window and uncertainty in inventory. This approach led to the routes with minimum cost of transportation while satisfying all inventory in a given bounded set of uncertainty. The problem is formulated as a robust optimization problem. Since the resulted problem illustrates that grows up time in this method is progressive, and in order to solve the large-scale problems, eCGA (Extended Compact Genetic Algorithm) has been proposed. The efficiency and effectiveness of the eCGA to this optimization problem is tested and the results are presented. The results show the ability of the eCGA to efficiently optimal solution for the cases considered. Investigated example showed that this method has the ability to obtain a solution more accurate than other optimization methods. [ABSTRACT FROM AUTHOR]

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

We argue that the concepts ofresiliencein engineering science androbustnessin mathematical optimisation are strongly related. Using evacuation planning as an example application, we demonstrate optimisation techniques to improve solution resilience. These include a direct modelling of the uncertainty for stochastic or robust optimisation as well as taking multiple objective functions into account. [ABSTRACT FROM PUBLISHER]

Info-Gap Decision Theory is adopted to assess the robustness of a technique aimed at identifying the optimal excitation signal to be used for active sensing approaches to damage detection. Here the term "active sensing" refers to procedures where a known input is applied to the structure to enhance the damage detection process. Given limited system response measurements and ever-present physical limits on the level of excitation, the ultimate goal of the mentioned technique is to improve the detectability of damage by increasing the difference between measured outputs of the undamaged and damaged systems. In particular, a two degree-of-freedom mass-spring-damper system characterized by the presence of a nonlinear stiffness is considered. Uncertainty is introduced to the system in the form of deviations of its parameters (mass, stiffness, damping ratio) from their nominal values. Variations in the performance of the mentioned technique are then evaluated both in terms of changes in the estimated difference between the responses of the damaged and undamaged systems and in terms of deviations of the identified optimal input signal from its nominal estimation. Finally, plots of the performances of the analyzed algorithm for different levels of uncertainty are obtained, enabling a clear evaluation of the risks connected with designing excitation signals for damage detection, when the parameters that dictate system behavior (e.g. stiffness, mass) are poorly characterized or improperly modeled. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for optimal staged development of water supply systems that ensures robust and sustainable solutions. This problem is formulated as a multi-objective optimisation problem under uncertainty with objectives being the minimisation of average present value of intervention costs and greenhouse gas emissions, and the maximisation of supply robustness. The above methodology was validated and demonstrated on southern portion of the regional water supply system of Adelaide. The results obtained illustrate the importance of identifying optimal staged solutions to ensure robustness and sustainability of water supply into uncertain long-term future. [ABSTRACT FROM AUTHOR]

In this paper, a practical modeling and robust controller optimization strategy is presented for an ultraprecision positioning stage with position-dependent dynamics to achieve ultraprecision positioning accuracy. A linear-fractional-transformation structured uncertainty modeling procedure is proposed to describe the varying dynamics of the stage. The modeling process involves the global curve fitting of frequency response functions and dimensionality reduction for the uncertainty structure so that the uncertainty set could be minimized. Then, a robust loop-shaping controller optimization method is presented to improve the control performances. The optimization objective includes the control bandwidth and the disturbance rejection ability, and $\mu$ analysis is employed as a nonconservative robust condition with respect to the structured uncertainty. A genetic algorithm is then utilized to determine the optimal parameters of the controller. Comparative experiments on a developed ultraprecision positioning stage are finally conducted, and the results validate that significant improvements on rising time, settling time, and positioning accuracy have been achieved. [ABSTRACT FROM PUBLISHER]

In this study, an inexact mixed-integer fuzzy robust linear programming model for coupled management of coal and power with consideration of CO2emissions mitigation system planning (IMIFLP-CCPM) was developed under uncertainty. This model could reach into the closed relationship and interactive characteristics of China’s coal production, electric power generation, and CO2emissions in coupled coal and power management system and thus explore the applicability of the decarburization facilities and mechanism incorporated in the system through scenario analysis. Based on the integration of interval linear programming, fuzzy robust linear programming, and mixed-integer linear programming, the IMIFLP-CCPM could effectively incorporate and handle uncertainties presented in terms of interval values and fuzzy sets. Also, dynamic analysis of capacity expansion, facility improvement, and inventory planning within a multi-period and multi-option context could be facilitated in this model. The developed IMIFLP-CCPM was applied to a long-term coupled coal and power management with CO2reduction systems in Subei region, Northeast China. One base scenario and four CO2reduction scenarios were presented and analyzed to examine the optimal coal-flow allocation patterns and carbon mitigation schemes for the studied system when forced to comply with a given CO2emission limit. The results indicated that the IMIFLP-CCPM model could provide in-depth analysis of tradeoffs between system costs, energy security, and CO2emission reduction, thus helping investigate interactive relationships among multiple economical, environmental, and energy structural targets within the study system. Moreover, the attempt of planning coupled coal and power management with CO2mitigation under uncertainty would provide an effective reference to cope with the dilemma of energy development and CO2mitigation under the climate change situation in China. [ABSTRACT FROM AUTHOR]

This paper presents a robust network design model for the supply of blood during and after disasters. A practical optimization model is developed that can assist in blood facility location and allocation decisions for multiple post-disaster periods. The application of the proposed model is investigated in a case problem where real data is utilized to design a network for emergency supply of blood during potential disasters. Our analysis on the tradeoff between solution robustness and model robustness arrives at important practical insights. The performance of the proposed ‘robust optimization’ approach is also compared with that of an ‘expected value’ approach. [ABSTRACT FROM AUTHOR]

This paper focuses on the design of a distribution network problem in a three-tiered supply chain under uncertainty. The objective is to determine the optimal number, locations and capacities of plants and warehouses to minimize the overall network costs over a variety of economic growth scenarios. For this purpose, a mixed integer linear programming model is extended in a robust optimization framework and then three heuristic approaches based on genetic and memetic algorithms and a mathematical programming approach are used to solve this problem. The effectiveness of the proposed heuristics and the trade-off between model robustness and solution robustness is investigated and directions for further researches are presented. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust model predictive control (RMPC) with saturations and packet dropouts. In this model, polytopic uncertainties are adopted to describe the inconsistency arising from the discretization process of sampling, while the occurrence probabilities of packet dropouts are time-varying and saturations are taken into account to describe input and output signals. The problem of exponential RMPC with saturations and packet dropouts is solved and characterized by a convex optimization problem. The developed results of RMPC are then applied to networked flotation processes, which are made up of three layers: direct control layer, set-point control layer, and optimization layer. The RMPC is used for compensating the output information from the optimization layer to the direct control layer such that the desired economic objective can be achieved. Simulations are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we present new concepts of efficiency for uncertain multi-objective optimization problems. We analyze the connection between the concept of minmax robust efficiency presented by Ehrgott et al. (Eur J Oper Res, , doi:) and the upper set less order relation $$\preceq _s^u$$ introduced by Kuroiwa (, ). From this connection we derive new concepts of efficiency for uncertain multi-objective optimization problems by replacing the set ordering with other set orderings. Those are namely the lower set less ordering (see Kuroiwa , ), the set less ordering (see Nishnianidze in Soobshch Akad Nauk Gruzin SSR 114(3):489-491, ; Young in Math Ann 104(1):260-290, , doi:; Eichfelder and Jahn in Vector Optimization. Springer, Berlin, ), the certainly less ordering (see Eichfelder and Jahn in Vector Optimization. Springer, Berlin, ), and the alternative set less ordering (see Ide et al. in Fixed Point Theory Appl, , doi:; Köbis ). We analyze the resulting concepts of efficiency and present numerical results on the occurrence of the various concepts. We conclude the paper with a short comparison between the concepts, and an outlook to further work. [ABSTRACT FROM AUTHOR]

This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]