Robustly Multi-Microgrid Scheduling: Stakeholder-Parallelizing Distributed Optimization

†‡ § ** In traditional structural optimization, the geometric properties of the product are optimized for a specific set of material properties. This paper seeks to extend the domain of product optimization to also include the material modeling parameters by treating the product and material as a hierarchical multilevel system that can be decomposed and solved using the analytical target cascading (ATC) method. Two material models are considered here. The low-fidelity model is based on a simple elastic-plastic constitutive law with linear hardening whereas the high-fidelity model is based on an internal-state-variable representation that is influenced by the microstructural features of the material. The ATC method is applied to product-material design optimization of a multi-cell, thin-walled tube for impact energy absorption and durability. The integrated product-material optimization problem is solved using both single and multilevel approaches with results compared.

Optimization of piping supports is a well-known problem. The paper considers the optimization of piping supports with respect to cost and the loads transmitted to the supporting structural elements, when the orientation of the supporting structure is to be determined. This is the case, when new structural elements need to be added to the existing building structure to support components and piping systems that come as a new addition to a nuclear plant. The analytical target cascading (ATC) method is used for the optimization, combining the support loads from different piping analyses in a hierarchical framework. It is shown that the ATC method can be used for an optimized location of structural elements simultaneously supporting complex piping systems and implemented in a structural analysis software.

Analytical target cascading based real-time distributed voltage control for MV and LV active distribution networks

Purpose – In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy. Design/methodology/approach – Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution. Findings – The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method. Originality/value – This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.

Trajectory/propulsion integrated design optimization of the manned lunar lander propelled by hybrid rocket motors using analytical target cascading

A parallel approach with the strategy-proof mechanism for large-scale group decision making: An application in industrial internet

This chapter presents a methodology for analytical target cascading (ATC) under uncertainty to address the risk management problem. The proposed hierarchical ATC structure is exactly corresponding to the systematic risk management, which is a multidisciplinary optimization procedure. Since the uncertainty induces risks, the proposed probabilistic algorithm reformulates the ATC method by setting random variables and probabilistic constraints. The proposed ATC method decomposes risk management problem into hierarchical sub-problems, which are linked directly above and below using mean values and standard deviations. With the given risk targets from upper levels transmitting downward, each sub-problem at each level of the hierarchy operates the adaptive optimization method to narrow the gaps between responses and the distributed targets. Once the convergence is attained by iterating between top and bottom, variables and parameters are optimized to reduce the risks. The Risk can be regarded as an optimization target together with efficiency and cost, or it can be contained in constraints in each sub-problem to optimize the efficiency and cost within the prescribed risk boundary. A case of risk management optimization is given to verify the proposed methodology. The results confirm the applicability and efficiency of the probabilistic ATC method under uncertainty in risk management.

The design of manufacturing systems, such as steel manufacturing, involves sharing and coordinating information flow between multiple interrelated disciplines involving the material, product, and process. Achieving system performance necessitates exploring multiple disciplines with multiple goals simultaneously while ensuring consistency between level-specific design decisions. This necessitates “co-design” exploration, where design decision-makers from multiple disciplines collaboratively share information and resources to make informed decisions. In this paper, we present a multi-goal, multidisciplinary decision support framework for co-design exploration. The framework integrates the compromise Decision Support Problem (cDSP) formulation with the Analytical Target Cascading (ATC) method for multi-goal, multidisciplinary coupled problem formulation and a machine learning-based tool called interpretable Self-Organizing Maps (iSOM) for solution space visualization and exploration. The cDSP enables the formulation of decision-support problems and managing multiple conflicting goals within a discipline, while the ATC method captures the multidisciplinary interactions, maintaining consistency among coupled and shared variables. The machine learning-based visualization tool iSOM enables designers to explore high-dimensional multidisciplinary design spaces simultaneously in two dimensions efficiently and interpretably. Using the framework, designers are able to (i) concurrently design across multiple disciplines while addressing multiple goals, (ii) account for interactions and couplings among multiple disciplines, and (iii) perform co-design exploration in multidisciplinary solution space. The framework’s efficacy is demonstrated using an industry-inspired hot rod rolling process chain problem involving multiple interacting disciplines (namely the material, the product, and the manufacturing process) and conflicting goals. The framework is generic and supports the co-design exploration of systems characterized by multidisciplinary, multi-goal interactions.

Extending analytical target cascading for optimal configuration of supply chains with alternative autonomous suppliers

Platforming is not only a powerful approach to new product development by sharing common and modular components and processes but also allows the supply chain to gain benefits from risk-pooling effect through shared resources. Analytical target cascading (ATC) is a decentralised method suitable for configuring a hierarchical supply chain of an assembled product while accommodating necessary degree of decision autonomy and information privacy of individual enterprises. Because product variants in a family share platform components, the supply chain structure becomes a weakly networked hierarchy where a small number of elements are laterally linked. In addition, multiple customers who share a common platform component may require the corresponding supplier to use different strategies such as just-in-time (JIT) and lowest price to supply the component. As a result, different decision variables may be involved in the interaction between a shared lower-level element and its different parental elements. This paper develops a new ATC method suitable for dealing with these two special characteristics in supply chain configuration (SCC) for a product family. Numerical results demonstrate that the new method produces better results than those obtained from using the ATC method that only allows a supplier to optimise the supply of the platform component to all its customers with the same strategy.

The area of Multiparametric Optimization (MPO) solves problems that contain unknown problem data represented by parameters. The solutions map parameter values to optimal design and objective function values. In this paper, for the first time, MPO techniques are applied to improve and advance Multidisciplinary Design Optimization (MDO) to solve engineering problems with parameters. A multiparametric subgradient algorithm is proposed and applied to two MDO methods: Analytical Target Cascading (ATC) and Network Target Coordination (NTC). Numerical results on test problems show the proposed parametric ATC and NTC methods effectively solve parametric MDO problems and provide useful insights to designers. In addition, a novel Two-Stage ATC method is proposed to solve nonparametric MDO problems. In this new approach elements of the subproblems are treated as parameters and optimal design functions are constructed for each one. When the ATC loop is engaged, steps involving the lengthy optimization of subproblems are replaced with simple function evaluations.

For the multidisciplinary design optimization (MDO) question of autonomous rendezvous spacecraft, first, the analysis model and coupling relations of payload, propulsion and structure discipline are discussed; then the updated analytical target cascading (UATC) method is introduced and compared with the widely used collaborative optimization (CO). Results prove that the UATC method requires 54.8% fewer average subspace iterations than the CO and is more efficient for practical engineering MDO problem. Finally, based on the UATC method, a MDO problem of autonomous rendezvous spacecraft is solved and gets reasonable and effective results. The process proves the effectiveness of UATC method solving spacecraft MDO problem.

Analytic target cascading with fuzzy uncertainties based on global sensitivity analysis for overall design of launch vehicle powered by hybrid rocket motor

On the one hand, the dynamic characteristics of gas-heat flow in the IES (integrated energy system) are important in achieving multi-energy coupling, improving system scheduling flexibility, and increasing energy regulation potential. On the other hand, the uncertainty of new energy causes fluctuations in the interactive power between the upper TG (transmission grid) and the lower IES, and its coupling characteristics weaken the autonomy of each system. Therefore, this paper proposes a robust two-stage scheduling strategy for TG-IES, considering gas-heat dynamic characteristics. Firstly, according to the characteristic equation of gas-heat energy flow, the dynamic model of the gas-heat network is established and applied to system scheduling. Secondly, aiming at the uncertainty problem, a TG-IES two-stage robust model is constructed, and the ATC (analytical target cascading) method and the C&CG (column and constraint generation) algorithm are combined to realize the distributed solution of the non-convex coupling model. Finally, the effectiveness of the model and strategy is verified by using the IEEE-39 system as TG and the IEEE39 Grid-20 Gas Grid-6 Heat Network system as IES. The simulation results show that using a two-stage robust model and considering the dynamic characteristics of gas and heat can effectively reduce system operating costs and improve the environmental friendliness of system scheduling.

Under dynamic conditions, the dynamic force between the suspended equipment and the car body is substantially increased. This increase not only affects the ride comfort but also substantially raises the likelihood of fatigue damage to the suspended equipment. A multiobjective analytical target cascading (ATC) optimization is proposed to improve the ride comfort of high-speed trains and reduce the vibration of the suspended equipment. A mathematical simulation model of the vehicle equipment system is established, and the acceleration frequency-response function expression of the car body and the suspension system is obtained. The comfort index of the car body and the acceleration root mean square (RMS) of the suspended equipment are calculated by combining the German vertical irregular track spectrum and the comfort filter function. Meanwhile, the ATC method is used to optimize the car body comfort index and the acceleration RMS of the underframe suspended equipment. Then, the availability of the optimization method is evaluated via numerical simulation. Compared with the original suspension scheme of the underframe equipment, when the running speed of the vehicle is 300 km/h, the RMS value of the vibrational acceleration of the underframe equipment after optimization decreases by 19.9 %, and the ride comfort indexes at the car body center and above the front and rear bogies are improved by 6.4 %, 0.1 %, and 1.1 %, respectively. Simulation results demonstrate that ATC optimization can improve the railway vehicle ride comfort and reduce the vibration of the suspended equipment. This paper provides a new approach to the suspension parameter design of equipment.