Network Target Coordination for Design Optimization of Decomposed Systems

A complex engineered system is often decomposed into a number of different subsystems that interact on one another and together produce results not obtainable by the subsystems alone. Effective coordination of the interdependencies shared among these subsystems is critical to fulfill the stakeholder expectations and technical requirements of the original system. The past research has shown that various coordination methods obtain different solution accuracies and exhibit different computational efficiencies when solving a decomposed system. Addressing these coordination decisions may lead to improved complex system design. This dissertation studies coordination methods through two types of decomposition structures, hierarchical, and nonhierarchical. For coordinating hierarchically decomposed systems, linear and proximal cutting plane methods are applied based on augmented Lagrangian relaxation and analytical target cascading (ATC). Three nonconvex, nonlinear design problems are used to verify the numerical performance of the proposed coordination method and the obtained results are compared to traditional update schemes of subgradient-based algorithm. The results suggest that the cutting plane methods can significantly improve the solution accuracy and computational efficiency of the hierarchically decomposed systems. In addition, a biobjective optimization method is also used to capture optimality and feasibility. The numerical performance of the biobjective algorithm is verified by solving an analytical mass allocation problem. For coordinating nonhierarchically decomposed complex systems, network target coordination (NTC) is developed by modeling the distributed subsystems as different agents in a network. To realize parallel computing of the subsystems, NTC via a consensus alternating direction method of multipliers is applied to eliminate the use of the master problem, which is required by most distributed coordination methods. In NTC, the consensus is computed using a locally update scheme, providing the potential to realize an asynchronous solution process. The numerical performance of NTC is verified using a geometrical programming problem and two engineering problems

A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX

Sequential Linear Programming Coordination Strategy for Deterministic and Probabilistic Analytical Target Cascading.

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical systems, which was recently extended to probabilistic design. Solving the optimization problem requires propagation of uncertainty, namely, evaluating or estimating output distributions given random input variables. This uncertainty propagation can be a challenging and computationally expensive task for nonlinear functions, but is relatively easy for linear ones. In order to overcome the difficulty in uncertainty propagation, this dissertation introduces the use of Sequential Linear Programming (SLP) for solving ATC problems, and specifically extends this use for Probabilistic Analytical Target Cascading (PATC) problems. A new coordination strategy is proposed for ATC and PATC, which coordinates linking variables among subproblems using sequential lineralizations. By linearizing and solving a hierarchy of problems successively, the algorithm takes advantage of the simplicity and ease of uncertainty propagation for a linear system. Linearity of subproblems is maintained using an infinite norm to measure deviations between targets and responses. A subproblem suspension strategy is used to temporarily suspend inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. A global convergence proof of the SLP-based coordination strategy is derived. Experiments with test problems show that, relative to standard ATC and PATC coordination, the number of subproblem evaluations is reduced considerably while maintaining accuracy. To demonstrate the applicability of the proposed strategies to problems of practical complexity, a hybrid electric fuel cell vehicle design model, including enterprise, powertrain, fuel cell and battery models, is developed and solved using the new ATC strategy. In addition to engineering uncertainties, the model takes into account unknown behavior by consumers. As a result, expected maximum profit is calculated using probabilistic consumer preferences with engineering constraints satisfied.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58506/1/shipge_1.pd

Control and Coordination in Hierarchical Systems

This book presents the applied theory of control and cooordination in hierarchical systems which are those where decision making has been divided in a certain way. It concentrates on various aspects of optimal control in large scale systems and covers a range of topics from multilevel methods for optimizing by interactive feedback procedures to methods for sequential, hierarchical control in large dynamic systems

Accuracy, Efficiency, and Parallelism in Network Target Coordination Optimization

The optimal design task of complex engineering systems requires knowledge in various domains. It is thus often split into smaller parts and assigned to different design teams with specialized backgrounds. Decomposition based optimization is a multidisciplinary design optimization (MDO) technique that models and improves this process by partitioning the whole design optimization task into many manageable sub-problems. These sub-problems can be treated separately and a coordination strategy is employed to coordinate their couplings and drive their individual solutions to a consistent overall optimum. Many methods have been proposed in the literature, applying mathematical theories in nonlinear programming to decomposition based optimization, and testing them on engineering problems. These methods include Analytical Target Cascading (ATC) using quadratic methods and Augmented Lagrangian Coordination (ALC) using augmented Lagrangian relaxation. The decomposition structure has also been expanded from the special hierarchical structure to the general network structure. However, accuracy, efficiency, and parallelism still remain the focus of decomposition based optimization research when dealing with complex problems and more work is needed to both improve the existing methods and develop new methods. In this research, a hybrid network partition in which additional sub-problems can either be disciplines or components added to a component or discipline network respectively is proposed and two hybrid test problems are formulated. The newly developed consensus optimization method is applied on these test problems and shows good performance. For the ALC method, when the problem partition is given, various alternative structures are analyzed and compared through numerical tests. A new theory of dual residual based on Karush-Kuhn-Tucker (KKT) conditions is developed, which leads to a new flexible weight update strategy for both centralized and distributed ALC. Numerical tests show that the optimization accuracy is greatly improved by considering the dual residual in the iteration process. Furthermore, the ALC using the new update is able to converge to a good solution starting with various initial weights while the traditional update fails to guide the optimization to a reasonable solution when the initial weight is outside of a narrow range. Finally, a new coordination method is developed in this research by utilizing both the ordinary Lagrangian duality theorem and the alternating direction method of multipliers (ADMM). Different from the methods in the literature which employ duality theorems just once, the proposed method uses duality theorems twice and the resulting algorithm can optimize all sub-problems in parallel while requiring the least copies of linking variables. Numerical tests show that the new method consistently reaches more accurate solutions and consumes less computational resources when compared to another popular parallel method, the centralized ALC