Shen Lu

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution.

Hybrid Power/Energy Generation Through Multidisciplinary and Multilevel Design Optimization With Complementarity Constraints

The optimal design of hybrid power generation systems (HPGSs) can significantly improve the technical and economic performance of power supply. However, the discrete-time simulation with logical disjunctions involved in HPGS design usually leads to a nonsmooth optimization model, to which well-established techniques for smooth nonlinear optimization cannot be directly applied. This paper casts the HPGS design optimization problem as a multidisciplinary design optimization problem with complementarity constraints, a formulation that introduces a complementarity formulation of the nonsmooth logical disjunction, as well as a time horizon decomposition framework, to ensure a fast local solution. A numerical study of a stand-alone hybrid photovoltaic/wind power generation system is presented to demonstrate the effectiveness of the proposed approach.

Parallel, Multistage Model for Enterprise System Planning and Design

This paper describes a parallel, multistage optimization approach for enterprise system design and planning where the design of a system is linked with its planing and operations (resource allocation). Our approach is composed of two parts: a multistage formulation and a task-parallel algorithm. The formulation utilizes the quasi-separability of the multistage decision making structure, i.e., allowing relaxation by defining the linking variables for adjacent stages of decision making. The task-parallel algorithm enables optimal load balancing of the tasks, and it is validated in the demonstration case where an airline plans to introduce multiple new aircraft to capture dynamically changing travel demand. A linearly increasing computational load is assumed as the number of stages increases due to the complexity added onto the upcoming future stages in the optimization processes. The proposed task parallel algorithm demonstrates significant speedups and parallel performances by utilizing this linearity.

Analytical Target Cascading for Multi-Mode Design Optimization: An Engine Case Study

Advances in design and information science have enabled the engineering community to look into changeable systems that work under multiple operating scenarios or modes. In this paper, a multidisciplinary design optimization approach for changeable systems is presented, with its focus on sharing a uniform part of system configuration across all the operating scenarios. Compared to the fully adaptive system approach, this approach enables reduction in the computational expense due to the repetitive mode-by-mode optimization, which becomes impractical as the number of modes increases. In the proposed approach, Analytical Target Cascading (ATC), a hierarchical optimization methodology, models the multi-mode design optimization in a two-level structure: the subsystem problems achieve the performance targets through optimizing local copies of the system configuration; and the system problem coordinates system configuration copies at multiple modes to obtain consistency. Local objectives are introduced to accommodate (unattainable) targets assigned locally for the individual systems, and a weight-updating scheme utilizing local objective information is proposed to balance among performance deviations at multiple modes. A case study on industrial engine simulation parameter identification demonstrates the effectiveness of the proposed approach.

Wind Farm Layout Design Optimization Through Multidisciplinary Design Optimization with Complementarity Constraints

This paper presents a multidisciplinary design optimization with complementarity constraints (MDO-CC) approach to wind farm layout design to maximize the wind power production under region boundary and interturbine distance constraints. A complementarity formulation technique is introduced such that the wind farm layout design can be described with a continuously differentiable optimization model; and a multi-scenario decomposition approach is proposed to ensure efficient solution with local optimality. To combine global exploration and local optimization, a hybrid solution algorithm is presented, which combines the MDO-CC approach with a bi-objective genetic algorithm that maximizes power production and minimizes constraint violations simultaneously. A numerical case study demonstrates the effectiveness of the proposed approach.

Hybrid power/energy generation system design through multistage design optimization problem with complementarity constraints

The optimal design of hybrid power generation systems (HPGS) can significantly improve the economical and technical performance of power supply. However, the discrete-time simulation with logical disjunctions involved in HPGS design usually leads to a nonsmooth optimization model, to which well established techniques for smooth nonlinear optimization could not be directly applied. This paper proposes a multistage design optimization problem with complementarity constraints approach for HPGS design, which introduces a complementarity formulation of the nonsmooth logical disjunction, as well as a multistage decomposition framework, to ensure a fast local solution. A numerical study of a stand-alone hybrid photovoltaic (PV)/wind power generation system is presented to demonstrate the effectiveness of the proposed approach.Copyright

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problem With Complementarity Constraints

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution. DOI: 10.1115/1.4001206

Parallel, multistage model for enterprise system of systems

This paper describes a parallel, multistage optimization approach to enterprise system design and operations where a system design is linked with system operations (e.g., resource allocation) along the multistage decision making horizon. Our approach is composed of two parts: multistage formulation, and task-parallel algorithm. The formulation utilizes the quasi-separability of the multistage decision making structure, i.e., allowing relaxation by defining the linking variables for adjacent stages of decision making. The task-parallel algorithm enables optimal load balancing of the tasks and it is validated in the demonstration case where an airline plans to introduce multiple new aircraft to capture dynamically changing travel demand. Due to the complexity added onto the upcoming future stages in the optimization processes, a linearly increasing computational load is assumed as the number of stages increases. By utilizing this linearity, the proposed task- parallel algorithm demonstrates significant speedups and parallel performances.

Multidisciplinary and multilevel design optimization problems with equilibrium constraints

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO). We introduce MDO problems with complementarity constraints to model such equilibrium problems in this paper. Also introduced is a Stackelberg game to model design decision making process in MDO with shared variables. We provide solution schemes based on the inexact penalty and augmented Lagrangian techniques. Two classes of problems are solved in the paper: a regular MDO modeled as a Stackelberg game and a new MDO with complementarity constraints. The proposed method was tested for Golinski’s speed reducer design and shows promising results with convergence to the all-in-one solution.