Bi-level Optimization Strategy Research Articles

Bilevel Optimization Strategy for Aircraft Wing Design Using Parallel Computing

A new bilevel optimization strategy for wing design is developed, in which the optimizations of the wing-planform and wing-airfoil shapes are decoupled from each other. The design of the wing-planform shape and the shape of the airfoils in several spanwise positions are considered as the goal of the optimization. In the new approach, the design problem is decomposed into a series of subproblems based on the design variables. The design variables defining the wing-planform shape are optimized in a top-level optimization, and the design variables defining the shape of airfoils in several spanwise positions are optimized in several sublevel optimizations. To take into account the influence of the airfoil shape in a specific spanwise position on the shape of the airfoils in other spanwise positions, a series of design variables are added to the design vector of the top-level optimization. The top-level optimizer is responsible for the consistency of the optimization. Using this approach, the number of design variables in the top-level optimization is reduced; the airfoils in several spanwise positions are optimized in parallel; and, instead of complex three-dimensional aerodynamic and structural solvers, much simpler and faster two-dimensional airfoil analysis tools can be used.

A lamination parameter-based strategy for solving an integer-continuous problem arising in composite optimization

A bi-level optimization strategy for finding the optimal ply numbers and stacking sequence in composite structures has become one of the most popular techniques in recent years. When the optimization technique is based on the use of lamination parameters, the top level optimization has two subsets of design variables for each substructure (e.g., a panel in wing design): lamination parameters treated as continuous design variables, and three integers that define the number of plies of 0°, 90° and ±45° orientation. When a continuous optimizer is used at the top level, there is a need for an algorithm to find an integer representation of the obtained continuous number of plies that, ideally, does not alter the mechanical performance of a panel. The focus of this paper is on solving the top level optimization problem whereas the description of local level optimization problem that arranges the stacking sequence can be found in the authors’ previous work. In order to determine the integer values of the ply numbers, two schemes based on the lamination parameter matching are introduced in this paper. The strategy is to use a binary code controlling the integer representation of ply numbers in order to obtain a discrete number of plies of each orientation per composite panel. An optimization problem is formulated where the objective function (to be minimized) defines how close the lamination parameter values and the panel thickness, obtained in the top level optimization, are to their values when integer ply numbers are considered. Such an optimization problem is solved by a permutation GA for each individual panel. A wing box benchmark problem is used to demonstrate the potential of these methods.

Static and dynamic collaborative optimization of ship hull structure

The goal of this effort was to provide a static and dynamic collaborative optimization (CO) model for the design of ship hull structure. The CO model integrated with static, mode and dynamic analyses. In the system-level optimization model, a new objective function was advised, integrating all the subsystem-levels’ objective functions, so as to eliminate the effects of dimensions and magnitude order. The proposed CO architecture enabled multi-objectives of the system and subsystem-level to be considered at both levels during optimization. A bi-level optimization strategy was advised, using the multi-island genetic algorithm. The proposed model was demonstrated with a deck optimization problem of container ship stern. The analysis progress and results of example show that the CO strategy is not only feasible and reliable, but also well suited for use in actual optimization problems of ship design.

Optimization of composite stiffened panels subject to compression and lateral pressure using a bi-level approach

Composite stiffened panel optimization is typically a mixed discrete-continuous design problem constrained by buckling and material strength. Previous work applied a bi-level optimization strategy to the problem by decomposing the mixed problem to continuous and discrete levels to reduce the optimization search space and satisfy manufacturing constraints. A fast-running optimization package, VICONOPT, was used at the continuous optimization level where the buckling analysis was accurately and effectively performed. However, the discrete level was manually adjusted to satisfy laminate design rules. This paper develops the strategy to application on continuously long aircraft wing panels subjected to compression and lateral pressure loading. The beam-column approach used to account for lateral loading for analysis during optimization is reported. A genetic algorithm is newly developed and applied to the discrete level for automated selection of laminated designs. The results that are presented show at least 13% weight saving compared with an existing datum design.