A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

考虑位移要求的大型三维连续体结构拓扑优化数值技术研究

大型复杂三维结构拓扑优化设计既具有理论意义,又具有重要的应用价值。基于等效转换的非奇异的结构优化模型,研究结构位移要求的最小结构重量设计问题。首先,介绍了位移约束的三维结构优化准则和公式。而后,为了提高拥有数万个单元以上的三维结构的计算效率,结合结构位移计算的迭代方法,在分析用于结构特性参数计算模型的基础上,建立了一套三维结构拓扑优化的求解策略和算法。最后,给出了几个典型和复杂的三维结构的拓扑优化设计算例。算例表明求解策略和算法是正确和有效的,且具有广泛的工程应用前景。     

遗传算法在工程爆破参数优化中的应用

工程爆破中的参数优化问题是个复杂的非线性规划问题。以矿山爆破参数优化数学模型为例，采用遗传算法实现了爆破参数的优化。结果证实了利用遗传算法进行爆破参数优化的可行性与高效性，为求解该问题提供了一个有效的新途径。     

Delamination detection in laminated composite beams using hybrid elements

This investigation pursues two goals. One of them is developing a three-dimensional finite element with an embedded interface for analyzing the laminated composite structure. The composite element efficiency is numerically proven. Delaminatoin is an important failure mechanism in certain types of composite structures. Detecting this type of damage is currently a problem of interest to the structural health monitoring community. The second goal of the paper is presenting a novel and well-organized procedure for the identification of delaminatoin in laminated composite beams. The damage identification scheme is formulated by an inverse problem, where analysis data from related finite element modeling, are used to quantify the magnitude and local of delaminatoin. The inverse problem is then transformed to an optimization statement, and the optimum delaminatoin parameters are found by minimizing the objective function. In this study, a genetic algorithm is used for the optimization process. Several numerical examples are analyzed for the accuracy test, and a few of them are presented here.     

Generalized shape optimization of three-dimensional structures using materials with optimum microstructures

This paper deals with generalized shape optimization of linearly elastic, three-dimensional continuum structures, i.e. we consider the problem of determining the structural topology (or layout) such that the shape of external as well as internal boundaries and the number of inner holes are optimized simultaneously. For prescribed static loading and given boundary conditions, the optimum solution is sought from the condition of maximum integral stiffness (minimum elastic compliance) subject to a specified amount of structural material within a given three-dimensional design domain. This generalized shape optimization problem requires relaxation which leads to the introduction of microstructures. A class of optimum three-dimensional microstructures and explicit analytical expressions for their optimum effective stiffness properties have been developed by Gibiansky and Cherkaev (1987) [Gibiansky, L.V., Cherkaev, A.V., 1987. Microstructures of composites of extremal rigidity and exact estimates of provided energy density (in Russian). Report (1987) No. 1155. A.F. Ioffe Physical-Technical Institute, Academy of Sciences of the USSR, Leningrad. English translation in: Kohn, R.V., Cherkaev, A.V. (Eds.), Topics in the Mathematical Modelling of Composite Materials. Birkhaüser, New York. 1997]. The present paper gives a brief account of the results in Gibiansky and Cherkaev (1987) which will be utilized for our microlevel problem analysis. It is a characteristic feature that the use of optimum microstructures renders the global problem convex if an appropriate parametrization is applied. Hereby local optima can be avoided and we can construct a simple gradient based numerical method of mathematical programming for solution of the complete optimization problem. Illustrative examples of optimum layout and topology designs of three-dimensional structures are presented at the end of the paper.     

Optimization of multipass turning operations with genetic algorithms

The paper proposes a new optimization technique based on genetic algorithms for the determination of the cutting parameters in multipass machining operations. The cutting process simultaneously considers multipass rough machining and finish machining. The optimum machining parameters are determined by minimizing the unit production cost subject to practical machining constraints. The cutting model formulated is a non-linear-constrained programming (NCP) problem with 20 machining parameter constraints. Experimental results show that the proposed genetic algorithm-based procedure for solving the NCP problem is both effective and efficient, and can be integrated into an intelligent manufacturing system for solving complex machining optimization problems.     

Optimum design of weaving structure of 3-D woven fabric composites by using genetic algorithms

This paper discusses the optimum design method of the weaving structure of three-dimensional (3-D) reinforced composites. We propose the design method which combines the genetic algorithms (GA) and the finite element analysis. GA is one of the optimization techniques for the combinatorial optimization problem. In the finite element analysis, we used the original structure model which can express the fiber arrangement state in the 3-D composites faithfully. In this study, the original weaving structure model is constructed by combining the basic structure which has the fiber bundle and the cubic grid of resin. From analysis results, in the small design region, we can obtain the optimum weaving structure. Moreover, we proposed a new genetic operation, to design the weaving structure at the larger design region. These operations aim to prevent the failure of the partial weaving structure in the analytical model as much as possible. From the analysis results, the optimum weaving structure is obtained at the large design region, similar to above results. Consequently, it seems that the proposed method enables the design of the optimum weaving structure in the 3-D composites.     

Two-dimensional phase unwrapping using a hybrid genetic algorithm

A novel hybrid genetic algorithm (HGA) is proposed to solve the branch-cut phase unwrapping problem. It employs both local and global search methods. The local search is implemented by using the nearest-neighbor method, whereas the global search is performed by using the genetic algorithm. The branch-cut phase unwrapping problem [a nondeterministic polynomial (NP-hard) problem] is implemented in a similar way to the traveling-salesman problem, a very-well-known combinational optimization problem with profound research and applications. The performance of the proposed algorithm was tested on both simulated and real wrapped phase maps. The HGA is found to be robust and fast compared with three well-known branch-cut phase unwrapping algorithms.     

On solving three-dimensional open-dimension rectangular packing problems

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.     

Performance-based multi-objective optimization of large steel structures

In recent years, the importance of economical considerations in the field of structures has motivated many researchers to propose new methods for minimizing the initial and life cycle cost of the structures subjected to seismic loading. In this paper, a new framework is presented to solve the performance-based multi-objective optimization problem considering the initial and life cycle cost of large structures. In order to solve this problem, a non-dominated sorting genetic algorithm (NSGA-II) using differential evolution operators is employed to solve the optimization problem, while a specific meta-model is utilized for reducing the number of fitness function evaluations. The required computational time for pushover analysis is decreased by a simple numerical method. The constraints of the optimization problem are based on the FEMA codes. The presented results for application of the proposed framework demonstrate its capability in solving the present complex multi-objective optimization problem.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Shape optimization using the boundary element method with substructuring

Applications of the boundary element method for two- and three-dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub-structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non-linear programming problem for the optimization is solved by the generalized reduced gradient method. B-spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three-dimensional elasticity problems.     

Cause and effect analysis by fuzzy relational equations and a genetic algorithm

This paper proposes using a genetic algorithm as a tool to solve the fault diagnosis problem. The fault diagnosis problem is based on a cause and effect analysis which is formally described by fuzzy relations. Fuzzy relations are formed on the basis of expert assessments. Application of expert fuzzy relations to restore and identify the causes through the observed effects requires the solution to a system of fuzzy relational equations. In this study this search for a solution amounts to solving a corresponding optimization problem. An optimization algorithm is based on the application of genetic operations of crossover, mutation and selection. The genetic algorithm suggested here represents an application in expert systems of fault diagnosis and quality control.     

Numerical homogenization of hardened cement paste

Based upon a three-dimensional computer-tomography of hardened cement paste, a finite-element mesh at micrometer length scale is introduced. Effective material properties are obtained through numerical homogenization techniques using representative volume elements. Statistical tests, two- and three-dimensional computations and a comparison with experimental data are shown. For the hydration products of hardened cement paste a visco-plastic constitutive equation of Perzyna type including isotropic damage is introduced. The inelastic material parameters are identified solving an optimization problem through a combination of a stochastic genetic algorithm and the deterministic Levenberg-Marquardt method. The time-consuming evaluations of the corresponding objective function are distributed within a network environment automatically.     

Flight path optimization passing through waypoints for autonomous flight control systems

Trajectory optimization is performed to generate a flight path passing specified waypoints. To deal with the unspecified time of passing through a waypoint, an auxiliary variable is introduced. Normalization of the time variable by the auxiliary variable transforms the waypoint optimization problem into the conventional optimization problem. The condition for passing through the waypoints can be relaxed, so that the vehicle passes specified waypoints within a certain acceptable range. Sequential quadratic programming is used to solve the optimization problem. As a numerical example, six degree-of-freedom vehicle dynamics is considered. Two-dimensional and three-dimensional trajectory optimization problems with several waypoints are solved to verify the effectiveness of the proposed algorithm.     

复杂非线性函数最优化问题的一种实用智能算法

对浮点编码遗传算法加以改进,并与DFP变尺度算法相结合,经加速循环,构建新型混合加速遗传算法(以下简称NHAGA);协同求解具有变量边界约束的非凸、高度非线性的复杂函数最优化问题。算例测试表明,该法兼顾了改进浮点编码遗传算法全局搜索能力和DFP算法快速局部搜索能力的优点,成功搜索全局最优点的概率较高,是一种求解非凸、高度非线性全局优化问题的有效智能算法。     

Availability allocation to repairable systems with genetic algorithms: a multi-objective formulation

This paper describes a methodology based on genetic algorithms (GA) and experiments plan to optimize the availability and the cost of reparable parallel-series systems. It is a NP-hard problem of multi-objective combinatorial optimization, modeled with continuous and discrete variables. By using the weighting technique, the problem is transformed into a single-objective optimization problem whose constraints are then relaxed by the exterior penalty technique. We then propose a search of solution through GA, whose parameters are adjusted using experiments plan technique. A numerical example is used to assess the method.     

Trajectory optimization of spacecraft high-thrust orbit transfer using a modified evolutionary algorithm

This article introduces a new method to optimize finite-burn orbital manoeuvres based on a modified evolutionary algorithm. Optimization is carried out based on conversion of the orbital manoeuvre into a parameter optimization problem by assigning inverse tangential functions to the changes in direction angles of the thrust vector. The problem is analysed using boundary delimitation in a common optimization algorithm. A method is introduced to achieve acceptable values for optimization variables using nonlinear simulation, which results in an enlarged convergence domain. The presented algorithm benefits from high optimality and fast convergence time. A numerical example of a three-dimensional optimal orbital transfer is presented and the accuracy of the proposed algorithm is shown.     

New conceptual design of aeroelastic wing structures by multi-objective optimization

Internal structural layouts and component sizes of aircraft wing structures have a significant impact on aircraft performance such as aeroelastic characteristics and mass. This work presents an approach to achieve simultaneous partial topology and sizing optimization of a three-dimensional wing-box structure. A multi-objective optimization problem is assigned to optimize lift effectiveness, buckling factor and mass of a structure. Design constraints include divergence and flutter speeds, buckling factor and stresses. The topology and sizing design variables for wing internal components are based on a ground element approach. The design problem is solved by multi-objective population-based incremental learning (MOPBIL). The Pareto optimum results lead to unconventional wing structures that are superior to their conventional counterparts.     

Efficiently Solving the Redundancy Allocation Problem Using Tabu Search

A tabu search meta-heuristic has been developed and successfully demonstrated to provide solutions to the system reliability optimization problem of redundancy allocation. Tabu search is particularly well-suited to this problem and it offers distinct advantages compared to alternative optimization methods. While there are many forms of the problem, the redundancy allocation problem generally involves the selection of components and redundancy levels to maximize system reliability given various system-level constraints. This is a common and extensively studied problem involving system design, reliability engineering and operations research. It is becoming increasingly important to develop efficient solutions to this reliability optimization problem because many telecommunications (and other) systems are becoming more complex, yet with short development schedules and very stringent reliability requirements. Tabu search can be applied to a more diverse problem domain compared to mathematical programming methods, yet offers the potential of greater efficiency compared to population-based search methodologies, such as genetic algorithms. The tabu search is demonstrated on numerous variations of three different problems and compared to integer programming and genetic algorithm solutions. The results demonstrate the benefits of tabu search for solving this type of problem.