Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.     

Optimization of truss topology using tabu search

A design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This non-linear programming problem is solved using a memory-based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.     

Optimization of actively controlled structures using goal programming techniques

The problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed-loop system is formulated and solved as a multiobjective optimization problem. The purpose of control is to effectively suppress structural vibrations due to initial excitation. The cross-sectional areas of the members are treated as design variables. The structural weight and the controlled system energy are considered as objective functions for minimization. The goal programming approach is used for the solution of the multiobjective optimization problems. The procedure is illustrated through numerical simulations using two-bar and twelve-bar truss structures.     

Structural optimization of uncertain dynamical systems considering mixed-design variables

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete-continuous sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal and quadratic approximations. The approximations are combined with an effective sensitivity analysis of the reliability constraints in order to generate explicit expressions of the constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. The optimization scheme exhibits monotonic convergence properties. Two numerical examples showing the effectiveness of the approach reported herein are presented.     

Multi-stage optimization method for air-intake system of hovercraft based on autonomous optimization

Abstract

In this study, an optimal structural design program was designed and developed for Computational Fluid Dynamics based on self-optimization, effectively reducing the time required for structural optimization. Through experimental design using this program, the effects of various design variables on the optimization objectives were evaluated, and an adaptive simulated annealing algorithm was used for global optimization. Furthermore, response surface methodology and a nonlinear quadratic programming algorithm were utilized to obtain a global optimum solution after repeated iterations. Moreover, using a hovercraft air-intake system as the optimized object, the total pressure loss of the system was completely optimized by using a porous medium model and Matlab analysis program, and the accuracy of the structural design optimization program was validated. After the global optimization, the total pressure loss of the air-intake system was reduced by 20.5% compared to the original model. An average nonuniformity of 4.36% of engine inlet speed and 5% local nonuniformity of 11.19% satisfy the design requirements of the hovercraft engine. This method can be directly applied to engineering optimization problems as well as multiobjective optimization tasks after improving the relevant methodologies.     

Reliability and cost optimization of electronic devices considering the component failure rate uncertainty

The objective of this paper is to present an efficient computational methodology to obtain the optimal system structure of electronic devices by using either a single or a multiobjective optimization approach, while considering the constraints on reliability and cost. The component failure rate uncertainty is taken under consideration and it is modeled with two alternative probability distribution functions. The Latin hypercube sampling method is used to simulate the probability distributions. An optimization approach was developed using the simulated annealing algorithm because of its flexibility to be applied in various system types with several constraints and its efficiency in computational time. This optimization approach can handle efficiently either the single or the multiobjective optimization modeling of the system design. The developed methodology was applied to a power electronic device and the results were compared with the results of the complete enumeration of the solution space. The stochastic nature of the best solutions for the single objective optimization modeling of the system design was sampled extensively and the robustness of the developed optimization approach was demonstrated.     

Tradeoff analysis of non-linear dynamical systems under stochastic excitation

An efficient methodology to carry out multi-objective optimization of non-linear structural systems under stochastic excitation is presented. Specifically, an efficient determination of particular Pareto or non-inferior solutions is implemented. Pareto solutions are obtained by compromise programming which is based on the minimization of the distance between the point that contains the individual optima of each of the objective functions and the Pareto set. The response of the structural system is characterized in terms of the first two statistical moments of the response process, i.e. the mean and variance. An efficient sensitivity analysis of non-inferior solutions with respect to the design variables becomes possible with the proposed formulation. Such information is used for decision making and tradeoff analysis. The compromise programming problem is solved by an efficient procedure that combines a local statistical linearization approach, modal analysis, global approximation concepts, and a sequential optimization scheme. Numerical results show that the total number of stochastic analyses required during the multi-objective optimization process is in general very small. Hence, different compromise solutions including the design that best represents the outcome that the designer considers potentially satisfactory are obtained in an efficient manner. In this way, the analyst can conduct a decision-making analysis through an efficient interactive procedure.     

Structural optimization of non-linear systems under stochastic excitation

This work concentrates on the structural optimization of a class of non-linear systems with deterministic structural parameters subject to stochastic excitation. The optimization problem is formulated as the minimization of an objective function subject to constraints on the response level. The stochastic response is characterized by its first two statistical moments, which are computed by a statistical equivalent linearization technique. The implicit structural optimization problem is replaced by a sequence of explicit sub-optimization problems. The sub-problems are constructed by using a conservative first-order approximation of the objective and constraint functions. The applicability of the proposed design process is demonstrated in three numerical examples where the methodology is applied to systems with nonlinearity of hardening and hysteretic type. The effects of the nonlinearity on the general performance of the final designs are discussed. At the same time, some engineering implications of the results obtained in this work are addressed.     

Solving Quadratic Assignment Problems by 'Simulated Annealing'

Recently, an interesting analogy between problems in combinatorial optimization and statistical mechanics has been developed and has proven useful in solving certain traditional optimization problems such as computer design, partitioning, component placement, wiring, and traveling salesman problems. The analogy has resulted in a methodology, termed “simulated annealing,” which, in the process of iterating to an optimum, uses Monte Carlo sampling to occasionally accept solutions to discrete optimization problems which increase rather than decrease the objective function value. This process is counter to the normal 'steepest-descent' algorithmic approach. However, it is argued in the analogy that by taking such controlled uphill steps, the optimizing algorithm need not get “stuck” on inferior solutions.

This paper presents an application of the simulated annealing method to solve the quadratic assignment problem (QAP). Performance is tested on a set of “standard” problems, as well as some newly generated larger problems (n = 50 and n = 100). The results are compared to those from other traditional heuristics, e.g., CRAFT, biased sampling, and a revised Hillier procedure. It is shown that under certain conditions simulated annealing can yield higher quality (lower cost) solutions at comparable CPU times. However, the simulated annealing algorithm is sensitive to a number of parameters, some of whose effects are investigated and reported herein through the analysis of an experimental design.     

A simulated annealing method for design of laminates with required stiffness properties

Designing a laminate based on its stiffness properties requires finding the optimum lamination stacking sequence to yield the required stiffness properties. The design variables to be considered are the number of layers and orientation angle of fibers in each layer group, which are treated as discrete-variables. The optimum lamination is then obtained by minimizing a cost function composed of the relative difference between the calculated effective stiffness properties and weight of trial laminate and the desired properties. This error minimization problem was solved using a modified simulated annealing heuristic method. The new simulated annealing implementation comprises a cooling procedure in which the temperature decrease relied adaptively on the objective function evolution. It is shown that the proposed method can give rise to an improvement in convergence speed. To achieve a further improvement in the performance of the method, simulated annealing parallelization implemented using the proposed cooling process. The main features of this algorithm are described and its encouraging results are presented.     

Simulation and Optimization of Wiped-Film Poly-Ethylene Terephthalate (PET) Reactor Using Multiobjective Differential Evolution (MODE)

The multiobjective differential evolution (MODE), which is an extension of the Differential Evolution (DE), is applied to solve the multiobjective optimization problem (MOOP) of wet film Poly-Ethylene Terephthalate (PET) reactor considering minimization of acid end group and vinyl end group as the main objectives. The objective function is modified to solve five different possible cases. The results show that a Pareto set (a set of equally good solutions) is obtained for the cases when two of the parameters (residence time of the polymeric reaction mass, θ, and the speed of the wiped-film agitator, N) are considered as decision variables, unlike a unique solution obtained using Nondominated Sorting Genetic Algorithm (NSGA). The Pareto optimal front provides wide-ranging optimal sets of operating conditions. And an appropriate set of operating conditions can be selected based on the requirements of the user.     

基于直接搜索方法的层合板多目标优化设计

直接多目标搜索方法(DMS)是一种不需要计算梯度信息并且能实现全局收敛的多目标优化方法。基于直接多目标搜索方法,以简支层合板铺设角度为设计变量,基频和声功率为目标函数进行层合板结构振动与声多目标优化。分别以4层、8层复合材料层合板为例,用DMS方法对其优化设计,并与传统的遗传算法(GA)对比。结果表明,对于4层复合材料层合板,DMS方法比GA方法优化速度快,且能得到全局最优解;对于8层复合材料层合板,用DMS方法比4层板优化所需时间多,但相比GA方法,DMS方法优化更快。     

The use of optimization procedures in tuning vibration dampers

This paper presents an algorithm for minimizing the resonance amplitudes of vibrating systems with dynamic vibration dampers. Damper parameters are optimised using an objective function which describes the maximum of the resonance curve for the first resonance. The algorithm described here is based on a spectral transfer function and can be applied to multi-degree-of-freedom systems. The research makes use of models of discrete as well as discrete-continuous systems. A method for formulating minimization problems is proposed which allows global optimization using gradient procedures. Sequential linear and quadratic programming methods are used. Examples of different mechanical systems with vibration dampers are also presented.     

Determination of design alternatives and performance criteria for safety systems in a nuclear power plant via simulated annealing

This study presents an efficient methodology that derives design alternatives and performance criteria for safety functions/systems in commercial nuclear power plants. Determination of the design alternatives and intermediate-level performance criteria is posed as a reliability allocation problem. The reliability allocation is performed in a single step by means of the concept of two-tier noninferior solutions in the objective and risk spaces within the top-level probabilistic safety criteria (PSC). Two kinds of two-tier noninferior solutions are obtained: desirable design alternatives and intolerable intermediate-level PSC of safety functions/systems.The weighted Chebyshev norm (WCN) approach with an improved Metropolis algorithm in simulated annealing is used to find the two-tier noninferior solutions. This is very efficient in searching for the global minimum of the difficult multiobjective optimization problem (MOP) which results from strong nonlinearity of a probabilistic safety assessment (PSA) model and nonconvexity of the problem. The methodology developed in this study can be used as an efficient design tool for desirable safety function/system alternatives and for the determination of intermediate-level performance criteria.The methodology is applied to a realistic streamlined PSA model that is developed based on the PSA results of the Surry Unit 1 nuclear power plant. The methodology developed in this study is very efficient in providing the intolerable intermediate-level PSC and desirable design alternatives of safety functions/systems.     

Optimality criteria-based topology optimization of a bi-material model for acoustic–structural coupled systems

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.     

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first-order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing-box, showing that topology optimization for mass minimization of real-world structures can be considered using the proposed methodology.     

AN IMPROVED GENETIC ALGORITHM FOR CONTINUOUS AND MIXED DISCRETE-CONTINUOUS OPTIMIZATION

Modifications to the standard genetic algorithm through a finetuning strategy, a hillclimbing strategy and the use of independent subpopulations coupled with shuffling are described. The improvements obtained are demonstrated using two optimization problems; a continuous variable rainfall-runoff model calibration and a previously-studied mixed discrete-continuous optimization for cost minimization in pressure vessel manufacture. The use of independent Subpopulations and shuffling is found to considerably improve optimizations of the two problems whilst the finetuning and hillclimbing notably improve optimization in the model calibration but not the pressure vessel cost minimization. In the rainfall-runoff modelling the parameter sets obtained by the improved genetic algorithm are more consistent and seem more informative than those obtained with the standard genetic algorithm. With the pressure vessel design problem, lower costs are obtained than in previous studies.     

Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching

This article proposes a new multiobjective optimization method for structural problems based on multiobjective particle swarm optimization (MOPSO). A gradient-based optimization method is combined with MOPSO to alleviate constraint-handling difficulties. In this method, a group of particles is divided into two groups—a dominated solution group and a non-dominated solution group. The gradient-based method, utilizing a weighting coefficient method, is applied to the latter to conduct local searching that yields superior non-dominated solutions. In order to enhance the efficiency of exploration in a multiple objective function space, the weighting coefficients are adaptively assigned considering the distribution of non-dominated solutions. A linear optimization problem is solved to determine the optimal weighting coefficients for each non-dominated solution at each iteration. Finally, numerical and structural optimization problems are solved by the proposed method to verify the optimization efficiency.     

Engineering optimization using a real-parameter genetic-algorithm-based hybrid method

A hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is proposed. The proposed algorithm incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators such that its hill-climbing ability towards the optimum solution is improved. The algorithm is used to optimize the weight of four planar or space truss structures and the results are compared with those obtained using other well-known optimization schemes. The evaluation trials investigate the performance of the algorithm in optimizing over discrete sizing variables only and over both discrete sizing variables and continuous configuration variables. The results show that the proposed algorithm consistently outperforms the other optimization methods in terms of its weight-saving capabilities. It is also shown that the global searching ability and convergence speed of the proposed algorithm are significantly improved by the inclusion of adaptive mechanisms to adjust the values of the genetic operators. Hence the hybrid algorithm provides an efficient and robust technique for solving engineering design optimization problems.