A bilevel game theoretic approach to optimum design of flywheels

Multiobjective optimization problems arise frequently in mechanical design. One approach to solving these types of problems is to use a game theoretic formulation. This article illustrates the application of a bilevel, leader–follower model for solving an optimum design problem. In particular, the optimization problem is modelled as a Stackelberg game. The partitioning of variables between the leader and follower problem is discussed and a variable partitioning metric is introduced to compare various variable partitions. A computational procedure based on variable updating using sensitivity information is developed for exchanging information between the follower and leader problems. The proposed approach is illustrated through the design of a flywheel. The two objective functions used for the design problem include maximizing the kinetic energy stored in the flywheel while simultaneously minimizing the manufacturing cost.     

A multiple surrogate assisted evolutionary algorithm for optimization involving iterative solvers

In many real-world optimization problems, the underlying objective and constraint function(s) are evaluated using computationally expensive iterative simulations such as the solvers for computational electro-magnetics, computational fluid dynamics, the finite element method, etc. The default practice is to run such simulations until convergence using termination criteria, such as maximum number of iterations, residual error thresholds or limits on computational time, to estimate the performance of a given design. This information is used to build computationally cheap approximations/surrogates which are subsequently used during the course of optimization in lieu of the actual simulations. However, it is possible to exploit information on pre-converged solutions if one has the control to abort simulations at various stages of convergence. This would mean access to various performance estimates in lower fidelities. Surrogate assisted optimization methods have rarely been used to deal with such classes of problem, where estimates at various levels of fidelity are available. In this article, a multiple surrogate assisted optimization approach is presented, where solutions are evaluated at various levels of fidelity during the course of the search. For any solution under consideration, the choice to evaluate it at an appropriate fidelity level is derived from neighbourhood information, i.e. rank correlations between performance at different fidelity levels and the highest fidelity level of the neighbouring solutions. Moreover, multiple types of surrogates are used to gain a competitive edge. The performance of the approach is illustrated using a simple 1D unconstrained analytical test function. Thereafter, the performance is further assessed using three 10D and three 20D test problems, and finally a practical design problem involving drag minimization of an unmanned underwater vehicle. The numerical experiments clearly demonstrate the benefits of the proposed approach for such classes of problem.     

ARCHITECTURAL OPTIMIZATION-A REVIEW

The introduction of numerical methodologies to Architecture is very recent. However, the last ten years has seen the application of optimization techniques to many of the problems of Architecture previously considered to be non-numeric: this paper reviews the panoply of these applications. The optimization problem which appears to have attracted the most attention is that of the layout of spaces or planning. Various techniques have been applied to this combinatorial problem but as yet there appears to be no algorithm available which produces a global optimum. The development of sites in cities has also been treated as an optimization problem with considerable success; various search methods as well as dynamic programming have been applied here. The methods used to control the internal physical environment of buildings (building services) have been examined systematically from an optimizing viewpoint. Detailed services such as aii-conditioning and vertical transportation have been treated. Materials selection has been treated as a multi-factor optimization problem. Dynamic programming has found considerable use in architectural optimization in site development, vertical transportation, house planning and campus planning. Finally, the development of design systems which use optimizing techniques is discussed. An extensive list of references follows the conclusions which summarize some of the difficulties of using optimization in architecture     

Experiences with applying a genetic algorithm to determine an information systems architecture

While determining information systems architectures (ISA), business systems planning (BSP) is a well-known method to join processes and data classes to subsystems. BSP matrices have generally been rearranged without describing the underlying methods. Meanwhile, various techniques have been developed for solving the ISA problem. Since exact optimization methods often fail to provide results for large ISA problems, different heuristics have been applied. A new heuristic for solving the ISA problem is the application of genetic algorithms (GA). This paper examines the application of a simple GA to the ISA problem and compares the results of applying the GA with those obtained by exact methods.     

Filters in topology optimization based on Helmholtz‐type differential equations

The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non‐overlapping partitions. Obtaining information from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimization problems in linear elasticity, solved on serial and parallel computers. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of genetic and binary particle swarm optimization algorithms on system maintenance scheduling using prognostics information

Recent technical advances in condition-based maintenance technology have made it possible to not only diagnose existing failures, but also forecast future failures, which is called prognostics. A common method of maintenance scheduling in condition-based maintenance is to apply thresholds to prognostics information, which is not appropriate for systems consisting of multiple serially connected machinery. Maintenance scheduling is defined as a binary optimization problem and has been solved with a genetic algorithm. In this article, various binary particle swarm optimization methods are analysed and compared with each other and a genetic algorithm on a maintenance-scheduling problem for condition-based maintenance systems using prognostics information. The trade-off between maintenance and failure is quantified as the risk to be minimized. The forecasted failure probability of serially connected machinery is utilized in the analysis of the whole system. In addition to the comparison of a genetic algorithm and binary particle swarm optimization methods, a new binary particle swarm optimization that combines the good sides of two binary particle swarm optimizations is presented.     

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.     

基于分组策略的多目标三维装箱算法

目的 针对现有三维装箱算法优化目标单一、优化效率低的问题,提出适用于求解大规模货物装载问题的多目标装箱算法,以提高装箱规划效率,确保货物运输安全。方法 考虑5种现实约束条件,以体积利用率和装载垛型重心偏移量为优化目标,建立多目标货物装载优化模型。采用拟人式装箱对货物进行预分组,减小决策空间,然后结合分组信息与装箱算法生成初始解;引入数据驱动的装箱交叉算子提高算法收敛性;设计多策略变异算子提高算法结果的多样性。结果 以公共数据集和真实航空货物数据作为实验数据进行实验。实验结果表明,在满足多种约束条件下,集装箱装载强异构货物平均体积利用率达到92.0%,重心位置空间偏移从20 cm减少到7.5 cm,并且算法运行时间减少了73.5%。结论 本文所提算法应用于求解大规模多目标三维装箱问题,提高了装箱质量和效率,可为三维装箱算法的工程应用提供参考。     

Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach

A tensegrity structure is a prestressed pin-jointed structure consisting of discontinuous struts and continuous cables. For exploring new configurations of tensegrity structures, this paper addresses a topology optimization problem of tensegrity structures under the compliance constraint and the stress constraints. It is assumed that a cable loosens and loses the elongation stiffness when its tensile prestress vanishes due to the applied external load. It is shown that the topology optimization problem can be formulated as a mixed integer linear programming (MILP) problem. The proposed method does not require any connectivity information of cables and struts to be known in advance. Numerical experiments illustrate that various configurations of tensegrity structures can be found as the optimal solutions.     

A study on evolutionary multi-objective optimization for flow geometry design

In this paper, we investigate three recently proposed multi-objective optimization algorithms with respect to their application to a design-optimization task in fluid dynamics. The usual approach to render optimization problems is to accumulate multiple objectives into one objective by a linear combination and optimize the resulting single-objective problem. This has severe drawbacks such that full information about design alternatives will not become visible. The multi-objective optimization algorithms NSGA-II, SPEA2 and Femo are successfully applied to a demanding shape optimizing problem in fluid dynamics. The algorithm performance will be compared on the basis of the results obtained.     

Discrete material optimization of general composite shell structures

A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four‐point beam bending problem and a doubly curved laminated shell. Copyright © 2005 John Wiley & Sons, Ltd.     

3D preform shape optimization in forging using reduced basis techniques

Three-dimensional preform shape optimization of complex forgings with a weighted summation of multiple basis shapes is presented in this article. Currently, 2D preform shape optimization is well developed; however, in cases in which the parts are neither axisymmetric nor plane strain, 2D assumptions do not hold well. The number of design variables required to define the 3D preform shape is high, making most iterative design methods impractical for shape optimization. The goal here is to make design optimization practical and efficient by developing reduced-order modeling techniques for 3D preform shape optimization. The preform shape is treated as a linear combination of various billet shapes, called basis shapes, with the weights for each basis shape used as design variables, thereby reducing the number of design variables. It is very difficult to obtain the necessary gradient information for 3D forging simulations, so a non-gradient method is used to build the surrogate model on which optimization is performed. The optimization problem is formulated to minimize strain variance while placing constraints on underfill. Representative problems are used to demonstrate the effectiveness of the approach.     

Constrained optimization using a multipoint type chaotic Lagrangian method with a coupling structure

This article proposes a new constrained optimization method using a multipoint type chaotic Lagrangian method that utilizes chaotic search trajectories generated by Lagrangian gradient dynamics with a coupling structure. In the proposed method, multiple search points autonomously implement global search using the chaotic search trajectory generated by the coupled Lagrangian gradient dynamics. These points are advected to elite points (which are chosen by considering their objective function values and their feasibility) by the coupling in order to explore promising regions intensively. In this way, the proposed method successfully provides diversification and intensification for constrained optimization problems. The effectiveness of the proposed method is confirmed through application to various types of benchmark problem, including the coil spring design problem, the benchmark problems used in the special session on constrained real parameter optimization in CEC2006, and a high-dimensional and multi-peaked constrained optimization problem.     

Rate-Energy Tradeoff for Wireless Simultaneous Information and Power Transfer in Full-Duplex and Half-Duplex Systems

In this paper, we study the rate-energy tradeoff for wireless simultaneous information and power transfer in full-duplex and half-duplex scenarios. To this end, the weighting function of energy efficiency and transmission rate, as rate-energy tradeoff metric is first introduced and the metric optimization problem is formulated. Applying Karush-Kuhn-Tucker (KKT) conditions for Lagrangian optimality and a series of mathematical approximations, the metric optimization problem can be simplified. The closed-form solution of the power ratio is obtained, building direct relationship between power ratio and the rate-energy tradeoff metric. By choosing power ratio, one can make the tradeoff between information rate and harvested power in a straightforward and efficient way. Using the method similar to the half duplex systems, the optimal power ratio can be obtained in the full duplex systems, so as to balance the information transmission rate and energy transmission efficiency. Simulation results validate that the information rate is non-increasing with harvested power in half-duplex systems and the tradeoff of information rate and harvested power can be simply made. In the full duplex systems, the power ratio solution of the rate-energy tradeoff metric optimization problem can be used as the approximate optimal solution of the optimization problem and the approximation error is negligible.     

Test interval optimization of safety systems of nuclear power plant using fuzzy-genetic approach

Probabilistic safety assessment (PSA) is the most effective and efficient tool for safety and risk management in nuclear power plants (NPP). PSA studies not only evaluate risk/safety of systems but also their results are very useful in safe, economical and effective design and operation of NPPs. The latter application is popularly known as “Risk-Informed Decision Making”. Evaluation of technical specifications is one such important application of Risk-Informed decision making. Deciding test interval (TI), one of the important technical specifications, with the given resources and risk effectiveness is an optimization problem. Uncertainty is inherently present in the availability parameters such as failure rate and repair time due to the limitation in assessing these parameters precisely. This paper presents a solution to test interval optimization problem with uncertain parameters in the model with fuzzy-genetic approach along with a case of application from a safety system of Indian pressurized heavy water reactor (PHWR).     

An object‐oriented framework for the implementation of adjoint techniques in the design and control of complex continuum systems

Specific object‐oriented software design concepts are elaborated for a novel implementation of a class of adjoint optimization problems typical of the infinite‐dimensional design and control of continuum systems. For clarity, the design steps and ideas are elucidated using an inverse natural convection design problem. Effective application of software design concepts such as inheritance, data encapsulation, information hiding, etc., is demonstrated through instances from the example considered. Two test numerical examples are considered and the CPU statistics for one of these problems are compared with those corresponding to a procedural implementation of the same problem. The numerical examples include a three‐dimensional inverse design problem that demonstrates the effectiveness of the present object‐oriented approach in developing dimension‐independent robust design codes. Copyright © 2000 John Wiley & Sons, Ltd.     

Importance measures and genetic algorithms for designing a risk-informed optimally balanced system

This paper deals with the use of importance measures for the risk-informed optimization of system design and management. An optimization approach is presented in which the information provided by the importance measures is incorporated in the formulation of a multi-objective optimization problem to drive the design towards a solution which, besides being optimal from the points of view of economics and safety, is also ‘balanced’ in the sense that all components have similar importance values. The approach allows identifying design systems without bottlenecks or unnecessarily high-performing components and with test/maintenance activities calibrated according to the components’ importance ranking. The approach is tested at first against a multi-state system design optimization problem in which off-the-shelf components have to be properly allocated. Then, the more realistic problem of risk-informed optimization of the technical specifications of a safety system of a nuclear power plant is addressed.     

Constrained nonlinear method for estimating component spectra from multicomponent mixtures

A method is described for estimating the spectra of pure components from the spectra of unknown mixtures with various relative concentrations. This method is based on principal component analysis and a constrained nonlinear optimization technique and is applicable to qualitative analysis of mixtures of more than three components. The method gives two curves as the estimate of a component spectrum: one consists of the set of the maxima and the other consists of the set of the minima for all sampling points subject to a priori information. Experimental results of the estimation of the infrared absorption spectra of xylene-isomer mixtures are shown; the noise problem with this method is also discussed.     

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.     

Die shape optimal design in three-dimensional shape metal extrusion by the finite element method

A new approach to die shape optimal design in shape extrusion is presented. In this approach, the design problem is formulated as an optimization problem incorporating the three-dimensional finite element analysis model, and optimization of the die shape is conducted on the basis of the design sensitivities. The approach is applied to the determination of the die shapes for extrusion of parts with various cross sections including polygons and T sections. © 1998 John Wiley & Sons, Ltd.