An efficient global optimization algorithm for multifactor dynamic systems

Abstract

In this study we present an efficient global optimization method, DIviding RECTangle (DIRECT) algorithm, for parametric analysis of dynamic systems. In a bounded constrained problem the DIRECT algorithm explores multiple potentially optimal subspaces in one search. The algorithm also eliminates the need for derivative calculations which are required in some efficient gradient‐based methods. In this study the first optimization example is to find the dynamic parameters of a tennis racket. The second example is a biomechanical parametric study of a heel‐toe running model governed by six factors. The effectiveness of the DIRECT algorithm is compared with a genetic algorithm in an analysis of heel‐toe running. The result shows that the DIRECT algorithm obtains an improved result in 83% less execution time. It is demonstrated that the straightforward DIRECT algorithm provides a general procedure for solving global optimization problems efficiently and confidently.     

Modification of DIRECT for high-dimensional design problems

DIviding RECTangles (DIRECT), as a well-known derivative-free global optimization method, has been found to be effective and efficient for low-dimensional problems. When facing high-dimensional black-box problems, however, DIRECT's performance deteriorates. This work proposes a series of modifications to DIRECT for high-dimensional problems (dimensionality d>10). The principal idea is to increase the convergence speed by breaking its single initialization-to-convergence approach into several more intricate steps. Specifically, starting with the entire feasible area, the search domain will shrink gradually and adaptively to the region enclosing the potential optimum. Several stopping criteria have been introduced to avoid premature convergence. A diversification subroutine has also been developed to prevent the algorithm from being trapped in local minima. The proposed approach is benchmarked using nine standard high-dimensional test functions and one black-box engineering problem. All these tests show a significant efficiency improvement over the original DIRECT for high-dimensional design problems.     

Expected improvement based infill sampling for global robust optimization of constrained problems

A novel adaptive sampling scheme for efficient global robust optimization of constrained problems is proposed. The method addresses expensive to simulate black-box constrained problems affected by uncertainties for which only the bounds are known, while the probability distribution is not available. An iterative strategy for global robust optimization that adaptively samples the Kriging metamodel of the computationally expensive problem is proposed. The presented approach is tested on several benchmark problems and the average performance based on 100 runs is evaluated. The applicability of the method to engineering problems is also illustrated by applying robust optimization on an integrated photonic device affected by manufacturing uncertainties. The numerical results show consistent convergence to the global robust optimum using a limited number of expensive simulations.     

Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization

In this paper we describe some algorithms for noisy optimization in the context of problems from the gas transmission industry. The algorithms are implicit filtering, DIRECT, and a new hybrid of these methods, which uses DIRECT to find an intitial iterate for implicit filtering. We report on numerical results that illustrate the performance of the methods.     

Simultaneous topology,shape and size optimization of truss structures by fully stressed design based on evolution strategy

The most effective scheme of truss optimization considers the combined effect of topology, shape and size (TSS); however, most available studies on truss optimization by metaheuristics concentrated on one or two of the above aspects. The presence of diverse design variables and constraints in TSS optimization may account for such limited applicability of metaheuristics to this field. In this article, a recently proposed algorithm for simultaneous shape and size optimization, fully stressed design based on evolution strategy (FSD-ES), is enhanced to handle TSS optimization problems. FSD-ES combines advantages of the well-known deterministic approach of fully stressed design with potential global search of the state-of-the-art evolution strategy. A comparison of results demonstrates that the proposed optimizer reaches the same or similar solutions faster and/or is able to find lighter designs than those previously reported in the literature. Moreover, the proposed variant of FSD-ES requires no user-based tuning effort, which is desired in a practical application. The proposed methodology has been tested on a number of problems and is now ready to be applied to more complex TSS problems.     

Global Optimization of Nonlinear Blend-Scheduling Problems

The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR) and normalized multiparametric disaggregation technique (NMDT) to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.     

A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations

Overlapping in operations is an effective technology for productivity improvement in modern manufacturing systems. Thus far, however, there are still rare works on flexible job shop scheduling problems (FJSPs) concerning this strategy. In this paper, we present a hybrid artificial bee colony (hyABC) algorithm to minimise the total flowtime for a FJSP with overlapping in operations. In the proposed hyABC, a dynamic scheme is introduced to fine-tune the search scope adaptively. In view of poor exploitation ability of artificial bee colony algorithm, a modified migrating birds optimisation algorithm (MMBO) is developed and integrated into the search process for better balancing global exploration and local exploitation. In MMBO, a forward share strategy with one-job based crossover is designed to make good use of valuable information from behind solutions. Besides, an improved downward share scheme is adopted to increase diversification of the population, and thus alleviate the premature convergence. Extensive experiments based on benchmark instances with different scales are carried out and comparisons with other recent algorithms identify the effectiveness of the proposed hyABC.     

Robust optimization applied to uncertain production loading problems with import quota limits under the global supply chain management environment

Global supply chain management presents some special challenges and issues for manufacturing companies in planning production: these challenges are different from those discussed in domestic production plans. Globally loading production among different plants usually involves substantial uncertainty and great risk because of uncertain market demand, fluctuating quota costs incurred in the global manufacturing process, and shortening lead times. This study proposes a dual-response production loading strategy for two types of plants—company-owned and contracted—to hedge against the short lead time and uncertainty, and to be as responsive and flexible as possible to cope with the uncertainty and risk involved. Three types of robust optimization models are presented: the robust optimization model with solution robustness, the robust optimization model with model robustness, and the robust optimization model with the trade-off between solution robustness and model robustness. A series of experiments are designed to test the effectiveness of the proposed robust optimization models. Compared with the results of the two-stage stochastic recourse programming model, the robust optimization models provide a more responsive and flexible system with less risk, which is particularly important in the current context of global competitiveness.     

复杂封闭空间有源消声系统的建模新方法

针对具有两个弹性板的复杂封闭空间的有源消声系统。提出了一种新的建模方法。计算机仿真与实验结果验证了这一方法的正确性。该方法拓宽了利用结构声辐射进行有源消声的范围，可适用于任意形状的封闭空间。     

A moving superimposed finite element method for structural topology optimization

Level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. In this paper, a dynamic implicit boundary‐based moving superimposed finite element method (s‐version FEM or S‐FEM) is developed for structural topology optimization using the level set methods, in which the variational interior and exterior boundaries are represented by the zero level set. Both a global mesh and an overlaying local mesh are integrated into the moving S‐FEM analysis model. A relatively coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. In numerical integration using the Gauss quadrature rule, the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes. A double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co‐ordinate systems. An element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency. A simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint. A physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated PDE solving procedure. The proposed moving S‐FEM is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems. For the classical elasticity problems in the literature, the present S‐FEM can achieve numerical results in good agreement with those from the theoretical solutions and/or numerical results from the standard FEM. For the minimum compliance topology optimization problems in structural optimization, the present approach significantly outperforms the well‐recognized ‘ersatz material’ approach as expected in the accuracy of the strain field, numerical stability, and representation fidelity at the expense of increased computational time. It is also shown that the present approach is able to produce structures near the theoretical optimum. It is suggested that the present S‐FEM can be a promising tool for shape and topology optimization using the level set methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Spline interpolation techniques for variational methods

Interpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm. Among global interpolation techniques, bicubic splines and spline-blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper-elements, while high precision finite elements become convenient for very fine or irregular partition.     

正交临近既有铁路高边坡的高铁路堑爆破

在紧邻既有铁路进行高铁路堑石方开挖时,为保证既有铁路的安全正常运营,需对整体开挖方案、爆破设计和防护措施加以研究和分析。由于新建西成高铁剑门关车站路堑石方开挖爆破工程正交临近既有宝成铁路的高边坡,因此根据路堑距既有铁路远近进行分区,确定不同的开挖方法,即预留隔墙浅孔小台阶延时松动控制爆破和静态破碎机械配合开挖的方案。通过对各项爆破参数的设计和调整优化,爆体上覆盖防护、高边坡侧采用柔性网加钢排架的组合式防护措施,爆破飞石、滚石及爆破振动等有害效应得到了有效的控制,可为类似工程爆破方案的设计和安全管理提供借鉴经验。     

ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS

For design problems involving computation-intensive analysis or simulation processes, approximation models are usually introduced to reduce computation lime. Most approximation-based optimization methods make step-by-step improvements to the approximation model by adjusting the limits of the design variables. In this work, a new approximation-based optimization method for computation-intensive design problems - the adaptive response surface method(ARSM), is presented. The ARSM creates quadratic approximation models for the computation-intensive design objective function in a gradually reduced design space. The ARSM was designed to avoid being trapped by local optima and to identify the global design optimum with a modest number of objective function evaluations. Extensive tests on the ARSM as a global optimization scheme using benchmark problems, as well as an industrial design application of the method, are presented. Advantages and limitations of the approach are also discussed     

Optimization of ply angles in laminated composite structures by a hybrid,asynchronous, parallel evolutionary algorithm

An evolutionary algorithm approach aimed at the global optimization of ply angles in laminated composites is proposed. The algorithm is enriched by first-order local search and a niching strategy. Genetic variation operators are tailored to the special properties of ply angle optimization problems. Cyclic box-constraints are considered in the crossover, mutation, and niching operations. All experiments on three academic benchmark problems are able to identify a global optimal solution. Two case studies illustrate the applicability of the method on typical engineering problems.     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

基于IHHO算法的光伏电池工程模型的参数辨识

针对HHO算法存在搜索过程调整不够灵活,不能针对性地进行阶段性搜索,有时会陷入局部最优使算法搜索精度相对较差等问题,提出了一种基于改进哈里斯鹰优化(IHHO)算法的参数辨识方法.对HHO算法进行了两项改进:引人柔性递减策略,在迭代初期扩大全局搜索范围,在迭代后期延长局部搜索时间,从而加强了初期的全局搜索能力和后期的局部...     

Hybrid metamodel-based design space management method for expensive problems

Metamodel-based global optimization methods have been extensively studied for their great potential in solving expensive problems. In this work, a design space management strategy is proposed to improve the accuracy and efficiency of metamodel-based optimization methods. In this strategy, the whole design space is divided into two parts: the important region constructed using several expensive points and the other region. Combined with a previously developed hybrid metamodel strategy, a hybrid metamodel-based design space management method (HMDSM) is developed. In this method, three representative metamodels are used simultaneously in the search of the global optimum in both the important region and the other region. In the search process, the important region is iteratively reduced and the global optimum is soon captured. Tests using a series of benchmark mathematical functions and a practical expensive problem demonstrate the excellent performance of the proposed method.     

Studies of multi‐start clustering for global optimization

Global/multi‐modal optimization problems arise in many engineering applications. Owing to the existence of multiple minima, it is a challenge to solve the multi‐modal optimization problem and to identify the global minimum especially if efficiency is a concern. In this paper, variants of the multi‐start with clustering strategy are developed and studied for identifying multiple local minima in nonlinear global optimization problems. The study considers the sampling procedure, the use of Hessian information in forming clusters, the technique for cluster analysis and the local search procedure. Variations of multi‐start with clustering are applied to 15 multi‐modal problems. A comparative study focuses on the overall search effectiveness in terms of the number of local searches performed, local minima found and required function evaluations. The performance of these multi‐start clustering algorithms ranges from very efficient to very robust. Copyright © 2002 John Wiley & Sons, Ltd.     

A reduced basis method for parametrized variational inequalities applied to contact mechanics

We investigate new developments of the reduced-basis method for parametrized optimization problems with nonlinear constraints. We propose a reduced-basis scheme in a saddle-point form combined with the Empirical Interpolation Method to deal with the nonlinear constraint. In this setting, a primal reduced-basis is needed for the primal solution and a dual one is needed for the Lagrange multipliers. We suggest to construct the latter using a cone-projected greedy algorithm that conserves the non-negativity of the dual basis vectors. The reduction strategy is applied to elastic frictionless contact problems including the possibility of using nonmatching meshes. The numerical examples confirm the efficiency of the reduction strategy.     

Multidisciplinary Design Optimization with Quasiseparable Subsystems

Numerous hierarchical and nonhierarchical decomposition strategies for the optimization of large scale systems, comprised of interacting subsystems, have been proposed. With a few exceptions, all of these strategies lack a rigorous theoretical justification. This paper focuses on a class of quasiseparable optimization problems narrow enough for a rigorous decomposition theory, yet general enough to encompass many large scale engineering design problems. The subsystems for these problems involve local design variables and global system variables, but no variables from other subsystems. The objective function is a sum of a global system criterion and the subsystems' criteria. The essential idea is to give each subsystem a budget and global system variable values, and then ask the subsystems to independently maximize their constraint margins. Using these constraint margins, a system optimization then adjusts the values of the system variables and subsystem budgets. The subsystem margin problems are totally independent, always feasible, and could even be done asynchronously in a parallel computing context. An important detail is that the subsystem tasks, in practice, would be to construct response surface approximations to the constraint margin functions, and the system level optimization would use these margin surrogate functions. The purpose of the present paper is to present a decomposition strategy in a general context, provide rigorous theory justifying the decomposition, and give some simple illustrative examples.