A comparative study of controlled random search algorithms with application to inverse aerofoil design

This article presents a comparative study of some versions of the controlled random search algorithm (CRSA) in global optimization problems. The basic CRSA, originally proposed by Price in 1977 and improved by Ali et al. in 1997, is taken as a starting point. Then, some new modifications are proposed to improve the efficiency and reliability of this global optimization technique. The performance of the algorithms is assessed using traditional benchmark test problems commonly invoked in the literature. This comparative study points out the key features of the modified algorithm. Finally, a comparison is also made in a practical engineering application, namely the inverse aerofoil shape design.     

An improved harmony search algorithm with dynamically varying bandwidth

The present work demonstrates a new variant of the harmony search (HS) algorithm where bandwidth (BW) is one of the deciding factors for the time complexity and the performance of the algorithm. The BW needs to have both explorative and exploitative characteristics. The ideology is to use a large BW to search in the full domain and to adjust the BW dynamically closer to the optimal solution. After trying a series of approaches, a methodology inspired by the functioning of a low-pass filter showed satisfactory results. This approach was implemented in the self-adaptive improved harmony search (SIHS) algorithm and tested on several benchmark functions. Compared to the existing HS algorithm and its variants, SIHS showed better performance on most of the test functions. Thereafter, the algorithm was applied to geometric parameter optimization of a friction stir welding tool.     

Optimization of cardinality constrained portfolios with a hybrid local search algorithm

One of the main advantages of portfolios over single assets is that risk can be diversified without necessarily reducing the expected return - provided "proper" assets are selected and they are assigned the "proper" weights. Since in practice investors tend to restrict themselves to a rather small number of different assets, the decision which securities to include is a crucial one that turns out to be NP-hard. In this paper we suggest a hybrid local search algorithm which combines principles of Simulated Annealing and evolutionary strategies and which proved to highly efficiently approach this problem. Correspondence to: Dietmar MaringerThe authors would like to thank participants of the 4^th Metaheuristics International Conference and the Econometrics Research Seminar at the University of Geneva, U. Derigs, M. Gilli, H.-O. Günther, and two anonymous referees for valuable comments on earlier versions of this paper.     

A Robust Framework for Multi‐Response Surface Optimization Methodology

A robust multi‐response optimization framework is proposed for simultaneously optimizing multiple conflicting quality characteristics. Unlike prior methods, the proposed approach is insensitive to subjective inputs like target specifications and improves optimization process for correlated responses. The effectiveness of the proposed approach is demonstrated and compared with existing methods considering two examples from the literature. The proposed method yields similar results consistently for different assigned target values demonstrating repeatability of the model, hence demonstrating insensitivity to assigned subjective target values. Furthermore, the study also considers multiple correlated design characteristics issue to achieve better trade‐off during design optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Applying multiple objective tabu search to continuous optimization problems with a simple neighbourhood strategy

One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works with more than one solution (neighbourhood solutions) at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run. The selection and updating stages are modified to enable the original TS algorithm to work with more than one objective. In this paper, the multiple objective tabu search (MOTS) algorithm is applied to multiple objective non‐linear optimization problems with continuous variables using a simple neighbourhood strategy. The algorithm is applied to four mechanical components design problems. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that MOTS is able to find better and much wider spread of solutions than the reported ones. Copyright © 2005 John Wiley & Sons, Ltd.     

A cloud theory-based particle swarm optimization for multiple decision maker vehicle routing problems with fuzzy random time windows

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.     

An approach to multi‐start clustering for global optimization with non‐linear constraints

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.     

约束全局优化问题的一个单参数填充函数方法

类似于无约束全局优化问题,本文给出了求解约束全局优化问题的一个填充函数方法,首先给出了约束全局优化问题的填充函数定义,在此定义的基础上提出了一个单参数填允函数.讨论了该函数的性质,并设计了一个填充函数算法,数值计算结果显示该算法是有效的和可行的.     

An interval random perturbation method for structural‐acoustic system with hybrid uncertain parameters

An interval random model is introduced for the response analysis of structural‐acoustic systems that lack sufficient information to construct the precise probability distributions of uncertain parameters. In the interval random model, the uncertain parameters are treated as random variables, whereas some distribution parameters of random variables with limited information are expressed as interval variables instead of precise values. On the basis of the interval random model, the interval random structural‐acoustic finite element equation is constructed, and an interval random perturbation method for solving this interval random equation is proposed. In the proposed method, the interval random matrix and vector are expanded by the first‐order Taylor series, and the response vector of the structural‐acoustic system is calculated by the matrix perturbation method. According to the linear monotonicity of the response vector, the lower and upper bounds of the response vector are calculated by the vertex method. On the basis of the lower and upper bounds, the intervals of expectation and standard variance of the response vector are obtained by the random interval moment method. The numerical results on a shell structural‐acoustic model and an automobile passenger compartment with flexible front panel demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

A Prediction Region‐based Approach to Model Uncertainty for Multi‐response Optimization

Multi‐response optimization methods rely on empirical process models based on the estimates of model parameters that relate response variables to a set of design variables. However, in determining the optimal conditions for the design variables, model uncertainty is typically neglected, resulting in an unstable optimal solution. This paper proposes a new optimization strategy that takes model uncertainty into account via the prediction region for multiple responses. To avoid obtaining an overly conservative design, the location and dispersion performances are constructed based on the best‐case strategy and the worst‐case strategy of expected loss. We reveal that the traditional loss function and the minimax/maximin strategy are both special cases of the proposed approach. An example is illustrated to present the procedure and the effectiveness of the proposed loss function. The results show that the proposed approach can give reasonable results when both the location and dispersion performances are important issues. Copyright © 2015 John Wiley & Sons, Ltd.     

An improved crack analysis technique by element‐free Galerkin method with auxiliary supports

In this study, an improved crack analysis technique by element‐free Galerkin method (EFGM) with auxiliary supports is proposed. To efficiently model the singularity and the discontinuity of the crack, a singular basis function which varies only on the auxiliary supports is added to enrich the standard EFG approximation and the discontinuous shape function is used in the vicinity of the crack surface. The proposed technique improves the accuracy in the near tip field, by using only an initial node arrangement without any modification until the completion of an analysis. A parametric study, which can guide the analyst on the reasonable choice for the formulation and modelling parameters to be used in the technique, is performed on a relative stress norm error and stress intensity factor. In addition, some numerical examples are analysed to verify the effectiveness of the proposed technique for a crack problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Profit Maximizing Warranty Period with Sales Expressed by a Demand Function

The problem of determining the optimal warranty period, assumed to coincide with the manufacturer's lower specification limit for the lifetime of the product, is addressed. It is assumed that the quantity sold depends via a Cobb–Douglas‐type demand function on the sale price and on the warranty period, and that both the cost incurred for a non‐conforming item and the sale price increase with the warranty period. A general solution is derived using Response Modeling Methodology (RMM) and a new approximation for the standard normal cumulative distribution function. The general solution is compared with the exact optimal solutions derived under various distributional scenarios. Relative to the exact optimal solutions, RMM‐based solutions are accurate to at least the first three significant digits. Some exact results are derived for the uniform and the exponential distributions. Copyright © 2006 John Wiley & Sons, Ltd.