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Article
Publication date: 16 April 2018

Dianzi Liu, Chengyang Liu, Chuanwei Zhang, Chao Xu, Ziliang Du and Zhiqiang Wan

In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these…

Abstract

Purpose

In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

Design/methodology/approach

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

Findings

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

Originality/value

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 24 May 2013

Daniele Peri and Matteo Diez

The purpose of this paper is the introduction of a globally convergent algorithm into a framework for global derivative‐free optimization, such as particle swarm…

Abstract

Purpose

The purpose of this paper is the introduction of a globally convergent algorithm into a framework for global derivative‐free optimization, such as particle swarm optimization (PSO) for which a full proof of convergence is currently missing.

Design/methodology/approach

The substitution of the classical PSO iteration by the Newton method is suggested when the global minimum is not improved. Use of surrogate models for the computation of the Hessian of the objective function is a key point for the overall computational effort. Adoption of a trustregion approach guarantees the consistency of the present approach with the original formulation.

Findings

The approach proposed is mostly found to be an improvement of the classical PSO method. The use of surrogate models and the trustregion approach maintains the overall computational effort at the same level as the original algorithm.

Research limitations/implications

Although the number of algebraic test functions is pretty large, a single practical example is provided. Further numerical experiments are needed in order to increase the generality of the conclusions.

Practical implications

The proposed method improves the efficiency of the standard PSO algorithm.

Originality/value

Previous literature does not provide comprehensive systematic studies for coupling PSO with local search algorithms. This paper is a contribution for closing the gap.

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Article
Publication date: 8 July 2019

Saman Babaie-Kafaki and Saeed Rezaee

The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.

Abstract

Purpose

The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.

Design/methodology/approach

The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.

Findings

An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.

Practical implications

The algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.

Originality/value

The proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 12 no. 3
Type: Research Article
ISSN: 1756-378X

Keywords

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Article
Publication date: 3 October 2016

Slawomir Koziel and Adrian Bekasiewicz

Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated…

Abstract

Purpose

Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues.

Design/methodology/approach

The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach.

Findings

Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods.

Research limitations/implications

The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes.

Originality/value

Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

Details

Engineering Computations, vol. 33 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 May 2019

Jinbo Wang, Naigang Cui and Changzhu Wei

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency…

Abstract

Purpose

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

Design/methodology/approach

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Findings

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Practical implications

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

Originality/value

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

Details

Aircraft Engineering and Aerospace Technology, vol. 91 no. 4
Type: Research Article
ISSN: 1748-8842

Keywords

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Article
Publication date: 1 January 2004

Qingfu Zhang, Jianyong Sun, Edward Tsang and John Ford

This paper introduces a new hybrid evolutionary algorithm (EA) for continuous global optimization problems, called estimation of distribution algorithm with local search…

Abstract

This paper introduces a new hybrid evolutionary algorithm (EA) for continuous global optimization problems, called estimation of distribution algorithm with local search (EDA/L). Like other EAs, EDA/L maintains and improves a population of solutions in the feasible region. Initial candidate solutions are generated by uniform design, these solutions evenly scatter over the feasible solution region. To generate a new population, a marginal histogram model is built based on the global statistical information extracted from the current population and then new solutions are sampled from the model thus built. The incomplete simplex method applies to every new solution generated by uniform design or sampled from the histogram model. Unconstrained optimization by diagonal quadratic approximation applies to several selected resultant solutions of the incomplete simplex method at each generation. We study the effectiveness of main components of EDA/L. The experimental results demonstrate that EDA/L is better than four other recent EAs in terms of the solution quality and the computational cost.

Details

Engineering Computations, vol. 21 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 11 October 2011

Silvana Maria B. Afonso, Bernardo Horowitz and Marcelo Ferreira da Silva

The purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to…

Abstract

Purpose

The purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to demonstrate its efficiency in reducing the number of high fidelity (HF) runs in the optimization process.

Design/methodology/approach

In this work, surrogate models are built for space truss structures. This study uses functional as well as physical surrogates. In the latter, a grid analogy of the space truss is used thereby reducing drastically the analysis cost. Global and local approaches are considered. The latter will require a globalization scheme (sequential approximate optimization (SAO)) to ensure convergence.

Findings

Physically based surrogates were proposed. Classical techniques, namely Taylor series and kriging, are also implemented for comparison purposes. A parameter study in kriging is necessary to select the best kriging model to be used as surrogate. A test case was considered for optimization and several surrogates were built. The CPU time is reduced when compared with the HF solution, for all surrogate‐based optimization performed. The best result was achieved combining the proposed physical model with additive corrections in a SAO strategy in which C1 continuity was imposed at each trust region center. Some guidance for other engineering applications was given.

Originality/value

This is the first time that physical‐based surrogates for optimum design of space truss systems are used in the SAO framework. Physical surrogates typically exhibit better generalization properties than other surrogates forms, produce faster solutions, and do not suffer from dimensionality curse when used in approximate optimization strategies.

Details

Engineering Computations, vol. 28 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 2 October 2017

Xuepeng Zhan, Jianjun Wu, Mingzhi Wang, Yu Hui, Hongfei Wu, Qi Shang and Ruichao Guo

This paper aims to first apply more advanced anisotropic yield criterions as Yld91 and Yld2004 to spherical indentation simulations, and investigate plastic anisotropy…

Abstract

Purpose

This paper aims to first apply more advanced anisotropic yield criterions as Yld91 and Yld2004 to spherical indentation simulations, and investigate plastic anisotropy identified from indentation simulations following different yield criterions (Hill48, Yld91, Yld2004) to discover laws. It also aims to compare the difference in plastic anisotropy identified from indentation on three yield criterions and evaluate the applicability of plastic anisotropy.

Design/methodology/approach

This paper uses indentation simulations on different yield criterions to identify plastic anisotropy. First, the trust-region techniques based on the nonlinear least-squares method are used to determine anisotropy coefficients of Yld91 and Yld2004. Then, Yld91 and Yld2004 are implemented into ABAQUS software using user-defined material (UMAT) subroutines with the proposed universal structure. Finally, through considering comprehensively the key factors, the locations of the optimal data acquisition points in indentation simulations on different yield criterions are determined. And, the identified stress–strain curves are compared with experimental data.

Findings

This paper discovers that indentation on Yld2004 is able to fully identify difference in equivalent plastic strain between 0° and 90° directions when indentation depth ht is relatively smaller. And, this research demonstrates conclusively that plastic anisotropy identified from indentation on Yld2004 and Yld91 is more applicable at larger strains than that on Hill48, and that on Yld2004 is more applicable than that on Yld91, overall. In addition, the method on the determination of the locations of the optimal data acquisition points is demonstrated to be also valid for anisotropic material.

Originality/value

This paper first investigates plastic anisotropic properties and laws identified from indentation simulations following more advanced anisotropic yield criterions and provides reference for later research.

Details

Engineering Computations, vol. 34 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 20 December 2019

Anna Pietrenko-Dabrowska and Slawomir Koziel

The purpose of this study is to propose a framework for expedited antenna optimization with numerical derivatives involving gradient variation monitoring throughout the…

Abstract

Purpose

The purpose of this study is to propose a framework for expedited antenna optimization with numerical derivatives involving gradient variation monitoring throughout the optimization run and demonstrate it using a benchmark set of real-world wideband antennas. A comprehensive analysis of the algorithm performance involving multiple starting points is provided. The optimization results are compared with a conventional trust-region (TR) procedure, as well as the state-of-the-art accelerated TR algorithms.

Design/methodology/approach

The proposed algorithm is a modification of the TR gradient-based algorithm with numerical derivatives in which a monitoring of changes of the system response gradients is performed throughout the algorithm run. The gradient variations between consecutive iterations are quantified by an appropriately developed metric. Upon detecting stable patterns for particular parameter sensitivities, the costly finite differentiation (FD)-based gradient updates are suppressed; hence, the overall number of full-wave electromagnetic (EM) simulations is significantly reduced. This leads to considerable computational savings without compromising the design quality.

Findings

Monitoring of the antenna response sensitivity variations during the optimization process enables to detect the parameters for which updating the gradient information is not necessary at every iteration. When incorporated into the TR gradient-search procedures, the approach permits reduction of the computational cost of the optimization process. The proposed technique is dedicated to expedite direct optimization of antenna structures, but it can also be applied to speed up surrogate-assisted tasks, especially solving sub-problems that involve performing numerous evaluations of coarse-discretization models.

Research limitations/implications

The introduced methodology opens up new possibilities for future developments of accelerated antenna optimization procedures. In particular, the presented routine can be combined with the previously reported techniques that involve replacing FD with the Broyden formula for directions that are satisfactorily well aligned with the most recent design relocation and/or performing FD in a sparse manner based on relative design relocation (with respect to the current search region) in consecutive algorithm iterations.

Originality/value

Benchmarking against a conventional TR procedure, as well as previously reported methods, confirms improved efficiency and reliability of the proposed approach. The applications of the framework include direct EM-driven design closure, along with surrogate-based optimization within variable-fidelity surrogate-assisted procedures. To the best of the authors’ knowledge, no comparable approach to antenna optimization has been reported elsewhere. Particularly, it surmounts established methodology by carrying out constant supervision of the antenna response gradient throughout successive algorithm iterations and using gathered observations to properly guide the optimization routine.

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Article
Publication date: 27 June 2020

Abir Trabelsi and Hiroaki Matsukawa

This paper considers an option contract in a two-stage supplier-retailer supply chain (SC) when market demand is stochastic. The problem is a Stackelberg game with the…

Abstract

Purpose

This paper considers an option contract in a two-stage supplier-retailer supply chain (SC) when market demand is stochastic. The problem is a Stackelberg game with the supplier as a leader. This research assumes demand information sharing. The purpose of this study is to determine the optimal pricing strategy of the supplier along with the optimal order strategy of the retailer in three option contract cases.

Design/methodology/approach

The paper model the option contract pricing problem as a bilevel problem. The problem is then solved using bilevel programing methods. After computing, the generated outcomes are compared to a benchmark (wholesale price contract) to evaluate the contract.

Findings

The results reveal that only one of the contract cases can arbitrarily allocate the SC profit. In both other cases, the Stackelberg supplier manages to earn the total SC profit. Further analysis of the first contract, show that from the supplier’s perspective, the first stage forecast inaccuracy is beneficial, whereas the demand uncertainty in the second stage is detrimental. This contracting strategy guarantees both players better outcomes compared to the wholesale price contract.

Originality/value

To the best of the authors’ knowledge, this research is the first that links the option contract literature to the bilevel programing literature. It also the first to solve the pricing problem of the commitment option contract with demand update where the retailer exercises the option before knowing the exact demand.

Details

Journal of Modelling in Management, vol. 15 no. 4
Type: Research Article
ISSN: 1746-5664

Keywords

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