Interacting convection modes in a saturated porous medium of nearly square planform: a special case

The problem of differentiating non-smooth functions of specimen displacements, which are measured during the material removal, is discussed. This problem arises when employing the layer removal method, namely a method of rings and strips, for residual stress depth profiling. It is shown that this problem is ill-posed and special solution methods are required in order to obtain a stable solution. The stability of the solution affects to a high extent the resulting accuracy of the residual stress evaluation in the investigated material. The presented study discusses a numerical approach to solving such ill-posed problems. The proposed approach, which is based on the Tikhonov regularization and a regularized finite difference method, provides a stable approximate solution, including its pointwise error estimation. The advantage of this approach is that it does not require any knowledge about the unknown exact solution; the pointwise error estimation of the measured data is the only prior information that must be available. In addition, this approach provides a convergence of the approximate solution to the unknown exact one when the perturbation of the initial data approaches zero.     

Data clustering using <Emphasis Type="Italic">K</Emphasis>-Means based on Crow Search Algorithm

Cluster analysis is one of the popular data mining techniques and it is defined as the process of grouping similar data. K-Means is one of the clustering algorithms to cluster the numerical data. The features of K-Means clustering algorithm are easy to implement and it is efficient to handle large amounts of data. The major problem with K-Means is the selection of initial centroids. It selects the initial centroids randomly and it leads to a local optimum solution. Recently, nature-inspired optimization algorithms are combined with clustering algorithms to obtain the global optimum solution. Crow Search Algorithm (CSA) is a new population-based metaheuristic optimization algorithm. This algorithm is based on the intelligent behaviour of the crows. In this paper, CSA is combined with the K-Means clustering algorithm to obtain the global optimum solution. Experiments are conducted on benchmark datasets and the results are compared to those from various clustering algorithms and optimization-based clustering algorithms. Also the results are evaluated with internal, external and statistical experiments to prove the efficiency of the proposed algorithm.     

Minimisation of total tardiness for identical parallel machine scheduling using genetic algorithm

In recent years research on parallel machine scheduling has received an increased attention. This paper considers minimisation of total tardiness for scheduling of n jobs on a set of m parallel machines. A spread-sheet-based genetic algorithm (GA) approach is proposed for the problem. The proposed approach is a domain-independent general purpose approach, which has been effectively used to solve this class of problem. The performance of GA is compared with branch and bound and particle swarm optimisation approaches. Two set of problems having 20 and 25 jobs with number of parallel machines equal to 2, 4, 6, 8 and 10 are solved with the proposed approach. Each combination of number of jobs and machines consists of 125 benchmark problems; thus a total for 2250 problems are solved. The results obtained by the proposed approach are comparable with two earlier approaches. It is also demonstrated that a simple GA can be used to produce results that are comparable with problem-specific approach. The proposed approach can also be used to optimise any objective function without changing the basic GA routine.     

Coping with production time variability via dynamic lead-time quotation

In this paper, we propose two dynamic lead-time quotation policies in an M/GI/1 type make-to-stock queueing system serving lead-time sensitive customers with a single type of product. Incorporating non-exponential service times in an exact method for make-to-stock queues is usually deemed difficult. Our analysis of the proposed policies is exact and requires the numerical inversion of the Laplace transform of the sojourn time of an order to be placed. The first policy assures that the long-run probability of delivering the product within the quoted lead-time is the same for all backlogged customers. The second policy is a refinement of the first which improves the profitability if customers are oversensitive to even short delays in delivery. Numerical results show that both policies perform close to the optimal policy that was characterized only for exponential service times. The new insight gained is that the worsening impact of the production time variability, which is felt significantly in systems accepting all customers by quoting zero lead times, decreases when dynamic lead-time quotation policies are employed.     

基于序贯层次Kriging模型的微型飞行器机身结构设计优化

在基于仿真模型的工程设计优化中,采用高精度、高成本的分析模型会导致计算量大,采用低精度、低成本的分析模型会导致设计优化结果的可信度低,难以满足实际工程的要求。为了有效平衡高精度与低成本之间的矛盾关系,通过建立序贯层次Kriging模型融合高/低精度数据,采用大量低成本、低精度的样本点反映高精度分析模型的变化趋势,并采用少量高成本、高精度的样本点对低精度分析模型进行校正,以实现对优化目标的高精度预测。为了避免层次Kriging模型误差对优化结果的影响,将层次Kriging模型与遗传算法相结合,根据6σ设计准则计算每一代最优解的预测区间,具有较大预测区间的当前最优解即为新的高精度样本点。同时,在优化过程中序贯更新层次Kriging模型,提高最优解附近的层次Kriging模型的预测精度,从而保证设计结果的可靠性。将所提出的方法应用于微型飞行器机身结构的设计优化中,以验证该方法的有效性和优越性。采用具有不同单元数的网格模型分别作为低精度分析模型和高精度分析模型,利用最优拉丁超立方设计分别选取60个低精度样本点和20个高精度样本点建立初始层次Kriging模型,采用本文方法求解并与直接采用高精度仿真模型求解的结果进行比较。结果表明,所提出的方法能够有效利用高/低精度样本点处的信息,建立高精度的层次Kriging模型;本文方法仅需要少量的计算成本就能求得近似最优解,有效提高了设计效率,为类似的结构设计优化问题提供了参考。     

Continuum limit of discrete Sommerfeld problems on square lattice

A low-frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It is established that the exact solution of the discrete model converges to the solution of the continuum model, i.e., the continuous Sommerfeld problem, in the discrete Sobolev space defined by Hackbusch. A proof of convergence has been provided for both types of boundary conditions when the imaginary part of incident wavenumber is positive.     

Kinetics of Competitive Sorption in Decontamination of Materials from Radionuclides

kinetic model of the mass transfer of a microcomponent in the simplest competitive system from the sorbed state (A) into a solution (B) and then into a sorbent (C) in accordance with the scheme A ? B ? C was formulated within the framework of competitive sorption statics. The kinetic equations were solved numerically. The influence exerted by the weight of competing sorbents А and С and by the degree of reversibility of linear reactions on the nonequilibrium decontamination factor K_dec(t) was determined. The time in which the equilibrium decontamination factor is attained for the model of chemical sorption kinetics was estimated from the experimental data on the rate constants of direct and reverse heterogeneous reactions and on the distribution coefficients of Cs(I) in the SiO₂ (A)–CsCl solution (B)–Prussian Blue (C) system.     

Numerical solution of fuzzy boundary value problems using Galerkin method

This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the proposed method, an application problem related to heat conduction has also been studied. The results obtained by the proposed methods are compared with the exact solution and other existing methods for demonstrating the validity and efficiency of the present method.     

An exact method for solving the manufacturing cell formation problem

The cell formation problem is extensively studied in the literature, but very few authors have proposed exact methods. In this paper a linear binary programming formulation is introduced to generate a solution for the cell formation problem. To verify the behaviour of the proposed model, a set of 35 benchmark problems is solved using the branch and cut method implemented in the IBM ILOG CPLEX 10.11 Optimiser. Moreover, these results allow us to validate the quality of the solution generated with heuristic methods proposed in the literature. This experimentation indicates that, for the smaller problems, the best-known solutions are the same as those generated with CPLEX 10.11 Optimiser. These results indicate a fair confidence in the optimality of the best-known solutions generated by the heuristic methods. Furthermore, our approach is the first exact method providing results of this quality.     

A mixture of <Emphasis Type="Italic">g</Emphasis>-priors for variable selection when the number of regressors grows with the sample size

We consider the problem of variable selection in linear regression using mixtures of g-priors. A number of mixtures have been proposed in the literature which work well, especially when the number of regressors p is fixed. In this paper, we propose a mixture of g-priors suitable for the case when p grows with the sample size n, more specifically when \(p=O(n^b)\), \(0<b<1\). The marginal density based on the proposed mixture has a nice approximation with a closed form expression, which makes application of the method as tractable as an information criterion-based method. The proposed method satisfies fundamental properties like model selection consistency when the true model lies in the model space, and also consistency in an appropriate sense, under misspecified models setup. The method is quite robust in the sense that the above properties are not confined to normal linear models; they continue to hold under reasonable conditions for a general class of error distributions. Finally, we compare the performance of the proposed prior theoretically with that of some other mixtures of g-priors. We also compare it with several other Bayesian methods of model selection using simulated data sets. Theoretically, as well as in simulations, it emerges that unlike most of the other methods of model selection, the proposed prior is competent enough while selecting the true model irrespective of its dimension.     

Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions

In this paper, the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. Using this decomposition, it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes and the approach followed allows us to extend its validity to situations where the population distributions are elliptically contoured. A real-data example is presented and a simulation study is also conducted.     

On the optimal lot-sizing and scheduling problem in serial-type supply chain system using a time-varying lot-sizing policy

In this paper, we solve the optimal sequencing, lot-sizing and scheduling decisions for several products manufactured through several firms in a serial-type supply chain so as to minimise the sum of setup and inventory holding costs while meeting given demand from customers. We propose a three-phase heuristic to solve this NP-hard problem using a time-varying lot- sizing approach. First, based on the theoretical results, we obtain candidate sets of the production frequencies and cycle time using a junction-point heuristic. Next, we determine the production sequences for each firm using a bin-packing method. Finally, we obtain the production times of the products for each firm in the supply chain system by iteratively solving a set of linear simultaneous equations which were derived from the constraints. Then, we choose the best solution among the candidate solutions. Based on the numerical experiments, we show that the proposed three-phase heuristic efficiently obtains feasible solutions with excellent quality which is much better than the upper-bound solutions from the common cycle approach.     

A multi-commodity supply chain design problem

We consider a multi-commodity supply chain design problem in which we need to determine where to locate facilities and how to allocate customers to facilities so as to minimize total costs. The cost associated with each facility exhibits economies of scale. We show that this problem can be formulated as a nonlinear integer program and propose a Lagrangian-relaxation solution algorithm. By exploiting the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer program that must be solved in solving the Lagrangian relaxation subproblems. We also compare our approach with an existing algorithm.     

Integrated aggregate supply chain planning using memetic algorithm – A performance analysis case study

This paper aims to examine how a complex supply chain yields cost reduction benefits through the global integration of production and distribution decisions. The research is motivated by a complex real world supply chain planning problem facing a large automotive company. A mixed-integer nonlinear production-distribution planning model is solved using a customised memetic algorithm. The performance and effectiveness of the developed model and solution approach in achieving the global optimisation is investigated through experiments comparing the numerical results from the proposed integrated approach with those of a typical non-integrated (hierarchical) production–distribution optimisation.     

Designing a model for service facility protection with a time horizon based on tri-level programming

ABSTRACT

This study investigates the tri-level location problem of defence facilities with a time horizon. This research focuses on the r-interdiction median model over a finite time horizon. This research aims to protect the service facilities using the defence facilities against the most severe attack scenario of the attacker, so that the system is able to use its maximum power to serve the customers after being damaged. This problem is established on the basis of leader–follower games in the form of defender–attacker–defender. Moreover, attempts are made to make the model more realistic by considering a time horizon. To solve the problem, a combination of a genetic algorithm, simulated annealing and an exact method is used. Comparison of the solution method of the applied metaheuristic algorithm and the exact solution method in a number of small samples indicates the desirable performance of this algorithm in a reasonable time.     

Calibration by optimization without using derivatives

Applications in engineering frequently require the adjustment of certain parameters. While the mathematical laws that determine these parameters often are well understood, due to time limitations in every day industrial life, it is typically not feasible to derive an explicit computational procedure for adjusting the parameters based on some given measurement data. This paper aims at showing that in such situations, direct optimization offers a very simple approach that can be of great help. More precisely, we present a numerical implementation for the local minimization of a smooth function \(f:{\mathbb R}^n\rightarrow {\mathbb R}\) subject to upper and lower bounds without relying on the knowledge of the derivative of f. In contrast to other direct optimization approaches the algorithm assumes that the function evaluations are fairly cheap and that the rounding errors associated with the function evaluations are small. As an illustration, this algorithm is applied to approximate the solution of a calibration problem arising from an engineering application. The algorithm uses a Quasi-Newton trust region approach adjusting the trust region radius with a line search. The line search is based on a spline function which minimizes a weighted least squares sum of the jumps in its third derivative. The approximate gradients used in the Quasi-Newton approach are computed by central finite differences. A new randomized basis approach is considered to generate finite difference approximations of the gradient which also allow for a curvature correction of the Hessian in addition to the Quasi-Newton update. These concepts are combined with an active set strategy. The implementation is public domain; numerical experiments indicate that the algorithm is well suitable for the calibration problem of measuring instruments that prompted this research. Further preliminary numerical results suggest that an approximate local minimizer of a smooth non-convex function f depending on \(n\le 300 \) variables can be computed with a number of iterations that grows moderately with n.     

Harmony search optimization algorithm for a novel transportation problem in a consolidation network

This article presents a new harmony search optimization algorithm to solve a novel integer programming model developed for a consolidation network. In this network, a set of vehicles is used to transport goods from suppliers to their corresponding customers via two transportation systems: direct shipment and milk run logistics. The objective of this problem is to minimize the total shipping cost in the network, so it tries to reduce the number of required vehicles using an efficient vehicle routing strategy in the solution approach. Solving several numerical examples confirms that the proposed solution approach based on the harmony search algorithm performs much better than CPLEX in reducing both the shipping cost in the network and computational time requirement, especially for realistic size problem instances.     

Diffraction from arbitrarily shaped bodies of revolution: analytical regularization

A mathematically rigorous and numerically efficient approach, based on analytical regularization, for solving the scalar wave diffraction problem with a Dirichlet boundary condition imposed on an arbitrarily shaped body of revolution is described. Seeking the solution in an integral-equation formulation, the singular features of its kernel are determined, and the initial equation transformed so that its kernel can be decomposed into a singular canonical part and a regular remainder. An analytical transformation technique is used to reduce the problem equivalently to an infinite system of linear algebraic equations of the second kind. Such system can be effectively solved with any prescribed accuracy by standard numerical methods. The matrix elements of this algebraic system are expressible in the terms of the Fourier coefficients of the remainder. Due to the smoothness of the remainder a robust and efficient technique is obtained to calculate the matrix elements. Numerical investigations of structures, such as the prolate spheroid and bodies obtained by rotation of “Pascal’s Limaçon” and of the “Cassini Oval”, exhibit the high accuracy and wide possibilities of the approach.     

Modeling the planning and scheduling across the outsourcing supply chain: a Chaos-based fast Tabu–SA approach

Planning and Scheduling are the interrelated manufacturing functions and should be solved simultaneously to achieve the real motives of integration in manufacturing. In this paper, we have addressed the advanced integrated planning and scheduling problem in a rapidly changing environment, where the selection of outsourcing machine/operation, meeting the customers (single or multiple) due date, minimizing the makespan are the main objectives while satisfying several technological constraints. We developed a mixed integer programming model for integrated planning and scheduling across the outsourcing supply chain and showed how such models can be used to make strategic decisions. It is a computationally complex and mathematically intractable problem to solve. In this paper, a Chaos-based fast Tabu-simulated annealing (CFTSA) incorporating the features of SA, Tabu and Chaos theory is proposed and applied to solve a large number of problems with increased complexity. In CFTSA algorithm, five types of perturbation schemes are developed and Cauchy probability function is used to escape from local minima and achieve the optimal/near optimal solution in a lesser number of iterations. An intensive comparative study shows the robustness of proposed algorithm. Percentage Heuristic gap is used to show the effectiveness and two ANOVA analyses are carried out to show the consistency and accuracy of the proposed approach.     

A stabilized P1/P1 finite element for the mechanical analysis of solid metals

The aim of this paper is to propose a stabilized finite element P1/ P1 and to show that it is well suited for the finite-strain analysis of solid metals in the context of large von Mises elasto-viscoplastic or elasto-plastic transformations. The first part of this paper is dedicated to the finite element formulation which is detailed for an elasto-viscoplastic model problem. Then, a new stabilized formulation is proposed for the pressure solution. In the last part, examples are presented to show the relevance of the finite element P1/ P1 developed.