Parameters optimization of selected casting processes using teaching–learning-based optimization algorithm

In the present work, mathematical models of three important casting processes are considered namely squeeze casting, continuous casting and die casting for the parameters optimization of respective processes. A recently developed advanced optimization algorithm named as teaching–learning-based optimization (TLBO) is used for the parameters optimization of these casting processes. Each process is described with a suitable example which involves respective process parameters. The mathematical model related to the squeeze casting is a multi-objective problem whereas the model related to the continuous casting is multi-objective multi-constrained problem and the problem related to the die casting is a single objective problem. The mathematical models which are considered in the present work were previously attempted by genetic algorithm and simulated annealing algorithms. However, attempt is made in the present work to minimize the computational efforts using the TLBO algorithm. Considerable improvements in results are obtained in all the cases and it is believed that a global optimum solution is achieved in the case of die casting process.     

Simultaneous siting and sizing of distribution centers on a plane

The benefits of simultaneous consideration of siting and sizing of distribution centers have been well acknowledged in supply chain design. Most formulations assume that the potential DC sites are known and the decision on location is to select sites from the finite potential DC sites. However, the quality of this discrete version problem depends on the selection of potential DC sites. In this paper we present a planar version of the problem, which assumes that there is no a priori knowledge of DC sites and DCs can be located anywhere in the plane. The goal of the problem is to simultaneously find locations and sizing of DC sites. The solution of the planar problem provides a lower bound for the discrete problem. The objective of the problem is to minimize the total of inbound and outbound transportation costs and distribution center construction costs—which include its fixed charge cost and concave sizing cost. The problem is initially formulated as a nonlinear programming model. We then reformulate it as a set covering problem after establishing certain key properties. A greedy drop heuristic and a column generation heuristic are developed to solve the problem. Computational experiments are provided.     

Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm

This paper presents an approach for online learning of Takagi–Sugeno (T-S) fuzzy models. A novel learning algorithm based on a Hierarchical Particle Swarm Optimization (HPSO) is introduced to automatically extract all fuzzy logic system (FLS)’s parameters of a T–S fuzzy model. During online operation, both the consequent parameters of the T–S fuzzy model and the PSO inertia weight are continually updated when new data becomes available. By applying this concept to the learning algorithm, a new type T–S fuzzy modeling approach is constructed where the proposed HPSO algorithm includes an adaptive procedure and becomes a self-adaptive HPSO (S-AHPSO) algorithm usable in real-time processes. To improve the computational time of the proposed HPSO, particles positions are initialized by using an efficient unsupervised fuzzy clustering algorithm (UFCA). The UFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system, enhancing the HPSO’s tuning. The approach is applied to identify the dynamical behavior of the dissolved oxygen concentration in an activated sludge reactor within a wastewater treatment plant. The results show that the proposed approach can identify nonlinear systems satisfactorily, and reveal superior performance of the proposed methods when compared with other state of the art methods. Moreover, the methodologies proposed in this paper can be involved in wider applications in a number of fields such as model predictive control, direct controller design, unsupervised clustering, motion detection, and robotics.     

Comment on paper “Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization” by Wang and Li

This comment addresses the work of Wang and Li (DOI: 10.1007/s12293-009-0012-0, hereafter referred to as WL) published online on September 01, 2009 in a (special) issue of Memetic Computing. We respectfully beg to differ in opinion with WL and argue that the concept of multi-strategy evolutionary search used by WL is not particularly novel. Similar ideas have been presented elsewhere, and these publications date back to at least early 2007. For instance, in a series of papers published in PNAS (2007), SSSAJ (2008), WRR (2008), IEEE-TEVC (2009), JH (2010), Vrugt and coworkers have introduced AMALGAM, a multi-method (or ensemble) search approach to solve emerging single and multiple objective search and optimization problems. In the past few years, MATLAB, C++, Python, and R implementations of AMALGAM have been distributed extensively among researchers and practitioners in various fields of study.     

Evaluation of the genetic algorithm parameters on the optimization performance: a case study on pump-and-treat remediation design

In this study, the impacts of different crossover and encoding schemes on the performance of a genetic algorithm (GA) in finding optimal pump-and-treat (P&T) remediation designs are investigated. For this purpose, binary and Gray encodings of the decision variables are tested. Uniform and two-point crossover schemes are evaluated for two different crossover probabilities. Analysis is performed for two P&T system optimization scenarios. Results show that uniform crossover operator with Gray encoding outperforms the other alternatives for the complex problem with higher number of decision variables. On the other hand, when a simpler problem, which had a lower number of decision variables, is solved, the efficiency of GA is independent of the encoding and crossover schemes.     

A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem – A case study on supply chain model

The main goal of supply chain management is to coordinate and collaborate the supply chain partners seamlessly. On the other hand, bi-level linear programming is a technique for modeling decentralized decision. It consists of the upper level and lower level objectives. Thus, this paper intends to apply bi-level linear programming to supply chain distribution problem and develop an efficient method based on hybrid of genetic algorithm (GA) and particle swarm optimization (PSO). The performance of the proposed method is ascertained by comparing the results with GA and PSO using four problems in the literature and a supply chain distribution model.     

Optimal designs for weighted approximation and integration of stochastic processes on [0,∞)

We study minimal errors and optimal designs for weighted L₂-approximation and weighted integration of Gaussian stochastic processes X defined on the half-line [0,∞). Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration. The upper bounds are proven constructively for approximation and non-constructively for integration. For integration of the r-fold integrated Brownian motion, the upper bound is proven constructively and we have a matching lower bound.     

Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method

A method is presented for direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using global collocation at Legendre-Gauss-Radau (LGR) points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the nonlinear programming problem to the costates of the optimal control problem. More precisely, it is shown that the dual multipliers for the discrete scheme correspond to a pseudospectral approximation of the adjoint equation using polynomials one degree smaller than that used for the state equation. The relationship between the coefficients of the pseudospectral scheme for the state equation and for the adjoint equation is established. Also, it is shown that the inverse of the pseudospectral LGR differentiation matrix is precisely the matrix associated with an implicit LGR integration scheme. Hence, the method presented in this paper can be thought of as either a global implicit integration method or a pseudospectral method. Numerical results show that the use of LGR collocation as described in this paper leads to the ability to determine accurate primal and dual solutions for both finite and infinite-horizon optimal control problems.     

Optimal sensor placement for modal identification of structures using genetic algorithms—a case study: the olympic stadium in Cali,Colombia

Adequate sensor placement plays a key role in such fields as system identification, structural control, damage detection and structural health monitoring of flexible structures. In recent years, interest has increased in the development of methods for determining an arrangement of sensors suitable for characterizing the dynamic behavior of a given structure. This paper describes the implementation of genetic algorithms as a strategy for optimal placement of a predefined number of sensors. The method is based on the maximization of a fitness function that evaluates sensor positions in terms of natural frequency identification effectiveness and mode shape independence under various occupation and excitation scenarios using a custom genetic algorithm. A finite element model of the stadium was used to evaluate modal parameters used in the fitness function, and to simulate different occupation and excitation scenarios. The results obtained with the genetic algorithm strategy are compared with those obtained from applying the Effective Independence and Modal Kinetic Energy sensor placement techniques. The sensor distribution obtained from the proposed strategy will be used in a structural health monitoring system to be installed in the stadium.     

Optimal Lipschitz maps on one-holed tori and the Thurston metric theory of Teichmüller space

Geometriae Dedicata - We study Thurston’s Lipschitz and curve metrics, as well as the arc metric on the Teichmüller space of one-hold tori equipped with complete hyperbolic metrics with...     

Mathematical model of liquid–liquid equilibrium for a ternary system using the GMDH-type neural network and genetic algorithm

A GMDH type-neural network was used to predict liquid phase equilibrium data for the (water + ethanol + trans-decalin) ternary system in the temperature range of 300.2–315.2 K. In order to accomplish modeling, the experimental data were divided into train and test sections. The data set was divided into two parts: 70% were used as data for “training” and 30% were used as a test set. The predicted values were compared with those of experimental values in order to evaluate the performance of the GMDH neural network method. The results obtained by using GMDH type neural network are in excellent agreement with the experimental results.     

How do invariant transformations affect the calibration and optimization of the Kalman filtering algorithm used in the estimation of continuous-time affine term structure models?

Computational Management Science - In studying affine term structure models (ATSM), researchers have made significant theoretical advances in simplifying the burden of the Kalman filtering...     

On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. In this paper we discuss the mutual impact of linear algebra and optimization, focusing on interior point methods and on the iterative solution of the KKT system. Three critical issues are addressed: preconditioning, termination control for the inner iterations, and inertia control.     

Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

This paper examines the influence of two major aspects on the solution quality of surrogate model algorithms for computationally expensive black-box global optimization problems, namely the surrogate model choice and the method of iteratively selecting sample points. A random sampling strategy (algorithm SO-M-c) and a strategy where the minimum point of the response surface is used as new sample point (algorithm SO-M-s) are compared in numerical experiments. Various surrogate models and their combinations have been used within the SO-M-c and SO-M-s sampling frameworks. The Dempster–Shafer Theory approach used in the algorithm by Müller and Piché (J Glob Optim 51:79–104, 2011) has been used for combining the surrogate models. The algorithms are numerically compared on 13 deterministic literature test problems with 2–30 dimensions, an application problem that deals with groundwater bioremediation, and an application that arises in energy generation using tethered kites. NOMAD and the particle swarm pattern search algorithm (PSWARM), which are derivative-free optimization methods, have been included in the comparison. The algorithms have also been compared to a kriging method that uses the expected improvement as sampling strategy (FEI), which is similar to the Efficient Global Optimization (EGO) algorithm. Data and performance profiles show that surrogate model combinations containing the cubic radial basis function (RBF) model work best regardless of the sampling strategy, whereas using only a polynomial regression model should be avoided. Kriging and combinations including kriging perform in general worse than when RBF models are used. NOMAD, PSWARM, and FEI perform for most problems worse than SO-M-s and SO-M-c. Within the scope of this study a Matlab toolbox has been developed that allows the user to choose, among others, between various sampling strategies and surrogate models and their combinations. The open source toolbox is available from the authors upon request.     

Optimal error estimates and modified energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell’s equations

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain(ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell’s equations.Precisely,for the case with a perfectly electric conducting(PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete H 1-norm for the ADI-FDTD scheme,and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero,then the discrete L 2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time.The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell’s equations introduced in this paper.Furthermore,we prove that,in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws,the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws.This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms.Experimental results which confirm the theoretical results are presented.