Showing papers in "International Journal of Mathematical Modelling and Numerical Optimisation in 2013"
TL;DR: In this paper, the authors present a set of 175 benchmark functions for unconstrained optimisation problems with diverse properties in terms of modality, separability, and valley landscape.
Abstract: Test functions are important to validate and compare the performance of optimisation algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties to be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimisation problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and it can be expected that this complete set of functions can be used for validation of new optimisation in the future.
876 citations
TL;DR: A timely review of all the state-of-the-art developments in the last five years of Cuckoo search, including the discussions of theoretical background and research directions for future development of this powerful algorithm.
Abstract: Cuckoo search (CS) is an efficient swarm-intelligence-based algorithm and significant developments have been made since its introduction in 2009. CS has many advantages due to its simplicity and efficiency in solving highly non-linear optimisation problems with real-world engineering applications. This paper provides a timely review of all the state-of-the-art developments in the last five years, including the discussions of theoretical background and research directions for future development of this powerful algorithm.
86 citations
TL;DR: This paper has introduced a method based on the use of unsupervised type of regression-based algorithm (RBA) for solving ordinary differential equations (ODEs) with initial or boundary conditions and used error back propagation method for minimising the error function and modification of the parameters without direct use of other optimisation techniques.
Abstract: In this paper, we have introduced a method which is based on the use of unsupervised type of regression-based algorithm (RBA) for solving ordinary differential equations (ODEs) with initial or boundary conditions. Approximate solution of differential equation is differentiable and closed analytic. Here we have used error back propagation method for minimising the error function and modification of the parameters without direct use of other optimisation techniques. Initial weights are taken as combination of random as well as by proposed regression-based method. We present the method for solving a variety of problems and the results with arbitrary and regression-based initial weights are compared. Here the number of nodes in hidden layer has been fixed according to the degree of polynomial in the regression. The present model demonstrates to get also the approximate solutions for the differential equation inside and outside of the training domain.
20 citations
TL;DR: The proposed two-step procedure alleviates the pitfalls of both GA and HJ method and successfully determines the optimal flight planning parameters for a fairly complicated problem.
Abstract: Flight planning for airborne LiDAR data collection determines flight parameters, which in turn control the flight duration. While the former ensures desired quality of captured data the cost of the project is directly affected by the latter. This paper attempts to optimise flight planning problem. The flight duration is expressed as an objective function and the associated data requirements, preferences and limitations of flight planning problem are considered as constraints. Due to the typical characteristics of flight duration and flight parameters, a two-step procedure of optimisation that consists of genetic algorithms (GA) and Hooke and Jeeve’s (HJ) method of optimisation are adopted. The two-step procedure alleviates the pitfalls of both GA and HJ method and successfully determines the optimal flight planning parameters for a fairly complicated problem. Results obtained in this paper demonstrate that the proposed two-step procedure can be used for solving complex engineering problems like flight pla...
9 citations
TL;DR: This paper innovates the existing Keynesian macroeconomic literature by showing that the dynamics of the well-known IS-LM model may generate a double-scroll strange attractor, for a particular set of structural parameters.
Abstract: With the aim of exploring the conditions which determine a chaotic behavior in the long-run properties of an economic model, this paper innovates the existing Keynesian macroeconomic literature by showing that the dynamics of the well-known IS-LM model may generate a double-scroll strange attractor, for a particular set of structural parameters.
6 citations
TL;DR: These selection schemes adopted in harmony search algorithm are analysed in order to evaluate their effect on the performance of HSA and it is shown that linear rank selection provides the highest convergence speed and highest takeover time.
Abstract: Recently, common selection schemes used in harmony search algorithm (HSA) are altered in memory consideration operation to imitate the natural selection principle of survival of the fittest. The selection schemes adopted include: random, proportional, tournament, and linear rank. In this paper, these selection schemes are analysed in order to evaluate their effect on the performance of HSA. The analysis considers takeover time and convergence rate to measure the effectiveness of each selection scheme. Furthermore, a scaled proportional selection scheme is proposed to replace the proportional selection scheme to overcome its shortcoming with negative fitness values. To study the effect of these different selection schemes we use eight global optimisation functions with different characteristics. An experimental evaluation show that linear rank selection provides the highest convergence speed and highest takeover time. On the other hand, scaled proportional selection provides the slowest convergence speed and slowest takeover time. This indicates the effect of the type of the selection method used in memory consideration in takeover time and convergence rate.
5 citations
TL;DR: A structure of hybrid neural networks (NNs) is applied and it is shown that this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalisation and high accuracy.
Abstract: Integral equations play major roles in different fields of science and engineering, therefore, a new method for finding a solution of the Volterra integral equation is presented. So we have applied a structure of hybrid neural networks (NNs). The proposed neural net can get a real input vector and calculates its corresponding output vector. Next, a learning algorithm based on the gradient descent method has been defined for adjusting the connection weights. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalisation and high accuracy. The proposed method is illustrated by several examples with computer simulations.
4 citations
TL;DR: The main aim of this research work is the development and validation of a model, based on a numerical method, and its relevant simulation software, to solve the differential equations governing the drying process of gas pipelines.
Abstract: The main aim of this research work consists in the development and validation of a model, based on a numerical method, and its relevant simulation software, to solve the differential equations governing the drying process of gas pipelines. The knowledge of this phenomenon represents the key factor for performing effective pre-commissioning activities in petrochemical industry; in order to avoid hydrate formation and pipe corrosion, it is in fact necessary to achieve an effective removal of all water prior the introduction of hydrocarbon gas. This is normally achieved by performing a bulk dewatering operation, followed by a drying operation which efficiency is dependent on the air flow rate, air pressure and temperature. In this paper, the model implemented in a finite volume-based simulation software, as well as the considerations that have been made for its development, is presented. Its predictions are compared with available air drying field data of two existing gas pipeline systems.
3 citations
TL;DR: An asymptotic analysis of European and American call options in a jump-diffusion model for a single-asset market, where the jump size follows a binomial distribution, and the volatility is small compared to the drift terms.
Abstract: In this paper, we provide an asymptotic analysis of European and American call options in a jump-diffusion model for a single-asset market, where the jump size follows a binomial distribution $\cal B$(n, p) for n ≥ 1 and p ∈]0, 1[, and the volatility is small compared to the drift terms. An asymptotic formula for the perpetual call option for small volatility is also developed. It is showed that at leading order, the American call option, behaves in the same manner as a perpetual call, except in a boundary layer about the option’s expiry date. Next, we apply the obtained asymptotic results to approximate the same options in the Merton’s model. Precisely, we approximate the jump size normal distribution by a discrete binomial one for large number n, on the basis of the central limit theorem. Then, we use for small volatility, the binomial asymptotic expansion formulas to approximate European and American call prices, in the Merton’s model. Finally, the found expansion formulas for call prices are illustrat...
3 citations
TL;DR: Considering two kinds of mutation operator in generating neighbourhood solution makes the SA as an efficient approach to solve large size FLP problems as well as the NP-hardness of the problem.
Abstract: In this article, a facility location problem (FLP) is considered by the possibility of duplications for each machine type in the presence of alternative processing routes for each product. The objective of this study is to minimise the total distance that is travelled by the products. According to the NP-hardness of the problem, a simulated annealing (SA) is proposed to solve the FLP. Considering two kinds of mutation operator in generating neighbourhood solution makes the SA as an efficient approach to solve large size FLP problems.
3 citations
TL;DR: Evaluation of the main variables for wear during hot strip rolling, where the backup rolls receive the primary loads, and establishes a mathematical model to enable prediction of its wear behaviour from changes in these variable values along with an initial experimental validation for the generated model.
Abstract: Manufacturing line core mills in steel production for hot strip rolling shape steel and provide its characteristic sheet properties. A tandem mill is one of these configurations which restricts the strip thickness and removes the surface layer or scale. It is feasible to implement a mathematical model to enable prediction of the used backup roll behaviour during this production line phase. This article consists of the evaluation of the main variables for wear during hot strip rolling, where the backup rolls receive the primary loads, and establishes a mathematical model to enable prediction of its wear behaviour from changes in these variable values along with an initial experimental validation for the generated model. This validated model allows the prediction of information which is needed for making decisions about the manufacturing and business process. This can improve production work continuity and lower maintenance costs by guiding the decisions on preventive maintenance, roll stand rotations, and replacement to prevent failures which can affect production quality and throughput.
TL;DR: The optimality system is transformed into a biharmonic equation in the space-time domain and the convection dominated state and adjoint equations are stabilised using the streamline upwind/Petrov Galerkin (SUPG) method.
Abstract: We study the boundary control problem governed by diffusion-convection-reaction equations with and without control constraints. The optimality system is transformed into a biharmonic equation in the space-time domain. The system is then discretised in space and time simultaneously and solved by an equation-based finite element package. The convection dominated state and adjoint equations are stabilised using the streamline upwind/Petrov Galerkin (SUPG) method. Numerical results for Robin type boundary conditions are presented with and without stabilisation.
TL;DR: A numerical approach combining the use of the least squares method and the genetic algorithm (sequential and multi-core parallelisation approach) is proposed for the determination of temperature in an inverse hyperbolic heat conduction problem (IHHCP).
Abstract: In this paper, a numerical approach combining the use of the least squares method and the genetic algorithm (sequential and multi-core parallelisation approach) is proposed for the determination of temperature in an inverse hyperbolic heat conduction problem (IHHCP). Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that an excellent estimation can be obtained by implementation sequential genetic algorithm within a CPU with clock speed 2.4 GHz, and parallel genetic algorithm within a 16-core CPU with clock speed 2.4 GHz for each core.
TL;DR: The comparison of the results of a new proposed variational Pade technique for analysing large-amplitude free vibrations of cantilever beams carrying a lumped mass and rotary inertia, with those of other conventional methods ensures the excellent accuracy of the proposed method.
Abstract: In this study, a new method based on the variational iteration method and the Pade approximation is introduced to obtain accurate analytical solutions for some special types of non-linear differential equations, arising in modelling the dynamic behaviour of oscillators with inertia together with cubic stiffness non-linearities. The comparison of the results of a new proposed variational Pade technique for analysing large-amplitude free vibrations of cantilever beams carrying a lumped mass and rotary inertia, with those of other conventional methods, ensures the excellent accuracy of the proposed method.
TL;DR: A three layer neural network with feed forward topology and back propagation algorithm is considered as a basic neural network model and the process of finding the best combination of theses optimisation parameters, based on firefly algorithm, is presented.
Abstract: Selection of a proper neural network structure is a complicated work that is often done through the trial-and-error method. In this research, a three layer neural network with feed forward topology and back propagation algorithm is considered as a basic neural network model. The number of neurons in hidden layer, the activation function, the training algorithm and the normalisation procedure are considered as the parameters of the optimisation problem. A proper fitness function is defined and the process of finding the best combination of theses optimisation parameters, based on firefly algorithm, is presented. The proposed procedure is used to find an optimised neural network to predict the elongation of API X65 pipeline steel. The optimised neural network is used to investigate the effects of Ni and microalloying elements on the elongation of the tested steel. The results are in general agreement with the other published works.
TL;DR: As the value of the prey refuge constant is increased, the stripe like patterns breaks down and ultimately form spotted like patterns, revealing the typical dynamics of population density variation is the formation of isolated groups.
Abstract: In this paper, a spatial predator-prey system with Beddington-DeAngelis functional response and the modified Leslie-Gower type dynamics incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is considered. The qualitative properties, including the persistence property, local and global asymptotic stability of the unique positive homogeneous steady state are discussed. Furthermore, a series of numerical simulations are performed and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both. The results indicate that the effect of the prey refuge for pattern formation is remarkable. More specifically, as the value of the prey refuge constant is increased, the stripe like patterns breaks down and ultimately form spotted like patterns.
TL;DR: A numerical scheme for obtaining approximate solutions of optimal control problems governed by Schrodinger equations by considering a partition of the control space, and using an evolutionary algorithm, approximate optimal control is obtained as a piecewise linear function.
Abstract: In this paper, a numerical scheme for obtaining approximate solutions of optimal control problems governed by Schrodinger equations is presented. In this method, by considering a partition of the control space, discrete form of the problem is converted to a quasi assignment problem. Then using an evolutionary algorithm, approximate optimal control is obtained as a piecewise linear function. The comparison between the numerical solution and the exact solution for the test cases shows the good accuracy of the presented method.
TL;DR: The methods developed here are founded in Bayesian model averaging techniques and provide a practically and conceptually desirable way of accommodating behavioural model uncertainty in structural estimation in structural oligopoly models.
Abstract: The focus of this paper is on developing a methodology for dealing with behavioural model uncertainty in structural oligopoly models. It is well recognised that being an essential part of the identification strategy, the particular choice of a behavioural model embodies a highly influential, yet largely arbitrary, set of assumptions in the structural framework. The methods developed here are founded in Bayesian model averaging techniques and provide a practically and conceptually desirable way of accommodating behavioural model uncertainty in structural estimation. Moreover, a substantial feature of this approach is that it yields straightforward model comparison through the model posterior distribution. These methods are applied to estimate the parameters of the industry demand curve and firms' cost functions in oligopoly markets (e.g., marginal costs, markups, etc.). Three models of oligopoly behaviour are considered: one non-cooperative and two variations of cooperative with unobserved demand shocks. The specific industry analysed is the 1800s railroad cartel, commonly known as the Joint Executive Committee, which is widely familiar to industrial organisations economists. The results indicate that the algorithm performs quite well in correctly identifying cooperative behaviour, in additional to offering a clear view of the way in which model averaging resolves conflicts in inference arising from competing behavioural models.
TL;DR: This work compares optimisation methods of Newton and quasi-Newton type that use the fully converged state and derivative with an alternating algorithm that performs a parameter update already after a few steps of the state and derivatives iterations and shows that the alternating algorithm is able to produce the mentioned fast optimisation results.
Abstract: We show an exemplary optimisation problem for a fluid flow where a numerical optimisation run can be as fast as and even faster than a pure simulation. In this example, the optimisation parameter is the upper boundary value in a two-dimensional driven cavity flow, mathematically described by the stationary incompressible Navier-Stokes equations. The stationary solution of the equations is computed by pseudo-time stepping, i.e., by running a transient solver into a steady state, using additional inner pressure correction steps. We compare optimisation methods of Newton and quasi-Newton type that use the fully converged state and derivative with an alternating algorithm that performs a parameter update already after a few steps of the state and derivative iterations. All derivatives are computed via automatic differentiation. The alternating algorithm is able to produce the mentioned fast optimisation results. A second example configuration shows that this phenomenon is problem-dependent and cannot be generalised.
TL;DR: In this paper, sufficient conditions are derived to guarantee a class of stochastic Cohen-Grossberg neural networks with multiple time-varying delays to be globally exponential stability by using linear matrix inequality (LMI) approach.
Abstract: In this paper, together with some Lyapunov functionals and effective mathematical techniques, sufficient conditions are derived to guarantee a class of stochastic Cohen-Grossberg neural networks with multiple time-varying delays to be globally exponential stability by using linear matrix inequality (LMI) approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method by using MATLAB LMI toolbox.
TL;DR: The implementation of derivative-free optimisation method to determine feasible air pollution control policy is presented and four cases to investigate how to effectively control air quality are provided.
Abstract: Management decisions involving the locations of industrial pollution sources and remediation often depend on optimisation techniques to obtain an effective air quality control strategy. This paper presents the implementation of derivative-free optimisation method to determine feasible air pollution control policy. The gaseous pollutants and fine particulate pollutants in the air will be numerically investigated separately. The locations of industrial pollutant sources and pollutant emission reduction percentage for five chemical plants are chosen as the decision variables. Lastly, we provide four cases to investigate how to effectively control air quality.