The optimal combination: Grammatical swarm,particle swarm optimization and neural networks

Social behaviour is mainly based on swarm colonies, in which each individual shares its knowledge about the environment with other individuals to get optimal solutions. Such co-operative model differs from competitive models in the way that individuals die and are born by combining information of alive ones. This paper presents the particle swarm optimization with differential evolution algorithm in order to train a neural network instead the classic back propagation algorithm. The performance of a neural network for particular problems is critically dependant on the choice of the processing elements, the net architecture and the learning algorithm. This work is focused in the development of methods for the evolutionary design of artificial neural networks. This paper focuses in optimizing the topology and structure of connectivity for these networks.     

MATHEMATICAL ANALYSIS OF SOME NEURAL NETWORKS FOR SOLVING LINEAR AND QUADRATIC PROGRAMMING

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CFD modeling and multi-objective optimization of cyclone geometry using desirability function,artificial neural networks and genetic algorithms

The low-mass loading gas cyclone separator has two performance parameters, the pressure drop and the collection efficiency (cut-off diameter). In this paper, a multi-objective optimization study of a gas cyclone separator has been performed using the response surface methodology (RSM) and CFD data. The effects of the inlet height, the inlet width, the vortex finder diameter and the cyclone total height on the cyclone performance have been investigated. The analysis of design of experiment shows a strong interaction between the inlet dimensions and the vortex finder diameter. No interaction between the cyclone height and the other three factors was observed. The desirability function approach has been used for the multi-objective optimization. A new set of geometrical ratios (design) has been obtained to achieve the best performance. A numerical comparison between the new design and the Stairmand design confirms the superior performance of the new design. As an alternative approach for applying RSM as a meta-model, two radial basis function neural networks (RBFNNs) have been used. Furthermore, the genetic algorithms technique has been used instead of the desirability function approach. A multi-objective optimization study using NSGA-II technique has been performed to obtain the Pareto front for the best performance cyclone separator.     

Mathematical modeling and performance analysis of combed yarn production system: Based on few data

The paper describes the availability of combed sliver production system, a part of yarn production plant. The units under study are specialized single purpose machines. Performance analysis of the system is carried out to identify the key factors. The optimum value of ‘r’, where ‘r’ represent the number of repairman to repair the twelve carding machines (r ? 12), is calculated to maximizing the steady state availability of the system. The problem is formulated using probability consideration and supplementary variable technique. Probability considerations at various stages give differential-difference equations, which are solved using Lagrange method to obtain the state probabilities. The numerical analysis carried out helps in increasing the production rate by controlling the factors affecting the system i.e. availability optimization.     

International financial networks with intermediation: modeling,analysis, and computations

In this paper, we develop a framework for the modeling, analysis, and computation of solutions to international financial networks with intermediation. We consider three tiers of decision-makers consisting of: source agents in different countries, financial intermediaries, and consumers associated with the demand markets for different products in distinct currencies and countries. We model the behavior of the decision-makers, derive the equilibrium conditions, and establish the variational inequality formulation. We then utilize the variational inequality formulation to obtain qualitative properties of the equilibrium financial flow and price pattern as well as to propose an algorithm along with convergence results. Numerical examples are presented to illustrate both the model and the computational procedure. This research extends the recent results surrounding the modeling of financial networks with intermediation to the international dimension.Revised: January 2003, AMS Classification: 90, 91     

Global asymptotic stability analysis for integro-differential systems modeling neural networks with delays

In this paper, the global asymptotic stability of the equilibrium point of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global asymptotic stability. The results have shown to improve the previous global asymptotic stability results derived in the literature. Some examples are given to illustrate the correctness of our results.     

Structural optimization by wavelet transforms and neural networks

An efficient methodology is presented to achieve optimal design of structures for earthquake loading. In this methodology a combination of wavelet transforms, neural networks and evolutionary algorithms are employed. The stochastic nature of the evolutionary algorithms makes the slow convergence. Specially, when earthquake induced loads are taken into account. To reduce the computational burden, a discrete wavelet transform is used by means of which the number of points in the earthquake record is decreased. Then, by using a surrogate model, the dynamic responses of the structures are predicted. In order to investigate the efficiency of the proposed methodology, two structures are designed for optimal weight. The numerical results demonstrate the computational advantages of the proposed hybrid methodology to optimal dynamic design of structures.     

Derivative-free optimization and neural networks for robust regression

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.     

Performance modeling of heterogeneous data networks

A heterogeneous data network consists of Local Area Networks (LANs) interconnected with either leased lines, packet-switched networks, Metropolitan Area Networks (MANs), or combinations thereof. Heterogeneous networks are characterized by bursty traffic, nested segmentation and reassembly of packets, window flow control and round-robin channel access. We develop a performance methodology for estimating user perceived delay and buffer overflow in heterogeneous data networks. The methodology is based on well-known two-moment approximation schemes. Modifications of these schemes are proposed in order to model the bandwidth allocation policies of the MANs and to capture the burstiness of the traffic. The methodology is applied to several LAN-MAN and LAN-MAN-WAN network examples.Supported partially through AT&T Grant No. 5-20491 and partially through NSF Grant No. NCR-8914447.     

Performance modeling and optimization of networks of bridged LANs

An internetwork of LANs is modeled as a graph with LAN segments as edges and transparent bridges and repeaters as nodes. The graph model leads to a simple expression for the effective load on an arbitrary LAN segment, which takes into account the overhead traffic due to the learning mechanism of the transparent bridges. Simplifying assumptions for the operation of the MAC layer protocol lead to a simple expression for the average end-to-end delay in terms of the effective loads on the LAN segments.The problem of optimally locating bridges and repeaters on the nodes in order to minimize the average delay is then studied. It is shown that this problem is equivalent to the set partitioning problem, which is NP-complete, but for which good algorithms exist to solve large problems. The related problem of minimizing cost subject to a constraint on average end-to-end delay is also discussed. Finally, the problem of locating bridges and repeaters on a linear topology, as typically found in an office building with a large number of floors, is studied. This special case gives rise to anO(L ²) algorithm, whereL is the number of floors.Supported partially through AT&T grant 5-23690.     

Surrogate optimization of deep neural networks for groundwater predictions

Sustainable management of groundwater resources under changing climatic conditions require an application of reliable and accurate predictions of groundwater levels. Mechanistic multi-scale, multi-physics simulation models are often too hard to use for this purpose, especially for groundwater managers who do not have access to the complex compute resources and data. Therefore, we analyzed the applicability and performance of four modern deep learning computational models for predictions of groundwater levels. We compare three methods for optimizing the models’ hyperparameters, including two surrogate model-based algorithms and a random sampling method. The models were tested using predictions of the groundwater level in Butte County, California, USA, taking into account the temporal variability of streamflow, precipitation, and ambient temperature. Our numerical study shows that the optimization of the hyperparameters can lead to reasonably accurate performance of all models (root mean squared errors of groundwater predictions of 2 meters or less), but the “simplest” network, namely a multilayer perceptron (MLP) performs overall better for learning and predicting groundwater data than the more advanced long short-term memory or convolutional neural networks in terms of prediction accuracy and time-to-solution, making the MLP a suitable candidate for groundwater prediction.

     

Combining modeling,simulation, optimization and analysis under a unique framework

The virtual engineering design process is based on several phases and every phase is supported by special concepts, representations and tools. This process is complex and the transition and communication between phases is difficult because of conversions and transformations. Embodiment is the phase, which more time requires, in order to produce a definitive layout from the concept, hence, we are designing and developing a unique framework where the embodiment phase can be performed, integrated and combined without transformations and conversions. This approach will support the engineers with advanced techniques on modeling meshes, conceptual simulations and real time optimization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and efficient optimization methods for the distance-dependent rearrangement clustering problem

In this article we present a computational study for solving the distance-dependent rearrangement clustering problem using mixed-integer linear programming (MILP). To address sparse data sets, we present an objective function for evaluating the pair-wise interactions between two elements as a function of the distance between them in the final ordering. The physical permutations of the rows and columns of the data matrix can be modeled using mixed-integer linear programming and we present three models based on (1) the relative ordering of elements, (2) the assignment of elements to a final position, and (3) the assignment of a distance between a pair of elements. These models can be augmented with the use of cutting planes and heuristic methods to increase computational efficiency. The performance of the models is compared for three distinct re-ordering problems corresponding to glass transition temperature data for polymers and two drug inhibition data matrices. The results of the comparative study suggest that the assignment model is the most effective for identifying the optimal re-ordering of rows and columns of sparse data matrices.     

Perturbation analysis and optimization of queueing networks

A new time-domain-based approach is developed in this paper for the perturbation analysis of queueing networks. We show that, by observing a single sample path realization of the network trajectory, we can derive sensitivity information of the throughput of the system with respect to various parameters. This information can then be used for the optimization of queueing networks. Numerous experiments as well as analytical results demonstrating the validity of this new approach are given and discussed.     

Modeling, inference and optimization of regulatory networks based on time series data

In this survey paper, we present advances achieved during the last years in the development and use of OR, in particular, optimization methods in the new gene-environment and eco-finance networks, based on usually finite data series, with an emphasis on uncertainty in them and in the interactions of the model items. Indeed, our networks represent models in the form of time-continuous and time-discrete dynamics, whose unknown parameters we estimate under constraints on complexity and regularization by various kinds of optimization techniques, ranging from linear, mixed-integer, spline, semi-infinite and robust optimization to conic, e.g., semi-definite programming. We present different kinds of uncertainties and a new time-discretization technique, address aspects of data preprocessing and of stability, related aspects from game theory and financial mathematics, we work out structural frontiers and discuss chances for future research and OR application in our real world.     

Fuzzy regression analysis using neural networks

In this paper, we propose simple but powerful methods for fuzzy regression analysis using neural networks. Since neural networks have high capability as an approximator of nonlinear mappings, the proposed methods can be applied to more complex systems than the existing LP based methods. First we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input-output patterns. A nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks. Next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms. Nonlinear fuzzy models whose h-level sets approximately include all the given patterns can be derived. Last we show an application of the proposed methods to a real problem.     

Global analysis of planar neural networks

In this paper, the global qualitative analysis of cubic dynamical systems is established. These systems are used as learning models of planar neural networks.     

Mathematical modeling of rigid bodies motion through some non-Newtonian flows

The main novelty of this article is to reveal a weak formulation of rigid bodies motion arising from free boundaries evolution in visco-plastic flows governed by the incompressible Norton–Hoff operator with non-cylindrical coefficients. We supply the existence result of an interface between the two non-miscible fluids by the use of the non-smooth evolution theory. We prove that the fluid’s flow is converted to a rigid body when its viscosity is large enough. The established results are variants or extensions of the existing formulations.