Search results for: Discrete stochastic optimization

Authors: Pham Van Nha, Le Cam Binh

Abstract:

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

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Authors: Mikhail Vladimirovich Deryabin, Morten Willatzen

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In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.

Keywords: cylindrical quantum dots, electronic eigen energies, red and white Gaussian noise, ensemble averaging effects.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai

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One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

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Authors: Banaz Omer Rasheed, Parexan M. Aljaff

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In this paper, a wide band gain–flattened discrete Raman amplifiers utilizing four optimum pump wavelengths is demonstrated.

Keywords: Fiber Raman Amplifiers, Optimization, WaveLength Division Multiplexing.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: Gamal Abd El-Nasser A. Said, El-Sayed M. El-Horbaty

Abstract:

Container handling problems at container terminals are NP-hard problems. This paper presents an approach using discrete-event simulation modeling to optimize solution for storage space allocation problem, taking into account all various interrelated container terminal handling activities. The proposed approach is applied on a real case study data of container terminal at Alexandria port. The computational results show the effectiveness of the proposed model for optimization of storage space allocation in container terminal where 54% reduction in containers handling time in port is achieved.

Keywords: Container terminal, discrete-event simulation, optimization, storage space allocation.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: J. Levendovszky, I. Koncz, P. Boros

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The paper is concerned with developing stochastic delay mechanisms for efficient multicast protocols and for smooth mobile handover processes which are capable of preserving a given Quality of Service (QoS). In both applications the participating entities (receiver nodes or subscribers) sample a stochastic timer and generate load after a random delay. In this way, the load on the networking resources is evenly distributed which helps to maintain QoS communication. The optimal timer distributions have been sought in different p.d.f. families (e.g. exponential, power law and radial basis function) and the optimal parameter have been found in a recursive manner. Detailed simulations have demonstrated the improvement in performance both in the case of multicast and mobile handover applications.

Keywords: Multicast communication, stochactic delay mechanisms.

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Authors: Amel Abdoullah Ahmed Dghais, Mohd Tahir Ismail

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In this paper the core objective is to apply discrete wavelet transform and maximal overlap discrete wavelet transform functions namely Haar, Daubechies2, Symmlet4, Coiflet2 and discrete approximation of the Meyer wavelets in non stationary financial time series data from Dow Jones index (DJIA30) of US stock market. The data consists of 2048 daily data of closing index from December 17, 2004 to October 23, 2012. Unit root test affirms that the data is non stationary in the level. A comparison between the results to transform non stationary data to stationary data using aforesaid transforms is given which clearly shows that the decomposition stock market index by discrete wavelet transform is better than maximal overlap discrete wavelet transform for original data.

Keywords: Discrete wavelet transform, maximal overlap discrete wavelet transform, stationarity, autocorrelation function.

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Authors: Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad

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A new stochastic algorithm called Probabilistic Global Search Johor (PGSJ) has recently been established for global optimization of nonconvex real valued problems on finite dimensional Euclidean space. In this paper we present convergence guarantee for this algorithm in probabilistic sense without imposing any more condition. Then, we jointly utilize this algorithm along with control parameterization technique for the solution of constrained optimal control problem. The numerical simulations are also included to illustrate the efficiency and effectiveness of the PGSJ algorithm in the solution of control problems.

Keywords: Optimal Control Problem, Constraints, Direct Methods, Stochastic Algorithm

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Authors: Mohammad Mahdi Paydar, Armin Cheraghalipour, Mostafa Hajiaghaei-Keshteli

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Nowadays, in advanced countries, agriculture as one of the most significant sectors of the economy, plays an important role in its political and economic independence. Due to farmers' lack of information about products' demand and lack of proper planning for harvest time, annually the considerable amount of products is corrupted. Besides, in this paper, we attempt to improve these unfavorable conditions via designing an effective supply chain network that tries to minimize total costs of agricultural products along with minimizing shortage in demand points. To validate the proposed model, a stochastic optimization approach by using a branch and bound solver of the LINGO software is utilized. Furthermore, to accumulate the data of parameters, a case study in Mazandaran province placed in the north of Iran has been applied. Finally, using ɛ-constraint approach, a Pareto front is obtained and one of its Pareto solutions as best solution is selected. Then, related results of this solution are explained. Finally, conclusions and suggestions for the future research are presented.

Keywords: Perishable products, stochastic optimization, agricultural supply chain, ɛ-constraint.

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Authors: Serap Akcan, Ali Kokangul

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We consider a single-echelon, single-item inventory system where both demand and lead-time are stochastic. Continuous review policy is used to control the inventory system. The objective is to calculate the reorder point level under stochastic parameters. A case study is presented in Neonatal Intensive Care Unit.

Keywords: Inventory control system, reorder point level, stochastic demand, stochastic lead time

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Authors: Ejaz Khan, Conor Heneghan

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In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). In this paper we change the cost function proposed in [1] to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Keywords: Equalizer, target impulse response, convex optimization, matrix inequality.

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Authors: S. N. Deepa, G. Sugumaran

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This paper proposes the novel model order formulation scheme to design a discrete PID controller for higher order linear time invariant discrete systems. Modified PSO (MPSO) based model order formulation technique has used to obtain the successful formulated second order system. PID controller is tuned to meet the desired performance specification by using pole-zero cancellation and proposed design procedures. Proposed PID controller is attached with both higher order system and formulated second order system. System specifications are tabulated and closed loop response is observed for stabilization process. The proposed method is illustrated through numerical examples from literature.

Keywords: Discrete PID controller, Model Order Formulation, Modified Particle Swarm Optimization, Pole-Zero Cancellation

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Authors: F. Alborzi, H. Vafaei, M.H. Gholami, M.M. S. Esfahani

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In this article, the design of a Supply Chain Network (SCN) consisting of several suppliers, production plants, distribution centers and retailers, is considered. Demands of retailers are considered stochastic parameters, so we generate amounts of data via simulation to extract a few demand scenarios. Then a mixed integer two-stage programming model is developed to optimize simultaneously two objectives: (1) minimization the fixed and variable cost, (2) maximization the service level. A weighting method is utilized to solve this two objective problem and a numerical example is made to show the performance of the model.

Keywords: Mixed Integer Programming, Multi-objective Optimization, Stochastic Demand, Supply Chain Design, Two Stage Programming

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Authors: Abdolsalam Ghaderi

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In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

Abstract:

Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: Diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion equation, trends functions, bi-parameters Weibull density function.

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Authors: S. K. Tomar, R. Prasad, S. Panda, C. Ardil

Abstract:

Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Discrete System, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation, Particle Swarm Optimization, Integral Squared Error.

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Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

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This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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Authors: Toshihiko Matsuka, James E. Corter

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Most neural network (NN) models of human category learning use a gradient-based learning method, which assumes that locally-optimal changes are made to model parameters on each learning trial. This method tends to under predict variability in individual-level cognitive processes. In addition many recent models of human category learning have been criticized for not being able to replicate rapid changes in categorization accuracy and attention processes observed in empirical studies. In this paper we introduce stochastic learning algorithms for NN models of human category learning and show that use of the algorithms can result in (a) rapid changes in accuracy and attention allocation, and (b) different learning trajectories and more realistic variability at the individual-level.

Keywords: category learning, cognitive modeling, radial basis function, stochastic optimization.

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Authors: Sandeep Singh Gill, Rajeevan Chandel, Ashwani Chandel

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This paper presents a comparative study of Ant Colony and Genetic Algorithms for VLSI circuit bi-partitioning. Ant colony optimization is an optimization method based on behaviour of social insects [27] whereas Genetic algorithm is an evolutionary optimization technique based on Darwinian Theory of natural evolution and its concept of survival of the fittest [19]. Both the methods are stochastic in nature and have been successfully applied to solve many Non Polynomial hard problems. Results obtained show that Genetic algorithms out perform Ant Colony optimization technique when tested on the VLSI circuit bi-partitioning problem.

Keywords: Partitioning, genetic algorithm, ant colony optimization, non-polynomial hard, netlist, mutation.

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Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

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Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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Authors: T. T. Manikandan, Rajeev Sukumaran

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Coral Reefs are very important for the majority of marine ecosystems. But, such vital species are under major threat due to the factors such as ocean acidification, overfishing, and coral bleaching. To conserve the coral reefs, reef restoration activities are carried out across the world. After reef restoration, various parameters have to be monitored in order to ensure the overall effectiveness of the reef restoration. Underwater Wireless Sensor Network (UWSN) based  monitoring is widely adopted for such long monitoring activities. Since monitoring of coral reef restoration activities is time sensitive, the QoS guarantee offered by the network with respect to delay is vital. So this research focuses on the analytical modeling of network layer delay using Stochastic Network Calculus (SNC). The core focus of the proposed model will be on the analysis of stochastic dependencies between the network flow and deriving the stochastic delay bounds for the flows that traverse in tandem in UWSNs. The derived analytical bounds are evaluated for their effectiveness using discrete event simulations.

Keywords: Coral Reef Restoration, SNC, SFA, PMOO, Tandem of Queues, Delay Bound.

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Authors: Stephan Rupp, Matthias Elter, Michael Breitung, Walter Zink, Christian Küblbeck

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Camera calibration is an indispensable step for augmented reality or image guided applications where quantitative information should be derived from the images. Usually, a camera calibration is obtained by taking images of a special calibration object and extracting the image coordinates of projected calibration marks enabling the calculation of the projection from the 3d world coordinates to the 2d image coordinates. Thus such a procedure exhibits typical steps, including feature point localization in the acquired images, camera model fitting, correction of distortion introduced by the optics and finally an optimization of the model-s parameters. In this paper we propose to extend this list by further step concerning the identification of the optimal subset of images yielding the smallest overall calibration error. For this, we present a Monte Carlo based algorithm along with a deterministic extension that automatically determines the images yielding an optimal calibration. Finally, we present results proving that the calibration can be significantly improved by automated image selection.

Keywords: Camera Calibration, Discrete Optimization, Monte Carlo Method.

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Authors: Turgay Temel, John Hallam

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A recent neurospiking coding scheme for feature extraction from biosonar echoes of various plants is examined with avariety of stochastic classifiers. Feature vectors derived are employedin well-known stochastic classifiers, including nearest-neighborhood,single Gaussian and a Gaussian mixture with EM optimization.Classifiers' performances are evaluated by using cross-validation and bootstrapping techniques. It is shown that the various classifers perform equivalently and that the modified preprocessing configuration yields considerably improved results.

Keywords: Classification, neuro-spike coding, non-parametricmodel, parametric model, Gaussian mixture, EM algorithm.

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Authors: K. Thangavel, R. Rathipriya

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For the past one decade, biclustering has become popular data mining technique not only in the field of biological data analysis but also in other applications like text mining, market data analysis with high-dimensional two-way datasets. Biclustering clusters both rows and columns of a dataset simultaneously, as opposed to traditional clustering which clusters either rows or columns of a dataset. It retrieves subgroups of objects that are similar in one subgroup of variables and different in the remaining variables. Firefly Algorithm (FA) is a recently-proposed metaheuristic inspired by the collective behavior of fireflies. This paper provides a preliminary assessment of discrete version of FA (DFA) while coping with the task of mining coherent and large volume bicluster from web usage dataset. The experiments were conducted on two web usage datasets from public dataset repository whereby the performance of FA was compared with that exhibited by other population-based metaheuristic called binary Particle Swarm Optimization (PSO). The results achieved demonstrate the usefulness of DFA while tackling the biclustering problem.

Keywords: Biclustering, Binary Particle Swarm Optimization, Discrete Firefly Algorithm, Firefly Algorithm, Usage profile Web usage mining.

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Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

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There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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Authors: Fl. Loury, P. Sablonière

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In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.

Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.

Keywords: Molten Salt Storage System, Concentrated Solar Tower Power Plant, Robust Stochastic Model Predictive Control.

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