Modeling empowered by information and communication technologies

In this article, we describe our work with mathematical modeling (MM) at different educational levels and discuss how the use of information and communication technologies (ICTs) empowered such work. Characteristics of two trends in research which have influenced our work are presented: one is a Brazilian perspective of MM, and the other is the use of ICTs in mathematics classrooms seen through the lens of the theoretical construct “humans-with-media”. We introduce some key questions regarding the notion of mathematical model and the phases of the modeling process that were paramount for us. Finally, we describe and analyze two experiences using modeling in different educational contexts, and present some evidence of the empowering role of ICTs in such contexts.     

Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization

In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed.     

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.     

An information technologies and information systems industry-based classification in small and medium-sized enterprises: An institutional view

IT/IS assimilation in organizations has been analyzed mainly by large companies, where its greatest adoption is observed. However, studies that analyze the effects IT/IS have on SMEs (small and medium-sized enterprises) have also begun to appear. The institutional theory offers an approach to understanding IT/IS diffusion and the adoption process caused by isomorphism within the institutional environment, mainly industry. One of its main postulates is the institutionalization of organizations can be an answer to the pressures that organizations receive to be similar. With the purpose of analyzing this postulate, we have identified an IT/IS adoption typology through a sample of organizations coming from main industries, using multivariant analysis. This typology has allowed us to evaluate IT/IS institutionalization in SMEs, and to analyze the explanatory potential of the institutional theory in order to evaluate IT/IS assimilation in organizations.     

High contrast microwave tomography using topology optimization techniques

Microwave tomography for medical applications leads to a difficult reconstruction problem for the dielectric properties of biological tissue due to strongly diffracting waves in combination with large dielectric contrasts. We apply the material distribution technique used for topology optimization of elastic structures in order to solve the nonlinear least-squares problem underlying the reconstruction problem. Using simulated numerical data with an approximate signal-to-noise ratio of 40 dB and geometrical a priori information on the unknown objects, we obtain good estimates of the dielectric properties corresponding to biological objects.     

Coding and restoration of information by using dynamical systems

The theory of dynamical systems is used for solving some problems of information theory. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 54, Suzdal Conference–2006, Part 2, 2008.     

Incorporating operations research techniques to evaluate information systems impact on healthcare

Over the past 4 years, the Hospice Palliative Care Network Project, co-led by the Temmy Latner Centre for Palliative Care, Mount Sinai Hospital, and the Toronto Community Care Access Centre, has been working toward developing an innovative model of home palliative care coordination and service delivery. After a successful completion of stage one involving data collection of approximately 400 variables to a common Linux database repository, the current stage of the Project is to compare various modes of care delivery and disseminate the results to internal and external evaluation stakeholders. The Temmy Latner Centre's customized Panacea Information Management System (PIMS) had been linked to the Linux repository in order to customize reports to determine the optimal model of coordination and service delivery that could serve as a template for home palliative care delivery in Ontario. The objective of this paper is to outline the development and functionality of the PIMS and to evaluate its contribution in terms of improved data quality and health outcomes; in other words, to justify the information systems investment by demonstrating the relationship between this investment and improved health system delivery and effectiveness.     

Approximately global optimization for assortment problems using piecewise linearization techniques

Recently, Li and Chang proposed an approximate model for assortment problems. Although their model is quite promising to find approximately global solution, too many 0–1 variables are required in their solution process. This paper proposes another way for solving the same problem. The proposed method uses iteratively a technique of piecewise linearization of the quadratic objective function. Numerical examples demonstrate that the proposed method is computationally more efficient than the Li and Chang method.     

Differential optimization techniques

The relationship of Snyman's dynamic method for unconstrained minimization with other methods based on solving differential systems, is investigated. A modification of the dynamic method to enhance convergence properties is proposed and theoretically analysed.     

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.     

Modeling and optimization of biomass quality variability for decision support systems in biomass supply chains

Annals of Operations Research - A feasible alternative to the production of fossil fuels is the production of biofuels. In order to minimize the costs of producing biofuels, we developed a...     

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.     

Modeling networked systems using the topologically distributed bounded rationality framework

In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer‐to‐peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real‐world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game‐theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer‐to‐peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer‐to‐peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 123–137, 2016     

Modeling circulation systems in buildings using state dependent queueing models

Circulation systems within buildings are analyzed using M/G/C/C queueing models. Congestion aspects of the traffic flow are represented by introducing state dependent service rates as a function of the number of occupants in each region of the circulation system. Analytical models for unidirectional and multi-source/single sink flows are presented. Finally, use of the queueing models to analytically determine the optimal size and capacity of the links of the circulation systems is incorporated into a series of software programs available from the authors.This material is based upon work supported by the National Science Foundation under grant #MSM-8417942 and #MSM-8715152.     

Parameter identification for nonlinear dynamical systems using Multi Harmonic Balance techniques

An usual approach to investigate nonlinear systems in the frequency domain is the application of the Harmonic Balance Method (HBM), assuming that a harmonic excitation of the system leads to a harmonic response. However, for systems where the steady state response is not just harmonic but periodic or for systems which are excited periodically, this assumption does not longer lead to satisfying results. Therefore, the Multi Harmonic Balance Method (MHBM) is utilized. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)