Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

Machine-Part cell formation through visual decipherable clustering of Self Organizing Map

Machine-part cell formation is used in cellular manufacturing in order to process a large variety, quality, lower work in process levels, reducing manufacturing lead-time and customer response time while retaining flexibility for new products. This paper presents a new and novel approach for obtaining machine cells and part families. In the cellular manufacturing the fundamental problem is the formation of part families and machine cells. The present paper deals with the Self Organising Map (SOM) method an unsupervised learning algorithm in Artificial Intelligence, and has been used as a visually decipherable clustering tool of machine-part cell formation. The objective of the paper is to cluster the binary machine-part matrix through visually decipherable cluster of SOM color-coding and labelling via the SOM map nodes in such a way that the part families are processed in that machine cells. The Umatrix, component plane, principal component projection, scatter plot and histogram of SOM have been reported in the present work for the successful visualization of the machine-part cell formation. Computational result with the proposed algorithm on a set of group technology problems available in the literature is also presented. The proposed SOM approach produced solutions with a grouping efficacy that is at least as good as any results earlier reported in the literature and improved the grouping efficacy for 70% of the problems and found immensely useful to both industry practitioners and researchers.Comment: 18 pages,3 table, 4 figure

A contribution to support decision making in energy/water sypply chain optimisation

The seeking of process sustainability forces enterprises to change their operations. Additionally, the industrial globalization implies a very dynamic market that, among other issues, promotes the enterprises competition. Therefore, the efficient control and use of their Key Performance Indicators, including profitability, cost reduction, demand satisfaction and environmental impact associated to the development of new products, is a significant challenge. All the above indicators can be efficiently controlled through the Supply Chain Management. Thus, companies work towards the optimization of their individual operations under competitive environments taking advantage of the flexibility provided by the virtually inexistent world market restrictions. This is achieved by the coordination of the resource flows, across all the entities and echelons belonging to the system network. Nevertheless, such coordination is significantly complicated if considering the presence of uncertainty and even more if seeking for a win-win outcome. The purpose of this thesis is extending the current decision making strategies to expedite these tasks in industrial processes. Such a contribution is based on the development of efficient mathematical models that allows coordinating large amount of information synchronizing the production and distribution tasks in terms of economic, environmental and social criteria. This thesis starts presents an overview of the requirements of sustainable production processes, describing and analyzing the current methods and tools used and identifying the most relevant open issues. All the above is always within the framework of Process System Engineering literature. The second part of this thesis is focused in stressing the current Multi-Objective solution strategies. During this part, first explores how the profitability of the Supply Chain can be enhanced by considering simultaneously multiple objectives under demand uncertainties. Particularly, solution frameworks have been proposed in which different multi-criteria decision making strategies have been combined with stochastic approaches. Furthermore, additional performance indicators (including financial and operational ones) have been included in the same solution framework to evaluate its capabilities. This framework was also applied to decentralized supply chains problems in order to explore its capabilities to produce solution that improves the performances of each one of the SC entities simultaneously. Consequently, a new generalized mathematical formulation which integrates many performance indicators in the production process within a supply chain is efficiently solved. Afterwards, the third part of the thesis extends the proposed solution framework to address the uncertainty management. Particularly, the consideration of different types and sources of uncertainty (e.g. external and internal ones) where considered, through the implementation of preventive approaches. This part also explores the use of solution strategies that efficiently selects the number of scenarios that represent the uncertainty conditions. Finally, the importance and effect of each uncertainty source over the process performance is detailed analyzed through the use of surrogate models that promote the sensitivity analysis of those uncertainties. The third part of this thesis is focused on the integration of the above multi-objective and uncertainty approaches for the optimization of a sustainable Supply Chain. Besides the integration of different solution approaches, this part also considers the integration of hierarchical decision levels, by the exploitation of mathematical models that assess the consequences of considering simultaneously design and planning decisions under centralized and decentralized Supply Chains. Finally, the last part of this thesis provides the final conclusions and further work to be developed.La globalización industrial genera un ambiente dinámico en los mercados que, entre otras cosas, promueve la competencia entre corporaciones. Por lo tanto, el uso eficiente de las los indicadores de rendimiento, incluyendo rentabilidad, satisfacción de la demanda y en general el impacto ambiental, representa un area de oportunidad importante. El control de estos indicadores tiene un efecto positivo si se combinan con la gestión de cadena de suministro. Por lo tanto, las compañías buscan definir sus operaciones para permanecer activas dentro de un ambiente competitivo, tomando en cuenta las restricciones en el mercado mundial. Lo anterior puede ser logrado mediante la coordinación de los flujos de recursos a través de todas las entidades y escalones pertenecientes a la red del sistema. Sin embargo, dicha coordinación se complica significativamente si se quiere considerar la presencia de incertidumbre, y aún más, si se busca exclusivamente un ganar-ganar. El propósito de esta tesis es extender el alcance de las estrategias de toma de decisiones con el fin de facilitar estas tareas dentro de procesos industriales. Estas contribuciones se basan en el desarrollo de modelos matemáticos eficientes que permitan coordinar grandes cantidades de información sincronizando las tareas de producción y distribución en términos económicos, ambientales y sociales. Esta tesis inicia presentando una visión global de los requerimientos de un proceso de producción sostenible, describiendo y analizando los métodos y herramientas actuales así como identificando las áreas de oportunidad más relevantes dentro del marco de ingeniería de procesos La segunda parte se enfoca en enfatizar las capacidades de las estrategias de solución multi-objetivo, durante la cual, se explora el mejoramiento de la rentabilidad de la cadena de suministro considerando múltiples objetivos bajo incertidumbres en la demanda. Particularmente, diferentes marcos de solución han sido propuestos en los que varias estrategias de toma de decisión multi-criterio han sido combinadas con aproximaciones estocásticas. Por otra parte, indicadores de rendimiento (incluyendo financiero y operacional) han sido incluidos en el mismo marco de solución para evaluar sus capacidades. Este marco fue aplicado también a problemas de cadenas de suministro descentralizados con el fin de explorar sus capacidades de producir soluciones que mejoran simultáneamente el rendimiento para cada uno de las entidades dentro de la cadena de suministro. Consecuentemente, una nueva formulación que integra varios indicadores de rendimiento en los procesos de producción fue propuesta y validada. La tercera parte de la tesis extiende el marco de solución propuesto para abordar el manejo de incertidumbres. Particularmente, la consideración de diferentes tipos y fuentes de incertidumbre (p.ej. externos e internos) fueron considerados, mediante la implementación de aproximaciones preventivas. Esta parte también explora el uso de estrategias de solución que elige eficientemente el número de escenarios necesario que representan las condiciones inciertas. Finalmente, la importancia y efecto de cada una de las fuentes de incertidumbre sobre el rendimiento del proceso es analizado en detalle mediante el uso de meta modelos que promueven el análisis de sensibilidad de dichas incertidumbres. La tercera parte de esta tesis se enfoca en la integración de las metodologías de multi-objetivo e incertidumbre anteriormente expuestas para la optimización de cadenas de suministro sostenibles. Además de la integración de diferentes métodos. Esta parte también considera la integración de diferentes niveles jerárquicos de decisión, mediante el aprovechamiento de modelos matemáticos que evalúan lasconsecuencias de considerar simultáneamente las decisiones de diseño y planeación de una cadena de suministro centralizada y descentralizada. La parte final de la tesis detalla las conclusiones y el trabajo a futuro necesario sobre esta línea de investigaciónPostprint (published version

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

DEVELOPMENT OF METHODS FOR SUPPLY MANAGEMENT IN TRANSPORTATION NETWORKS UNDER CONDITIONS OF UNCERTAINTY OF TRANSPORTATION COST VALUES

The problem of transport management in a distributed logistics system "suppliers – consumers" is considered. Under the assumption of a random nature of transportation costs, an exact algorithm for solving this problem by a probabilistic criterion has been developed. This algorithm is implemented by an iterative procedure for sequential improvement of the transportation plan. The rate of convergence of a computational procedure to an exact solution depends significantly on the dimension of the problem and is unacceptably low in real problems. In this regard, an alternative method is proposed, based on reducing the original problem to solving a nontrivial problem of fractional-nonlinear programming. A method for solving this problem has been developed and substantiated. The corresponding computational algorithm reduces the fractional-nonlinear model to the quadratic one. The resulting problem is solved by known methods. Further, the original problem is supplemented by considering a situation that is important for practice, when in the conditions of a small sample of initial data there is no possibility of obtaining adequate analytical descriptions for the distribution densities of the random costs of transportation. In this case, the available volume of statistical material is sufficient only to estimate the first two moments of unknown distribution densities. For this marginal case, a minimax method for finding the transportation plan is proposed. The first step is to solve the problem of determining the worst distribution density with the given values of the first two moments. In the second step, the transportation plan is found, which is the best in this most unfavorable situation, when the distribution densities of the random cost of transportation are the worst. To find such densities, let’s use the modern mathematical apparatus of continuous linear programmin