Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells

We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.

Developing a decision framework for the strategic sourcing of biomass

The deployment of bioenergy technologies is a key part of UK and European renewable energy policy. A key barrier to the deployment of bioenergy technologies is the management of biomass supply chains including the evaluation of suppliers and the contracting of biomass. In the undeveloped biomass for energy market buyers of biomass are faced with three major challenges during the development of new bioenergy projects. What characteristics will a certain supply of biomass have, how to evaluate biomass suppliers and which suppliers to contract with in order to provide a portfolio of suppliers that best satisfies the needs of the project and its stakeholder group whilst also satisfying crisp and non-crisp technological constraints. The problem description is taken from the situation faced by the industrial partner in this research, Express Energy Ltd. This research tackles these three areas separately then combines them to form a decision framework to assist biomass buyers with the strategic sourcing of biomass. The BioSS framework. The BioSS framework consists of three modes which mirror the development stages of bioenergy projects. BioSS.2 mode for early stage development, BioSS.3 mode for financial close stage and BioSS.Op for the operational phase of the project. BioSS is formed of a fuels library, a supplier evaluation module and an order allocation module, a Monte-Carlo analysis module is also included to evaluate the accuracy of the recommended portfolios. In each mode BioSS can recommend which suppliers should be contracted with and how much material should be purchased from each. The recommended blend should have chemical characteristics within the technological constraints of the conversion technology and also best satisfy the stakeholder group. The fuels library is made up from a wide variety of sources and contains around 100 unique descriptions of potential biomass sources that a developer may encounter. The library takes a wide data collection approach and has the aim of allowing for estimates to be made of biomass characteristics without expensive and time consuming testing. The supplier evaluation part of BioSS uses a QFD-AHP method to give importance weightings to 27 different evaluating criteria. The evaluating criteria have been compiled from interviews with stakeholders and policy and position documents and the weightings have been assigned using a mixture of workshops and expert interview. The weighted importance scores allow potential suppliers to better tailor their business offering and provides a robust framework for decision makers to better understand the requirements of the bioenergy project stakeholder groups. The order allocation part of BioSS uses a chance-constrained programming approach to assign orders of material between potential suppliers based on the chemical characteristics of those suppliers and the preference score of those suppliers. The optimisation program finds the portfolio of orders to allocate to suppliers to give the highest performance portfolio in the eyes of the stakeholder group whilst also complying with technological constraints. The technological constraints can be breached if the decision maker requires by setting the constraint as a chance-constraint. This allows a wider range of biomass sources to be procured and allows a greater overall performance to be realised than considering crisp constraints or using deterministic programming approaches. BioSS is demonstrated against two scenarios faced by UK bioenergy developers. The first is a large scale combustion power project, the second a small scale gasification project. The Bioss is applied in each mode for both scenarios and is shown to adapt the solution to the stakeholder group importance and the different constraints of the different conversion technologies whilst finding a globally optimal portfolio for stakeholder satisfaction.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

Design of a genetic algorithm for bi-objective flow shop scheduling problems with re-entrant jobs

This paper presents a simulated genetic algorithm (GA) model of scheduling the flow shop problem with re-entrant jobs. The objective of this research is to minimize the weighted tardiness and makespan. The proposed model considers that the jobs with non-identical due dates are processed on the machines in the same order. Furthermore, the re-entrant jobs are stochastic as only some jobs are required to reenter to the flow shop. The tardiness weight is adjusted once the jobs reenter to the shop. The performance of the proposed GA model is verified by a number of numerical experiments where the data come from the case company. The results show the proposed method has a higher order satisfaction rate than the current industrial practices.

A novel algorithm of posture best fit based on key characteristics for large components assembly

Measurement and variation control of geometrical Key Characteristics (KCs), such as flatness and gap of joint faces, coaxiality of cabin sections, is the crucial issue in large components assembly from the aerospace industry. Aiming to control geometrical KCs and to attain the best fit of posture, an optimization algorithm based on KCs for large components assembly is proposed. This approach regards the posture best fit, which is a key activity in Measurement Aided Assembly (MAA), as a two-phase optimal problem. In the first phase, the global measurement coordinate system of digital model and shop floor is unified with minimum error based on singular value decomposition, and the current posture of components being assembly is optimally solved in terms of minimum variation of all reference points. In the second phase, the best posture of the movable component is optimally determined by minimizing multiple KCs' variation with the constraints that every KC respectively conforms to its product specification. The optimal models and the process procedures for these two-phase optimal problems based on Particle Swarm Optimization (PSO) are proposed. In each model, every posture to be calculated is modeled as a 6 dimensional particle (three movement and three rotation parameters). Finally, an example that two cabin sections of satellite mainframe structure are being assembled is selected to verify the effectiveness of the proposed approach, models and algorithms. The experiment result shows the approach is promising and will provide a foundation for further study and application. © 2013 The Authors.