Programming Approach For Optimization Research Articles

Rate control for robust video transmission over burst-error wireless channels

We study the problem of rate control for transmission of video over burst-error wireless channels, i.e., channels such that errors tend to occur in clusters during fading periods. In particular we consider a scenario consisting of packet based transmission with automatic repeat request (ARQ) error control and a back channel. We start by showing how the delay constraints in real time video transmission can be translated into rate constraints at the encoder, where the applicable rate constraints at a given time depend on future channel rates. With the acknowledgments received through the back channel we have an estimate of the current channel state. This information, combined with an a priori model of the channel, allows us to statistically model the future channel rates. Thus the rate constraints at the encoder can be expressed in terms of the expected channel behavior. We can then formalize a rate distortion optimization problem, namely, that of assigning quantizers to each of the video blocks stored in the encoder buffer such that the quality of the received video is maximized. This requires that the rate constraints be included in the optimization, since violating a rate constraint is equivalent to violating a delay constraint and thus results in losing a video block. We formalize two possible approaches. The first one seeks to minimize the distortion for the expected rate constraints given the channel model and current observation. The second approach seeks to allocate bits so as to minimize the expected distortion for the given model. We use both dynamic programming and Lagrangian optimization approaches to solve these problems. Our simulation results demonstrate that both the video distortion at the decoder and packet loss rate can be significantly reduced when incorporating the channel information provided by the feedback channel and the a priori model into the rate control algorithm.

The MINLP optimization approach to structural synthesis. Part I: A general view on simultaneous topology and parameter optimization

This paper presents the Mixed-Integer Non-linear Programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization. Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach. As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. © 1998 John Wiley & Sons, Ltd.

Chemical mass transfer in magmatic processes

Thermodynamic and mathematical relations are presented to facilitate the description of an algorithm for the calculation of chemical mass transfer in magmatic systems. This algorithm extends the silicate liquid solution model of Ghiorso et al. (1983) to allow for the quantitative modelling of natural magmatic processes such as crystal fractionation, equilibrium crystallization, magma mixing and solid-phase assimilation. The algorithm incorporates a new method for determining the saturation surface of a non-ideal multicomponent solid-solution crystallizing from a melt. It utilizes a mathematical programming (optimization) approach to determine the stable heterogeneous (solids+liquid) equilibrium phase assemblage at a particular temperature and pressure in magmatic systems both closed and open to oxygen. Closed system equilibria are computed by direct minimization of the Gibbs free energy of the system. Open system equilibria are determined by minimization of the Korzhinskii potential (Thompson 1970), where oxygen is treated as a perfectly mobile component. Magmatic systems undergoing chemical mass transfer processes are modelled in a series of discrete steps in temperature, pressure or bulk composition, with each step characterized by heterogeneous solid-liquid equilibrium. A numerical implementation of the algorithm has been developed (in the form of a FORTRAN 77 computer program) and calculations demonstrating its utility are provided in an accompanying paper (Ghiorso and Carmichael 1985).