Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove

The behavior of simulated annealing in stochastic optimization

In this thesis we examine the performance of simulated annealing (SA) on various response surfaces. The main goals of the study are to evaluate the effectiveness of SA for stochastic optimization, develop modifications to SA in an attempt to improve its performance, and to evaluate whether artificially adding noise to a deterministic response surface might improve the performance of SA. SA is applied to several different response surfaces with different levels of complexity. We first experiment with two basic approaches of computing the performance measure for stochastic surfaces, constant sample size and variable sample size. We found that the constant sample size performed best. At the same time we also show that artificially adding noise may improve the performance of SA on more complex deterministic response surfaces. We develop a hybrid version of SA in which the genetic algorithm is embedded within SA. The effectiveness of the hybrid approach is not conclusive and needs further investigation. Finally, we conclude with a brief discussion on the strengths and weaknesses of the proposed method and an outline of future directions

Optimization of low-head hydropower recovery in water supply networks

Small scale hydropower is emerging as a decentralized source to satisfy local demand for electricity. The interest in micro-hydropower, which refers to installed power below 100 kW, is increasing since this is a solution with low environmental impact. Water supply systems are one of the main manmade water systems presenting potential for micro-hydropower. Although some applications already exist in adduction lines, the urban distribution networks remain unexplored. Because these are complex systems in which flows and pressure vary constantly, specific technology and installation schemes for energy recovery are lacking. This work accesses the potential for hydropower within water supply networks (WSN) and presents an arrangement of micro-turbines specially conceived for this type of installation. The arrangement is based on a novel inline turbine suitable for pressurized systems and its best location within the networks is studied. The five blade tubular propeller (5BTP), preliminarily designed in the framework of the European Project HYLOW, was further developed and tested in this work. An experimental campaign was conducted with a large range of heads and torque measurements to access its characteristic curves and to obtain hill charts. The relative positioning of the turbine-generator shaft regarding the pipe bend was modified from a downstream position to an upstream position. Efficiencies of around 60% were found. The adequate locations in WSN for micro-hydropower plants are identified using an optimization algorithm which considers both the assessment of the energy production and sizing of the main equipment and works. A concept for the implementation of the 5BTP in the field was developed, consisting of an arrangement with up to four turbines inline within a buried chamber created around an existing pipe. Two objective functions, energy production and economic value respectively, are used. A simulated annealing process is developed to optimize the location of a given number of turbines. This procedure takes into account the hourly variation of flows throughout an average year and its effect on the turbine efficiency. The optimization is achieved by considering the characteristic and efficiency curves of a turbine with different impeller diameters and simulating the annual energy production in a coupled hydraulic model. After a convergence analysis for different restrictions and numbers of installed turbines, the algorithm was applied to analyze the feasibility of the proposed arrangement in two case studies in Switzerland: a sub-grid of the city of Lausanne and the complete WSN of the city of Fribourg. In both cases, the implementation of the proposed energy recovery solution seems to be feasible. A detailed analysis of the cost breakdown revealed that the cost of additional pipe work, which are required in each layout to guarantee a by-pass supply in case of maintenance, may have an important role on the investments. Also, the pressure reduction valves locations, if they exist, are likely to be the optimal solutions. Finally, a methodology to quantify the potential for hydropower based on the excess energy in a WSN is proposed and applied to case studies. It allowed to conclude how much the proposed arrangement can extract from the networksâ energy potential. In addition, an attempt was made to produce an expedite method to estimate the energy produced with one 5BTP based on network parameters and dimensional analysis