A Decomposition Algorithm for Nested Resource Allocation Problems

We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict convexity or differentiability is needed. The method solves a hierarchy of resource allocation subproblems, whose solutions are used to convert constraints on sums of resources into bounds for separate variables at higher levels. The resulting time complexity for the integer problem is $O(n \log m \log (B/n))$, and the complexity of obtaining an $\epsilon$-approximate solution for the continuous case is $O(n \log m \log (B/\epsilon))$, $n$ being the number of variables, $m$ the number of ascending constraints (such that $m < n$), $\epsilon$ a desired precision, and $B$ the total resource. This algorithm attains the best-known complexity when $m = n$, and improves it when $\log m = o(\log n)$. Extensive experimental analyses are conducted with four recent algorithms on various continuous problems issued from theory and practice. The proposed method achieves a higher performance than previous algorithms, addressing all problems with up to one million variables in less than one minute on a modern computer.Comment: Working Paper -- MIT, 23 page

An algorithm for the solution of non-linear optimization problems and its application in radiation protection

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Resource Management with Stochastic Recharge and Environmental Threats

Exploitation diminishes the capacity of renewable resources to with-stand environmental stress, increasing their vulnerability to extreme conditions that may trigger abrupt changes. The onset of such events depends on the coincidence of extreme environmental conditions (environmental threat) and the resource state (determining its resilience). When the former is uncertain and the latter evolves stochastically, the uncertainty regarding the event occurrence is the result of the combined effect of these two uncertain components. We analyzed optimal resource management in such a setting. Existence of an optimal stationary policy is established and long run properties are characterized. A numerical illustration based on actual data is presented.Stochastic stock dynamics, event uncertainty, Markov decision process, optimal stationary policy, Environmental Economics and Policy,

Improved Fitness Dependent Optimizer for Solving Economic Load Dispatch Problem

Economic Load Dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to Economic Load Dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness Dependent Optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness Dependent Optimizer (FDO) examines the search spaces based on the searching approach of Particle Swarm Optimization. To calculate the pace, the fitness function is utilized to generate weights that direct the search agents in the phases of exploitation and exploration. In this research, the authors have carried out Fitness Dependent Optimizer to solve the Economic Load Dispatch problem by reducing fuel cost, emission allocation, and transmission loss. Moreover, the authors have enhanced a novel variant of Fitness Dependent Optimizer, which incorporates novel population initialization techniques and dynamically employed sine maps to select the weight factor for Fitness Dependent Optimizer. The enhanced population initialization approach incorporates a quasi-random Sabol sequence to generate the initial solution in the multi-dimensional search space. A standard 24-unit system is employed for experimental evaluation with different power demands. Empirical results obtained using the enhanced variant of the Fitness Dependent Optimizer demonstrate superior performance in terms of low transmission loss, low fuel cost, and low emission allocation compared to the conventional Fitness Dependent Optimizer. The experimental study obtained 7.94E-12.Comment: 42 page

Fair and optimal resource allocation in wireless sensor networks

There is a large amount of research in wireless networks focuses on optimization of either network routing and power control alone. In contrast, this work aims at jointly optimizing the transmission power and routing path selection in order to optimize allocation of resources in interference constrained wireless environment. Moreover, we consider a multipath routing where multiple alternative paths are employed to transmit data between the end nodes. One of modern communication techniques that it applies to a network coding, though not explicitly implemented in this work. The proposed approach is first analyzed theoretically using Lagrangian optimization for a three-node scenario. We analyze this basic scenario, as it is essential for development of the overall multi-path routing schemes for multi-hop networks. The optimal solution for the three-node topology is replicated throughout the network to converge to a network-level solution. In contrast to existing studies, we explicitly consider interference from adjacent links, which varies with traffic flow thus optimizing the routing, and flow control decisions. The results and conclusions provide guidance as to the optimum routing decisions and a corresponding theoretical performance limits. The optimization of the throughput of the wireless network scenario is considered as a multi-variable optimization problem subject to flow and power constraints. Numerical analysis performed in Matlab-Simulink indicates that, given loose outage constraints, an optimal trade-off between the channel parameters renders optimum results even when the gain of the channel varies with time. The theoretical analysis and simulations demonstrate and validate that the channel capacity and efficiency are maximized when the routing decisions consider the network performance trade-offs. Next, the proposed routing and power control scheme is experimentally evaluated in hardware using universal software radio peripheral (USRP2). The USRP testbed utilizes the proposed multi-variable optimization algorithm. The communication system is implemented using GNU Radio software where the physical layer employs two direct-spread spectrum variants: (a) binary phase shift keying (DS-BPSK) and (b) orthogonal frequency division modulation (DS-OFDM) schemes. The experimental results are compared with the simulation results --Abstract, page iii

Managing server energy and reducing operational cost for online service providers

The past decade has seen the energy consumption in servers and Internet Data Centers (IDCs) skyrocket. A recent survey estimated that the worldwide spending on servers and cooling have risen to above $30 billion and is likely to exceed spending on the new server hardware . The rapid rise in energy consumption has posted a serious threat to both energy resources and the environment, which makes green computing not only worthwhile but also necessary. This dissertation intends to tackle the challenges of both reducing the energy consumption of server systems and by reducing the cost for Online Service Providers (OSPs). Two distinct subsystems account for most of IDC’s power: the server system, which accounts for 56% of the total power consumption of an IDC, and the cooling and humidifcation systems, which accounts for about 30% of the total power consumption. The server system dominates the energy consumption of an IDC, and its power draw can vary drastically with data center utilization. In this dissertation, we propose three models to achieve energy effciency in web server clusters: an energy proportional model, an optimal server allocation and frequency adjustment strategy, and a constrained Markov model. The proposed models have combined Dynamic Voltage/Frequency Scaling (DV/FS) and Vary-On, Vary-off (VOVF) mechanisms that work together for more energy savings. Meanwhile, corresponding strategies are proposed to deal with the transition overheads. We further extend server energy management to the IDC’s costs management, helping the OSPs to conserve, manage their own electricity cost, and lower the carbon emissions. We have developed an optimal energy-aware load dispatching strategy that periodically maps more requests to the locations with lower electricity prices. A carbon emission limit is placed, and the volatility of the carbon offset market is also considered. Two energy effcient strategies are applied to the server system and the cooling system respectively. With the rapid development of cloud services, we also carry out research to reduce the server energy in cloud computing environments. In this work, we propose a new live virtual machine (VM) placement scheme that can effectively map VMs to Physical Machines (PMs) with substantial energy savings in a heterogeneous server cluster. A VM/PM mapping probability matrix is constructed, in which each VM request is assigned with a probability running on PMs. The VM/PM mapping probability matrix takes into account resource limitations, VM operation overheads, server reliability as well as energy effciency. The evolution of Internet Data Centers and the increasing demands of web services raise great challenges to improve the energy effciency of IDCs. We also express several potential areas for future research in each chapter

Water-related modelling in electric power systems: WATERFLEX Exploratory Research Project: version 1

Water is needed for energy. For instance, hydropower is the technology that generates more electricity worldwide after the fossil-fuelled power plants and its production depends on water availability and variability. Additionally, thermal power plants need water for cooling and thus generate electricity. On the other hand, energy is also needed for water. Given the increase of additional hydropower potential worldwide in the coming years, the high dependence of electricity generation with fossil-fuelled power plants, and the implications of the climate change, relevant international organisations have paid attention to the water-energy nexus (or more explicitly within a power system context, the water-power nexus). The Joint Research Centre of the European Commission, the United States Department of Energy, the Institute for Advanced Sustainability Studies, the Midwest Energy Research Consortium and the Water Council, or the Organisation for Economic Co-operation and Development, among others, have raised awareness about this nexus and its analysis as an integrated system. In order to properly analyse such linkages between the power and water sectors, there is a need for appropriate modelling frameworks and mathematical approaches. This report comprises the water-constrained models in electric power systems developed within the WATERFLEX Exploratory Research Project of the European Commission’s Joint Research Centre in order to analyse the water-power interactions. All these models are deemed modules of the Dispa-SET modelling tool. The version 1 of the medium-term hydrothermal coordination module is presented with some modelling extensions, namely the incorporation of transmission network constraints, water demands, and ecological flows. Another salient feature of this version of Dispa-SET is the modelling of the stochastic medium-term hydrothermal coordination problem. The stochastic problem is solved by using an efficient scenario-based decomposition technique, the so-called Progressive Hedging algorithm. This technique is an Augmented-Lagrangian-based decomposition method that decomposes the original problem into smaller subproblems per scenario. The Progressive Hedging algorithm has multiple advantages: — It is easy parallelizable due to its inherent structure. — It provides solution stability and better computational performance compared to Benders-like decomposition techniques (node-based decomposition). — It scales better for large-scale stochastic programming problems. — It has been widely used in the technical literature, thus demonstrating its efficiency. Its implementation has been carried out through the PySP software package which is part of the Coopr open-source Python repository for optimisation. This report also describes the cooling-related constraints included in the unit commitment and dispatch module of Dispa-SET. The cooling-related constraints encompass limitations on allowable maximum water withdrawals of thermal power plants and modelling of the power produced in terms of the river water temperature of the power plant inlet. Limitations on thermal releases or water withdrawals could be imposed due to physical or policy reasons. Finally, an offline and decoupled modelling framework is presented to link such modules with the rainfall-runoff hydrological LISFLOOD model. This modelling framework is able to accurately capture the water-power interactions. Some challenges and barriers to properly address the water-power nexus are also highlighted in the report.JRC.C.7-Knowledge for the Energy Unio

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more