Optimal design of spatial distribution networks

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.Comment: 6 pages, 5 figure

Waterbath Design Equipped with Temperature Distribution Monitor

Waterbath is a device used to create a constant temperature. This tool is used to incubates in microbiology analysis. Temperature is maintained according to the desired range. The heating element is controlled by the heater driver. This module is created by using Arduino Atmega 328 as a minimum system and time controller, Using a PID controller as temperature control, and using a DS18B20 sensor as a temperature sensor. The design of this study uses pre-experimental methods after only design research. The measurement results are done by comparing the module with a standard measurement instrument that produces the biggest % error in setting temperature of 37 ˚C which is equal to 1.21%, it is related to the boundary between water temperature and temperature setting too short which is affected by the DS18B20 temperature sensor reader that need time, to get a stable temperature reading. The minimum % error located at 60 ˚C, because to reach the temperature setting needs a long time so that DS18B20 the sensor reading is stable of setting temperature which is equal to 0.11%. The value % error of the timer is 3.4 % which the amount of the error is affected by the number of DS18B20 which is used and the delay from the microcontroller. Based on the results obtained this module can be used properly because still on the maximum limit error value less than 5%

Reliability-based optimal design of water distribution networks

A considerable amount of research has been carried out on the reliability analysis and optimal design of water distribution systems, and it has been reported that each of the above problems is very difficult to solve (Eiger et al. 1994; Wagner et al. 1988). The authors are therefore to be commended for their work, which directly incorporated a sophisticated probabilistic reliability model into an optimization routine. The paper had other interesting and useful aspects, which, unfortunately, will not be elaborated upon here

Adaptive estimation of High-Dimensional Signal-to-Noise Ratios

We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand the impact of not knowing the sparsity of the regression parameter and not knowing the distribution of the design on minimax estimation rates of $\eta$. Depending on the sparsity $k$ of the regression parameter, optimal estimators of $\eta$ either rely on estimating the regression parameter or are based on U-type statistics, and have minimax rates depending on $k$. In the important situation where $k$ is unknown, we build an adaptive procedure whose convergence rate simultaneously achieves the minimax risk over all $k$ up to a logarithmic loss which we prove to be non avoidable. Finally, the knowledge of the design distribution is shown to play a critical role. When the distribution of the design is unknown, consistent estimation of explained variance is indeed possible in much narrower regimes than for known design distribution

Design Optimisation of Electromagnetic Devices Using Continuum Design Sensitivity Analysis Combined with Commercial EM Software

This paper deals with two kinds of optimisation problems, relevant to the optimised source distribution and the shape optimum design, using Continuum Design Sensitivity Analysis (CDSA) in combination with standard electromagnetic (EM) software. Fast convergence and compatibility with existing EM software are the distinctive features of the proposed implementation. In order to verify the advantages and also to facilitate understanding of the method itself, two design optimisation problems have been tested: one is an MRI design problem related to finding an optimal permanent magnet distribution and the other is a pole shape design problem of a BLDC motor for reducing cogging torque, using both 2D and 3D models

Design optimisation of electromagnetic devices using continuum design sensitivity analysis combined with commercial EM software

This paper deals with two types of optimisation problems: optimised source distribution and the shape optimum design, using Continuum Design Sensitivity Analysis (CDSA) in combination with standard electromagnetic (EM) software. Fast convergence and compatibility with existing EM software are the distinctive features of the proposed implementation. In order to verify the advantages and also to facilitate understanding of the method itself, two design optimisation problems have been tested using both 2D and 3D models: the first is a MRI design problem related to finding an optimal permanent magnet distribution and the second is a pole shape design problem to reduce the cogging torque in a BLDC

Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms