Experimental performance of a string module in a CPC reflector cavity

The purpose of the work is to develop a cost effective semistationary CPC concentrator for a string PV-module. A novel method of using annual irradiation distribution diagram projected in a north-south vertical plane is developed. This method allows us easily to determine the optimum acceptance angle of the concentrator and the required number of annual tilts. Concentration ranges of 2-5x are investigated with corresponding acceptance angles between 5 and 15°. The concentrator should be tilted 2-6 times per year. Experiments has been performed on a string module of 10 cells connected in a series and equipped with a compound parabolic concentrator with C = 3.3X. Measurement show that the output will increase with a factor of 2-2.5 for the concentrator module, compared to a reference module without concentrator. If very cheap aluminium reflectors are used the costs for the PV-module can be decreased nearly by a factor of two.

Electricity Supply Solutions for an Educational Center in Tanzania

The aim of this study was to investigate electricity supply solutions for an educationalcenter that is being built in Chonyonyo Tanzania. Off-grid power generation solutions andfurther optimization possibilities were studied for the case.The study was done for Engineers Without Borders in Sweden. Who are working withMavuno Project on the educational center. The school is set to start operating in year 2015with 40 girl students in the beginning. The educational center will help to improve genderequality by offering high quality education in a safe environment for girls in rural area.It is important for the system to be economically and environmentally sustainable. Thearea has great potential for photovoltaic power generation. Thus PV was considered as theprimary power generation and a diesel generator as a reliable backup. The system sizeoptimization was done with HOMER. For the simulations HOMER required componentdata, weather data and load data. Common components were chose with standardproperties, the loads were based on load estimations from year 2011 and the weather datawas acquired from NASA database. The system size optimization result for this base casewas a system with 26 kW PW; 5.5 kW diesel generator, 15 kW converter and 112 T-105batteries. The initial cost of the system was 55 875 €, the total net present cost 92 121 €and the levelized cost of electricity 0.264 €/kWh.In addition three optimization possibilities were studied. First it was studied how thesystem should be designed and how it would affect the system size to have night loads(security lights) use DC and could the system then be extended in blocks. As a result it wasfound out that the system size could be decreased as the inverter losses would be avoided.Also the system extension in blocks was found to be possible. The second study was aboutinverter stacking where multiple inverters can work as one unit. This type of connectionallows only the required number of inverters to run while shutting down the excess ones.This would allow the converter-unit to run with higher efficiency and lower powerconsumption could be achieved. In future with higher loads the system could be easilyextendable by connecting more inverters either in parallel or series depending on what isneeded. Multiple inverters would also offer higher reliability than using one centralizedinverter. The third study examined how the choice of location for a centralized powergeneration affects the cable sizing for the system. As a result it was found that centralizedpower generation should be located close to high loads in order to avoid long runs of thickcables. Future loads should also be considered when choosing the location. For theeducational center the potential locations for centralized power generation were found outto be close to the school buildings and close to the dormitories.

Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

How does data quality in a network affect heuristic solutions?

To have good data quality with high complexity is often seen to be important. Intuition says that the higher accuracy and complexity the data have the better the analytic solutions becomes if it is possible to handle the increasing computing time. However, for most of the practical computational problems, high complexity data means that computational times become too long or that heuristics used to solve the problem have difficulties to reach good solutions. This is even further stressed when the size of the combinatorial problem increases. Consequently, we often need a simplified data to deal with complex combinatorial problems. In this study we stress the question of how the complexity and accuracy in a network affect the quality of the heuristic solutions for different sizes of the combinatorial problem. We evaluate this question by applying the commonly used p-median model, which is used to find optimal locations in a network of p supply points that serve n demand points. To evaluate this, we vary both the accuracy (the number of nodes) of the network and the size of the combinatorial problem (p). The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 supply points we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000 (which is aggregated from the 1.5 million nodes). To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when the accuracy in the road network increase and the combinatorial problem (low p) is simple. When the combinatorial problem is complex (large p) the improvements of increasing the accuracy in the road network are much larger. The results also show that choice of the best accuracy of the network depends on the complexity of the combinatorial (varying p) problem.