Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

Performance Evaluation of Different PV-Array Configurations under Weak Light Conditions and Partial Shadings

The paper analyses empirical performance data of five commercial PV-plants in Germany. The purpose was on one side to investigate the weak light performance of the different PV-modules used. On the other hand it was to quantify and compare the shading losses of different PV-array configurations. The importance of this study relies on the fact that even if the behavior under weak light conditions or the shading losses might seem to be a relatively small percentage of the total yearly output; in projects where a performance guarantee is given, these variation can make the difference between meeting or not the conditions.When analyzing the data, a high dispersion was found. To reduce the optical losses and spectral effects, a series of data filters were applied based on the angle of incidence and absolute Air Mass. To compensate for the temperature effects and translate the values to STC (25°C), five different methods were assessed. At the end, the Procedure 2 of IEC 60891 was selected due to its relative simplicity, usage of mostly standard parameters found in datasheets, good accuracy even with missing values, and its potential to improve the results when the complete set of inputs is available.After analyzing the data, the weak light performance of the modules did not show a clear superiority of a certain technology or technology group over the others. Moreover, the uncertainties in the measurements restrictive the conclusiveness of the results.In the partial shading analysis, the landscape mounting of mc-Si PV-modules in free-field showed a significantly better performance than the portrait one. The cross-table string using CIGS modules did not proved the benefits expected and performed actually poorer than a regular one-string-per-table layout. Parallel substrings with CdTe showed a proper functioning and relatively low losses. Among the two product generations of CdTe analyzed, none showed a significantly better performance under partial shadings.

COMPARISON OF PARTIAL SHADING LOSSES IN FREE FIELD PV-PLANTS WITH DIFFERENT ARRAY CONFIGURATIONS

A common problem when planning large free field PV-plants is optimizing the ground occupation ratio while maintaining low shading losses. Due to the complexity of this task, several PV-plants have been built using various configurations. In order to compare the shading losses of different PV technologies and array designs, empirical performance data of five free field PV-plants operating in Germany was analyzed. The data collected comprised 140 winter days from October 2011 until March 2012. The relative shading losses were estimated by comparing the energy output of selected arrays in the front rows (shading-free) against that of shaded arrays in the back rows of the same plant. The results showed that landscape mounting with mc-Si PV-modules yielded significantly better results than portrait one. With CIGS modules, making cross-table strings using the lower modules was not beneficial as expected and had more losses than a one-string-per-table layout. Parallel substrings with CdTe showed relatively low losses. Among the two CdTe products analyzed, none showed a significantly better performance.