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Internet shopping optimization problem

100%
Błażewicz J., Kovalyov M., Musiał J., Urbański A., Wojciechowski A.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 2
385-390
EN
A high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.
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Genetic and combinatorial algorithms for optimal sizing and placement of active power filters

86%
Maciążek M., Grabowski D., Pasko M.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 2
269-279
EN
The paper deals with cost effective compensator placement and sizing. It becomes one of the most important problems in contemporary electrical networks, in which voltage and current waveform distortions increase year-by-year reaching or even exceeding limit values. The suppression of distortions could be carried out by means of three types of compensators, i.e., passive filters, active power filters and hybrid filters. So far, passive filters have been more popular mainly because of economic reasons, but active and hybrid filters have some advantages which should cause their wider application in the near future. Active power filter placement and sizing could be regarded as an optimization problem. A few objective functions have been proposed for this problem. In this paper we compare solutions obtained by means of combinatorial and genetic approaches. The theoretical discussion is followed by examples of active power filter placement and sizing.
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