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PL
Wyboru technologii realizacji domu mieszkalnego z zastosowaniem analizy wielokryterialnej dokonano, stosując do kodowania standaryzację oraz metodę Pattern. Przyjęto 3 warianty technologii realizacji budynku, a jako miary wariantów przyjęto 5 kryteriów. W przypadku poszczególnych wariantów założono 2 zestawy wag (priorytet czasu oraz ceny) oraz określono wskaźniki sumacyjne i skorygowane. Metoda pozwala na optymalny wybór rozwiązania technologicznego.
EN
The issue of choosing the technology for the construction of a residential house using multiple-criteria decision analysis, which was carried out using standardization and the Pattern method for coding. 3 variants of the building construction technology were adopted, 5 criteria were adopted as the measures of the variants. For individual variants, 2 sets of weights were assumed (priority of time and price), summative corrected indicators were defined. The method allows for the optimal selection of a technological solution.
PL
Aby poprawić rozkład naprężeń roboczych: w litych) ściankach grubościennych naczyń ciśnieniowych, przeprowadza się często proces przeprężania (autofretaż). W niniejszej pracy na podstawie analitycznego rozwiązania, określono ciśnienie przeprężania zapewniające w obciążonym zbiorniku korzystny rozkład naprężenia zastępczego na grubości ścianki. W podejściu analitycznym założono sprężysto-idealnie plastyczny model materiału płaszcza. Wykorzystano hipotezy wytężeniowe, najczęściej stosowane w obliczeniach inżynierskich. Otrzymane rozkłady naprężeń zastępczych porównano z rozkładami dla podobnych wymiarowo zbiorników litych i wielowarstwowych skurczowych. Ponadto, przeprowadzono numeryczną weryfikację rozwiązania analitycznego z uwzględnieniem rzeczywistych własności materiału i efektu Bauschingera. Przedstawiony przykład obliczeniowy ilustruje korzyści wynikające z przeprowadzenia procesu przeprężania zgodnie z podanymi zaleceniami.
EN
Autofrettage is often used to introduce advantageous residual stresses into thick-walled pressure vessels in order to enhance their pressure bearing capacity. An analytical approach based on the elastic-perfectiy plastic behaviour of the materiał is presented in the paper. The Tresca and von Mises yield criteria are applied to develop a procedurę in which the optimum autofrettage pressure is determined. The obtained equivalent stress distribution is compared with those of the solid virgin wali and of several optimum multi-layer shrink-fit vessels of comparable size. The results of the analytical approach are verified by the FEM modelling making use of the elastic-plastic analysis with the Bauschinger effect implemented. The tensile tests were carried out to determine the real mechanical properties of the materiał of the vessel. The presented example illustrates the advantages of the autofrettage technigue applied to the thick-walled cylinder.
EN
Thick-walled cylinders are widely used in various engineering applications. In an optimal design of pressurized thick-walled cylinders, an increase in the allowable internal pressure can be achieved by an autofrettage process. In the paper, analysis is carried out to develop a procedure in which the autofrettage pressure is determined analytically. The obtained equivalent stress distribution is compared with those of the conventional solid wall and of several multi-layer vessels. The results of the analytical approach are verified by FEM modelling. Tensile tests have been carried out to determine the real mechanical properties of the material of the vessel and to create a material model. The presented example illustrates the advantages of the autofrettage technique.
6
Content available remote Structure of approximate solutions for a class of optimal control systems
EN
We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states which arises in economic dynamics. To have this property means that the approximate solutions of the optimal control problems are determined mainly by an objective function, and are essentially independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property is stable under perturbations of an objective function.
EN
The purpose of our study is to present an improved grey dynamic programming model. Considering the uncertainty of information, the conception of grey dynamic programming is proposed in this paper. It also studies the programming model when the profit values are interval numbers and figure out the optimal solution by defining the superiority, inferiority and equipollence position degree. A case study is stated in the end to prove the applicability of the model. Our approach consists in treating profit value as positive interval grey number and we get the optimal strategy solution by means of defining standard interval grey number. As a result, an improved grey dynamic programming model is put forward. The algorithms of interval grey numbers and grey algebraic system of interval grey number should be improved further. The model is useful to realize optimal control in the process of uncertain manufacture such as production plan, storage, source distribution, investment and sorting problems. An algorithm based on position degree for the grey dynamic programming model is put forward.
8
Content available remote Systemy mrówkowe w zastosowaniu do rozwiązania problemu problemu komiwojażera
PL
Artykuł porusza dwa zagadnienia. Pierwsze określane jest jako problem komiwojażera popularnie nazywanego TSP (z ang. Traveling Salesman Problem), oraz systemy mrówkowe (z ang. Ant Systems) jako przedstawiciel nowatorskiego podejścia do rozwiązywania problemów optymalizacyjnych z grupy NP-trudnych. Problem TSP jest zagadnieniem optymalizacyjnym polegającym na znalezieniu drogi o najmniejszym koszcie dla wyznaczonej przez komiwojażera trasy. Systemy mrówkowe są to algorytmy wzorujące się na świece przyrody, a konkretniej na sposobie organizacji kolonii mrówek w poszukiwaniu najkrótszej drogi z mrowiska do pokarmu i z powrotem. Artykuł ma za zadanie zapoznać czytelnika z dwoma zakreślonymi powyżej zagadnieniami, zaprezentować zastosowanie systemów mrówkowych do rozwiązania TSP, zbadać efektywność algorytmów mrówkowych oraz algorytmów klasycznych w poszukiwaniu optimum dla określonych problemów TSP oraz przedstawić otrzymane wyniki wraz z wnioskami końcowymi. Dodatkową częścią artykułu są kierunki dalszych badań, jakie są podejmowane przez naukowców, przy wykorzystaniu filozofii systemów mrówkowych.
EN
The paper discusses two problems. The first one is known as the Travelling Salesman Problem (TSP), whereas the second one is defined as the Ant Systems being the representative of innovative attitude to solving optimization problems belonging to the NPhard group. The TSP problem is an optimizing issue that consists in finding the lowest cost travelling way for the route specified by the n travelling salesman. The ant systems are algorithms pattered after the nature, more specifically, after the way an ant colony is organized is order to find the shortest way from the anthill to food and back. The aim of the paper is to familiarize readers with the above two problems, to present application of ant systems to solve the TSP, to examine efficiency of ant algorithms and classical algorithms when searching for the optimum for specific TSP problems as well as to present obtained results together with final conclusions. As an additional part of this paper, the author presented further directions of research undertaken by scientists using philosophy of ant systems
9
Content available remote Optimal solution of a decision table: a rough set based software toolkit
EN
As the amount of information in the world is steadily increasing, there is a growing demand for tools to analyze information. Rough set methodology is very useful in data analysis of an information system such as in data generalization and data reduction. In this paper, we generalize the method proposed by Pawlak for reduction of a special and important class of an information system called decision table, where the attribute values are almost identical, not exactly equal. After simplification of decision table we obtain minimal solution (not necessarily unique) from a set of input data considering that they are almost equal. As the simplification of a decision table does not yield unique result, so, in general, many minimal solutions are possible and making choice of 'best' or 'optimal' solution from amongst them is not an easy task. The 'best' or 'optimal' criteria are different for different decision makers depending on their intensions. In this paper, a software toolkit (based on rough set theory) has been proposed for finding optimal solution(s) from amongst all possible minimal solutions of a decision table. As significance of attributes plays a very important role in rough set analysis, the proposed method for getting optimal solution(s) has been developed by using the measure of significance of attributes.
10
Content available remote Mathematical models in economic environmental problems
EN
The paper presents a review of mathematical models used in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources etc., with environmental models describing such phenomena like natural resources exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using e.g. such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution.
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