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1

Discrete multicriteria reliability-based optimization of spatial trusses

Jendo S., Paczkowski W. M., Silicka E.

Computer Assisted Mechanics and Engineering Sciences

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2007

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Vol. 14, No. 3

485-496

EN

The paper presents problem of discrete multicriteria optimization of two-layer regular orthogonal spatial trusses. Three criteria of evaluation are taken into account, namely: minimum of weight, maximum of reliability and maximum of stiffness of the structure. To simplify the problem, decomposition techniques are applied. The decision variables are cross-sections of the truss members. The best possible cross section is selected for each bar from a discrete catalogue. Other decision variables (coordinated variables) describe also the geometry of the structure. The multicriteria reliability-based algorithm allows for evaluating the objective functions values and then finding sets of nondominated evaluations and solutions. Reliability of the structure is expressed by the Hasofer–Lind reliability index beta.

2

A quasi-evolutionary identification attempt to modelling of steel frames

Paczkowski W. M., Badower A., Silicka E., Silicki A.

Computer Assisted Mechanics and Engineering Sciences

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2003

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Vol. 10, No. 2

211-221

EN

The work presents a process of analytical identification via a standard steel frame example. Some experimental tests are made to verify the identification process. Under controlled external loadings the values of displacements and strains are recorded and an approximate FEM-based model is formulated. The polyoptimization approach is employed to analyze that model. The compatibility criteria for comparison of theoretical and experimental models are assumed as square sums of differences between displacements and strains. The whole problem is proceeded in three cycles of evolution suggested by the authors.

3

Polioptymalizacja termorenowacji budynku mieszkalnego

Paczkowski W. M., Kęcka-Piotrowska K., Marks W.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Budownictwo

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2001

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Z. 39

303-311

PL

Przedstawiono problem zakresu termorenowacji budynku wzniesionego w latach 30-tych. Dokonano wyboru technologii docieplania i stosując metodę satysfakcji do zadania polioptymalizacji wielokryterialnej określono grubość materiału na docieplenie ścian i stropu nad piwnicą oraz rodzaj paliwa dla źródła ciepła.

EN

There have been soft and hard problem of multicriterial satisfaction analysed on a base of thermorenovation of a living house erected in 30-ies. By using a hard satisfaction method in a polyoptimization problem, the insulation technology , thickness of insulation layers for walls and ceilings and type of fuel for heating has been taken under consideration.

4

A polyoptimal catalogue of rolled profiles for a given class of spatial trusses

Badower A., Paczkowski W. M., Jendo S.

Computer Assisted Mechanics and Engineering Sciences

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2000

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Vol. 7, No. 1

103-116

EN

The purpose of this polyoptimization was to find optimal tubular cross section catalogues for the specified spatial trusses. Five different spans of trusses have been analyzed, starting from 24x24 m ending at 72x72 m, trusses supported at every other perimeter node, with loading conditions typical for roofs. Four decision variables were taken under consideration, i.e. the catalogue size t, its arrangement T in a metallurgical catalogue T_M, minimal and maximal diameters of tubular elements D_{min} and D_{max}. Two objective functions: truss mass and manufacturability of particular solutions were evaluated. For that purpose, some design, technological, and computational constraints were taken into account. For the specified spans L, different catalogues of cross sections were defined by TOPSIS method.

5

Wybrane problemy dyskretnej optymalizacji ewolucyjnej

Paczkowski W. M.

Prace Naukowe Politechniki Szczecińskiej. Instytut Inżynierii Lądowej

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1999

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Nr 544(33)

3-225

PL

W pracy przedstawiono problemy związane z formułowaniem i rozwiązywaniem zadań optymalizacji i polioptymalizacji realnych obiektów z dziedziny budownictwa - konstrukcji, produkcji materiałów i elementów, organizacji procesu budowlanego, identyfikacji modeli obliczeniowych, badań doświadczalnych. Zadanie optymalizacji sformułowano na zbiorach dyskretnych jako tzw. problem wielkich systemów. Dostosowano teorię zbioru faktów do problemu optymalizacji i na jej podstawie zaprezentowano sformułowanie zadania polioptymalizacji. Przedstawiono właściwości zmiennych decyzyjnych, parametrów zadania, obszaru dopuszczalnego, funkcji celu, zbioru ocen rozwiązań oraz wynikowych zbiorów niezdominowanych. Zestawiono 192 ogólne kryteria optymalizacji obiektów z dziedziny budownictwa: nadrzędne (14), ekonomiczne (45), konstrukcyjne (40), architektoniczne (24), technologiczne (36), funkcjonalne (12) i ekologiczne (21). Sformułowano wskazania doboru rodzajów i liczby kryteriów optymalizacji obiektów z zakresu budownictwa. Zaproponowano oryginalną, orto-diagonalną metodę optymalizacji i polioptymalizacji obiektów dyskretnych. Rozbudowanym algorytmem metody można sterować z zewnątrz lub za pomocą systemu ekspertowego, prowadząc poszukiwania w ograniczonym, lecz niekoniecznie jednospójnym obszarze dopuszczalnym. Przybliżono zagadnienia dekompozycji i koordynacji zadań polioptymalizacji. Zdefiniowano i opisano różne formy dekompozycji wektora zmiennych decyzyjnych, obszaru dopuszczalnego, wektora funkcji celu, metody i obiektu optymalizacji. Zastosowano je bezpośrednio w ewolucyjnym modelu optymalizacji. Wskazano na konieczność i możliwości stosowania dekompozycji w kształtowaniu realnych obiektów. Sformułowanie problemu optymalizacji uzupełniono o jedno- i wielokryterialne zadanie satysfakcji. Przedstawiono zalety i wady ewolucyjnego rozwiązania problemów technicznych.

EN

This work presents some aspects associated with formulation and solution of optimization and multicriteria optimization (polyoptimization) problems of real objects from the construction field - structure, materials production, management of the construction process, identification of computational models, experimental research. Problem of optimization has been formulated on discrete sets as so called large-scale systems problems. The facts set theory has been readjusted to an optimization problem and on this base multicriteria optimization problem has been formulated and presented. The characteristic of design variables, problem parameters, feasible domain, objective function, evaluation set of solution and final nondominated set have been presented. 192 general optimization criterion from the conctruction field have been specified: superior (14), economical (45), constructional (40), architectural (24), technological (36), functional (12) and ecological (21). Indication for selection of types and number of criteria of objects from construction field have been formulated. Original ortho-diagonal method of optimization and multicriteria optimization of discrete objects has been proposed. The expanded algorithm of above mentioned method can be controlled from outside or by the mean of the expert system from the limited but not necessary connected feasible domain. Problems of decomposition and coordination of the tasks of multicriterion optimization have been made more accessible. Different forms of decomposition of design variables vector, feasible domain, objective function vector, method and object of optimization, have been defined and described. They were directly used in the evolutionary optimization model. The necessity and possibility of using of decomposition in optimum design of real objects has been pointed out. Formulation of the problem of optimization has been completed with single and multiobjective satisfaction problem. The advantages and disadvantages of evolutional solutions of technical problems have been presented.

6

An application of a decomposed ortho-diagonal method to discrete polyoptimization of a hall with spatial grid structure

Paczkowski W. M., Jendo S.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 2

137-162

EN

The paper deals with application of the ortho-diagonal (O-D) method of finding the nondominated sets of solutions and evaluations for discrete polyoptimization problems. First, the (O-D) method was modified for finding minimum of a scalar function. The monotonicity property of a vector objective function is used by the (O-D) method for consecutive finding of j-th-criteria partial nondominated sets, j \in {1,2,...,J}. To find the nondominated evaluations sets the discrete neighbourhoods S of the point x_i are investigated starting from the solution x*_1 which minimizes the first objective function. In this way the consecutive nondominated solutions x*_{ND} are determined. An accuracy of solution and CPU computing time depend on the way the discrete neighbourhoods S of the point x_i in the design space are defined. The algorithm of the (O-D) method is applied to solve the discrete polyoptimization of a hall with spatial grid structure.