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1

On tangential approximations of the solution set of set-valued inclusions

Uderzo Amos

Journal of Applied Analysis

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2022

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Vol. 28, nr 1

11--33

EN

In the present paper, the problem of estimating the contingent cone to the solution set associated with certain set-valued inclusions is addressed by variational analysis methods and tools. As a main result, inner (resp. outer) approximations, which are expressed in terms of outer (resp. inner) prederivatives of the set-valued term appearing in the inclusion problem, are provided. For the analysis of inner approximations, the evidence arises that the metric increase property for set-valued mappings turns out to play a crucial role. Some of the results obtained in this context are then exploited for formulating necessary optimality conditions for constrained problems, whose feasible region is defined by a set-valued inclusion.

2

Cost Problems for Parametric Time Petri Nets

Lime Didiera, Roux Olivier H., Seidner Charlotte

Fundamenta Informaticae

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2021

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Vol. 183, nr 1-2

97--123

EN

We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for time constraints on the firing of transitions and we want to synthesise all their values such that some marking is reachable, with a cost that is either minimal or simply less than a given bound. We first prove that the mere existence of values for the parameters such that the latter property holds is undecidable. We nonetheless provide symbolic semi-algorithms for the two synthesis problems and we prove them both sound and complete when they terminate. We also show how to modify them for the case when parameter values are integers. Finally, we prove that these modified versions terminate if parameters are bounded. While this is to be expected since there are now only a finite number of possible parameter values, our algorithms are symbolic and thus avoid an explicit enumeration of all those values. Furthermore, the results are symbolic constraints representing finite unions of convex polyhedra that are easily amenable to further analysis through linear programming. We finally report on the implementation of the approach in Romeo, a software tool for the analysis of time Petri nets.

3

GIS and AHP based modeling for landfill site selection (case study: west side of Mosul city)

Faisal R. M., Ahmed M. F.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2018

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Vol. 28, No. 4

425--437

EN

The accumulation of large quantities of solid waste inside Mosul city becomes a real residential and municipal management problem. There are many reasons including the existence of unplanned dumping sites within the city boundaries, and the absence of scientific researches which applies modern techniques for selecting the optimal solid waste landfill. This study uses geographic information system (GIS) and analytic hierarchical process (AHP) which is used to extract the weights with the help of Super Decision SD software. The studied variables data can be classified according to specified processing method into two types: continuous data, and discrete data. The ranking map has been designed after multiplying each variable with its extracted weight, then the final map has been created based on the values obtained from the ranking map. The results show that the optimal landfill area is located at south west Mosul city. This study aims at building a model by using GIS to determine the optimal and potential solid waste landfill site.

4

(F, ρ)-invexity of higher order for multiobjective fractional variational problem

Kumar P., Sharma B.

Control and Cybernetics

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2018

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Vol. 47, no. 2

131--146

EN

Multiobjective fractional variational problem is considered and suﬃcient optimality conditions, characterizing eﬃciency of higher order, are obtained under the assumptions of (F,ρ)−invexity of higher order on the functionals involved. Parametric higher order dual of the above stated problem is proposed. Duality theorems are proved to relate eﬃcient solutions of higher order for primal and its dual problem using generalized class of functionals.

5

Optimizing plant's maintenance cost using strategic switching approach

Kareem B.

Research in Logistics & Production

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2013

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Vol. 3, No. 3

193--212

EN

Inadequate supply of public electricity in Nigeria has affected the productivity of many manufacturing industries. Electric generating plant is being used as a standby supplement to public electricity at outage hours. The high cost of running and maintenance of this generating plant has adversely affected the sustainability of the industry. A maintenance strategic switching approach was developed to minimize the cost of running the electric generating plant in the industries. Maintenance strategic switching and cost control parameters are preventive, repair/corrective and replacement. The maintenance cycle for each of the components served as tool for the determination of cumulative sum of maintenance cost from which the minimum cost schedule was selected. Data collected on power machinery from a water generating company was used to test the model. The least probability of failure (non-progressive deterioration) for components was recommended for adoption. There was a significant saving in maintenance cost of components under the non-progressive deterioration. In the 750 schedule, while the cost of maintenance with progressive deterioration was N149, 677, that of non-progressive, least failure probability was N75, 960.35 with savings of 49.25% over the former. Therefore, most economic schedule was 750 cycles. This scheme predicted for the organization the optimal maintenance strategy to utilize.

6

Is Minimax really an optimal strategy in games

Kościuk K.

Zeszyty Naukowe Politechniki Białostockiej. Informatyka

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2010

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Z. 6

63-75

EN

In theory, the optimal strategy for all kinds of games against an intelligent opponent is the Minimax strategy. Minimax assumes a perfectly rational opponent, who also takes optimal actions. However, in practice, most human opponents depart from rationality. In this case, the best move at any given step may not be one that is indicated by Minimax and an algorithm that takes into consideration human imperfections will perform better. In this paper, we show how modeling an opponent and subsequent modification of the Minimax strategy that takes into account that the opponent is not perfect, can improve a variant of the Tic-Tac-Toe game and and the game of Bridge. In Bridge we propose a simple model, in which we divide players into two classes: conservative and risk-seeking. We show that knowing which class the opponent belongs to improves the performance of the algorithm.

PL

Algorytmy grające w gry często używają strategii Minimax. Algorytm Minimax zakłada perfekcyjność przeciwnika, który wybiera zawsze najlepsze ruchy. Gracze jednakże mogą nie działać całkiem racjonalnie. Algorytm, który weźmie to pod uwagę może dawać lepsze wyniki niż Minimax. W pracy przedstawiono jak modelowanie gracza i modyfikacje algorytmu Minimax mogą poprawić wyniki w grze kółko-krzyżyk i w brydżu. W brydżu zaproponowany został prosty model, dzielący graczy na dwie kategorie - konserwatywny i ryzykowny. Eksperymenty pokazały, że wiedza, do której klasy graczy należy przeciwnik, poprawia działanie algorytmu.

7

Numeryczna analiza tarcz kompozytowych zbrojonych włóknami szklanymi i węglowymi w warunkach złożonego stanu obciążenia

Bieniaś J., Dębski H.

Kompozyty

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2010

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R. 10, nr 2

127-132

PL

Celem badań była analiza numeryczna struktury kompozytowej pod kątem doboru optymalnego układu warstw laminatu i uzyskania najkorzystniejszych parametrów wytrzymałościowych struktury poddanej działaniu złożonego stanu obciążenia (obciążenia rozciągającego i ścinającego). Przedmiot badań stanowiły materiały kompozytowe o osnowie Żywicy epoksydowej wzmocnione włóknami szklanymi i węglowymi (jednokierunkowe taśmy prepreg, system HexPly M12, Excel) wytworzone metodą autoklawową. Obydwa systemy kompozytowe wykorzystywane są w budowie łopat śmigłowców i charakteryzują się wysoką trwałością zmęczeniową oraz dobrymi właściwościami eksploatacyjnymi. Budowę modelu numerycznego kompozytowych tarcz oparto na technice Layup-Ply, stanowiącej jeden z podstawowych sposobów modelowania materiałów kompozytowych w programie Abaqus. Podstawę oszacowania wytrzymałości badanych struktur stanowiły kryteria: maksymalnych naprężeń, Tsai-Hilla, kryterium tensorowe Tsai-Wu oraz kryterium Azzi-Tsai-Hilla. Obliczenia numeryczne stanowiły również wstępną analizę zniszczenia materiałów kompozytowych, polegającą na ocenie modelu numerycznego pod kątem występowania obszarów, w których na skutek obciążenia zewnętrznego istnieje ryzyko uszkodzenia laminatu. Przeprowadzona analiza numeryczna kompozytowych tarcz poddanych działaniu złożonego stanu obciążenia (rozciąganie i ścinanie techniczne) wykazała dominującą wytrzymałość badanych konstrukcji na przenoszenie obciążenia rozciągającego. Na podstawie otrzymanych wyników stwierdzono wyższą wytrzymałość kompozytu zbrojonego włóknami węglowymi w porównaniu z kompozytem zbrojonym włóknami szklanymi, pomimo prawie dwukrotnie mniejszej grubości tarczy. Wykorzystanie w tym zakresie metody elementów skończonych umożliwia optymalizację struktury kompozytu oraz doboru najkorzystniejszych parametrów materiałowych już na etapie projektowania konstrukcji.

EN

Numerical analysis was a purpose of researches on a composite structure in terms of two aspects. The first was to choose optimum configuration of a layer laminate and the second was to obtain the best parameters of strength structure, which was subjected to analysis in complex load (tension and shearing loads). A subject of researches was made by composite materials by a matrix epoxy reinforcement glass and carbon fibers (unidirectional tape of pre-pregs, system HexPly M12 Excel) which was created by an autoclave technology. These two composite systems are used to build helicopter blade. They are characterised a very high stability on fatigue and good exploitation properties. The build of numerical model in composite shield was founded on a technique Layup-Ply, which was one of the basic way for modelling composite materials in a program Abaqus. Grounds for estimate to strength researches structures were criterions: Maximum Stress Criterion, Tsai-Hill's criterion, tensor criterion of Tsai-Wu's and Azzi-Tsai-Hill's criterion. Numerical calculations were an introductory analysis of failure composite materials. It was depend on judge numerical model in terms of appearance areas, in which a risk of damage laminate was existed by an effect of external loads. Numerical analysis in plates composites was carried out, where the plates were under complex loads (technical tension and shear). It was shown a dominant strength of researching construction for transfer a tension load. On the basis of receiving solutions was found a higher strength of composite which was created from carbon fibres in compare with glass fibres. The shield was nearly twice thinner. In this range using FEM is very useful and makes possible to optimality composite structure. It is easier to choose the best parameters of a material on the first step of projecting the construction.

8

Optimality and duality for nonsmooth multiobjective optimization problems with generalized V-r-invexity

Mishra S. K., Singh V., Wang S. Y., Lai K. K.

Journal of Applied Analysis

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2010

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Vol. 16, nr 1

49-58

EN

In this paper, a new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V-r-type I functions. The generalized Karush-Kuhn-Tucker sufficient optimality conditions are proved and duality theorems are established for a non-smooth multiobjective optimization problems involving K-r-type I functions with respect to the same function η.

9

Why life histories are diverse

Kozlowski Jan

Polish Journal of Ecology

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2006

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Vol. 54, nr 4

585-605

EN

Why do some animals weigh a fraction of a milligram and others many tons? Why do some animals mature after a few days and others need several years? Why do some animals grow and then reproduce without growing, while others continue growing after maturation? Why are growth curves so often well-approximated by von Bertalanffy's equation? Why do some animals produce myriads of tiny eggs and others produce only a few large offspring? Evolution of life histories is driven basically by the size-dependences of three parameters: the resource acquisition rate, metabolic rate and mortality risk. The combinations of size-dependences of this trio produce a plethora of locally optimal life histories, and even more sub-optimal strategies which must coexist with optimal ones in the real world. Additionally, selection forces differ depending on whether a population stays most of the time at equilibrium or in an expansion phase. Life history evolution cannot be understood without mathematical modelling, and optimization of life-time resource allocation is a powerful approach to that, though not the only one. Modelling outcomes from studies based on resource allocation optimization are presented here mainly as graphs.

10

Stochastic multivariable self-tuning tracker for non-Gaussian systems

Filipovic V.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 3

351-357

EN

This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker’s product is used, which allows us to represent unknown parameters in the form of vectors. For parameter estimation a stochastic approximation algorithm is employed. Using the concept of the stochastic Lyapunov function, global stability and optimality of the feedback system are established.