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1
Content available Stability kernel in finite games with perturbed payoffs
Emelichev Vladimir, Nikulin Yury
Control and Cybernetics
|
2022
|
Vol. 51, No. 1
6--20
EN
The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.
2
Content available Assessment of the historical policy mixes for Poland using the game approach
Kruś L., Woroniecka-Leciejewicz I.
Control and Cybernetics
|
2018
|
Vol. 47, no. 3
277--300
EN
The study here presented pertains to the analysis of mutual interactions of the monetary and fiscal policies in the case of Poland. The historical policies carried out during different periods of time and their economic effects are compared with the possible strategies, obtained from the analysis of the proposed monetaryfiscal game. In the study, the methods of non-cooperative game theory are combined with macroeconomic modeling. The respective game is formulated for monetary and fiscal authorities as players. Strategies of these players refer to the respective instruments of their policies: the real interest rate and the budget deficit in relation to GDP. Payoffs include inflation and GDP growth, respectively. The payoffs are calculated using a recursive macroeconomic model estimated for the Polish economy. The model describes influences of the instruments of the monetary and fiscal policies on the state of the economy. The best response strategies, the Nash equilibria and Pareto optimality are analyzed. Changes of the policies towards the more restrictive or more expansive ones and their effects in comparison to the historically applied are discussed. This is performed for two different time periods – the time of recovery after 2004 and the time of the global financial crisis after 2008.
3
Content available Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players
Dall'Aglio M., Di Luca C., Milone L.
Operations Research and Decisions
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2017
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Vol. 27, No. 3
35--50
EN
We consider the allocation of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationship between two geometric objects of fair division: The Individual Pieces Set (IPS) and the Radon–Nykodim Set (RNS). The algorithm can be considered as an extension of the Adjusted Winner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness.
4
Content available Biogeography-inspired multiobjective optimization for helping MEMS synthesis
Di Barba P., Mognaschi M. E., Venini P., Wiak S.
Archives of Electrical Engineering
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2017
|
Vol. 66, nr 3
607--623
EN
The aim of the paper is to assess the applicability of a multi-objective biogeography- based optimisation algorithm in MEMS synthesis. In order to test the performances of the proposed method in this research field, the optimal shape design of an electrostatic micromotor, and two different electro-thermo-elastic microactuators are considered as the case studies.
5
Content available remote Metodyka wykorzystania optymalizacji wielokryterialnej do określenia postaci geometrycznej implantu ortopedycznego
Muzalewska M., Moczulski W.
Mechanik
|
2016
|
R. 89, nr 2
121--124
PL
Celem badań było opracowanie metodyki postępowania podczas wielokryterialnej optymalizacji postaci geometrycznej implantu ortopedycznego przeznaczonego do rekonstrukcji więzadła krzyżowego przedniego znajdującego się w stawie kolanowym. Implant powinien dokładnie zakotwiczać przeszczep w tunelu kostnym oraz przyspieszać wrastanie tkanki kostnej w przeszczep, tak aby mógł on przejąć rolę zerwanego więzadła. Starano się określić optymalną postać geometryczną implantu z uwzględnieniem dwóch kryteriów: wykorzystania maksymalnych własności wytrzymałościowych nieprzekraczających wartości dopuszczalnych oraz optymalnego nasączenia implantu krwią.
EN
The scientific goal of the project is multicriterial optimization of the design of an orthopedic implant responsible for supporting the reconstruction of the anterior cruciate ligament. The implant should not only precisely anchor the tendon in the tunnel but, above all – thanks to appropriately selected geometric shape and other design features – accelerate the ingrowth of bone tissue into the grafted tendon. The aim of this research is to define an optimal geometric shape of implants and to determine the impact of this geometric shape on the strength properties and the process of blood perfusion through the implant. All data would be obtained by the computer simulation and scrutiny where the input object is a virtual model describing optimum geometric shape of an implant under multicriterial optimization process for a specific set of criteria.
6
Content available remote Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices
Ábele-Nagy K., Bozóki S.
Fundamenta Informaticae
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2016
|
Vol. 144, nr 3/4
279--289
EN
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the latter’s components is at least as close to the corresponding element of the pairwise comparison matrix as the one of the former’s components is, and the latter’s approximation is strictly better in at least one position. A pairwise comparison matrix is called simple perturbed if it differs from a consistent pairwise comparison matrix in one element and its reciprocal. One of the classical weighting methods, the eigenvector method is analyzed. It is shown in the paper that the principal right eigenvector of a simple perturbed pairwise comparison matrix is efficient. An open problem is exposed: the search for a necessary and sufficient condition of that the principal right eigenvector is efficient.
7
Content available Analysis of strategies in a monetary-fiscal game. The case of Poland
Krus L., Woroniecka-Leciejewicz I.
Control and Cybernetics
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2016
|
Vol. 45, no. 2
163--183
EN
A monetary-fiscal game describing the interactions of the fiscal and monetary authorities is formulated and analyzed. A macroeconomic model for the Polish economy has been formulated on the basis of the concept of New Neoclassical Synthesis and respectively extended so as to accommodate the effects of fiscal policy. Several variants of the model have been estimated using statistical data for the Polish economy. It is assumed in the game that each party (monetary and fiscal) tries to achieve its own goal: the fiscal authority – the assumed GDP growth, and the monetary authority – an inflation level. The best response strategies of the authorities and the Nash equilibria are calculated and analyzed in two cases, namely when the decisions are made simultaneously and sequentially. The simulation results obtained indicate that when the authorities try to achieve independently their goals, in a general case the Nash equilibrium is not Pareto optimal. The best response strategies may lead to conflict escalation and to results which are not beneficial for both parties.
8
Content available remote Methodology of Optimization of the Design of an Orthopedic Implant
Muzalewska M., Moczulski W.
Machine Dynamics Research
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2015
|
Vol. 39, No. 2
133-141
EN
The scientific goal of the project is multicriterial optimization of the design of an orthopedic implant responsible for supporting the reconstruction of the anterior cruciate ligament. The implant should not only precisely anchor the tendon in the tunnel but, above all, - thanks to appropriately selected geometric shape and other design features - accelerate the ingrowth of bone tissue into the grafted tendon. The condition for the correct ingrowth of the bone tissue is to enable optimal perfusion of blood and other body fluids into the ligament prosthesis (grafted tendon). Therefore, the geometrical shape of the implant should allow accumulating active biological factors in the vicinity of the grafted tendon, thus accelerating the healing process. The research hypothesis is that there is a specific number of holes of a certain shape and a specific arrangement of these holes, which ensure optimum blood perfusion by maintaining adequate mechanical properties. Finding the optimum is possible by methods such as Artificial Immune Systems from heuristic algorithms class.
9
Content available Hyperbolicity of Systems Describing Value Functions in Differential Games which Model Duopoly Problems
Zwierzchowska J.
Decision Making in Manufacturing and Services
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2015
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Vol. 9, no. 1
89--100
EN
Based on the Bressan and Shen approach (Bressan and Shen, 2004; Shen, 2009), we present an extension of the class of non-zero sum differential games for which value functions are described by a weakly hyperbolic Hamilton–Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly.
10
Content available Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model
Michalak A., Studniarski M.
Opuscula Mathematica
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2014
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Vol. 34, no. 4
827--835
EN
In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.
11
Content available Multi-objective conceptual design optimization of a domestic unmanned airship
Amani S., Pourtakdoust S. H., Pazooki F.
Journal of Theoretical and Applied Mechanics
|
2014
|
Vol. 52 nr 1
47--60
EN
Autonomous airships have gained a high degree of importance over the last decades, both theoretically as well and practically. This is due to their long endurance capability needed for monitoring, observation and communication missions. In this paper, a Multi-Objective Optimization approach (MOO) is followed for conceptual design of an airship taking aerody- namic drag, static stability, performance as well as the production cost that is proportional to the helium mass and the hull surface area, into account. Optimal interaction of the afo- rementioned disciplinary objectives is desirable and focused through the MOO analysis. Standard airship configurations are categorized into three major components that include the main body (hull), stabilizers (elevators and rudders) and gondola. Naturally, component sizing and positioning play an important role in the overall static stability and performance characteristics of the airship. The most important consequence of MOO analysis is that the resulting design not only meets the mission requirement, but will also be volumetrically optimal while having a desirable static and performance characteristics. The results of this paper are partly validated in the design and construction of a domestic unmanned airship indicating a good potential for the proposed approach.
12
Content available remote Non-dominated Rank based Sorting Genetic Algorithms
Ghosh A., Das M.K.
Fundamenta Informaticae
|
2008
|
Vol. 83, nr 3
231-252
EN
In this paper a new concept of ranking among the solutions of the same front, along with elite preservation mechanism and ensuring diversity through the nearest neighbor method is proposed for multi-objective genetic algorithms. This algorithm is applied on a set of benchmark multi-objective test problems and the results are compared with that of NSGA-II (a similar algorithm). The proposed algorithm is seen to over perform the existing algorithm. More specifically, the new approach has been used to solve the deceptive multi-objective optimization problems in a better way.
13
Equilibrium in competing supply-demand flow problems
Bielli M., Felici G., Mecoli M., Pacifici A.
Systems Science
|
2007
|
Vol. 33, no 1
7-17
EN
In this work, we consider a basic version of the Supply-Demand Flow Problem with a set of clients whose demand has to be satisfied by two sets of production centers, each owned by one agent. The agents want to choose the demand centers optimally according to their own independent objective functions. We formulate the problem of efficiently determining an equilibrium solution. We prove that the solution is Pareto-optimal and equivalent to a Kalai-Smorodinsky solution of a suitably defined bargaining problem. Moreover, the results of a computational study are reported, showing that such an equilibrium provides a good compromise between agents' expectations and a reasonable solution in terms of the total cost experienced by the two agents. The proposed approach fits in many competitive problems arising in the management of distributed supply chains.
14
Content available remote New trends in optimization in electromagnetics
Sykulski J.
Przegląd Elektrotechniczny
|
2007
|
R. 83, nr 6
13-18
EN
This paper reviews recent advances in optimisation of electromagnetic problems. CAD assisted optimal design often necessitates repetitive usage of numerically intensive field computation where cost-effective approaches are required. Modern algorithms increasingly rely on surrogate modelling, kriging-assisted methods, pareto-optimality and design sensitivity.
PL
Nowoczesne metody projektowania oparte na wspomaganiu komputerowym z wykorzystaniem numerycznego oblicznia pól elektromagnetycznych wymagają skutecznych, a przede wszystkim szybkich i efektywnych metod optymalizacyjnych. Ostatnie lata przyniosły eksplozję nowych podejść i algorytmów. Artykuł jest próbą uogólnienia efektów ostatnich badań – w tym również dorobku autora – ze szczególnym uwzględnieniem najnowszych osiągnięć i spodziewanych nowych rozwiązań.
15
Content available remote Niching mechanisms in evolutionary computations
Kowalczuk Z., Białaszewski T.
International Journal of Applied Mathematics and Computer Science
|
2006
|
Vol. 16, no 1
59-84
EN
Different types of niching can be used in genetic algorithms (GAs) or evolutionary computations (ECs) to sustain the diversity of the sought optimal solutions and to increase the effectiveness of evolutionary multi-objective optimization solvers. In this paper four schemes of niching are proposed, which are also considered in two versions with respect to the method of invoking: a continuous realization and a periodic one. The characteristics of these mechanisms are discussed, while as their performance and effectiveness are analyzed by considering exemplary multi-objective optimization tasks both of a synthetic and an engineering (FDI) design nature.
16
Optimality conditions and duality for multiobjective control problems
Gulati T. R., Husain I., Ahmed A.
Journal of Applied Analysis
|
2005
|
Vol. 11, nr 2
225-245
EN
Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual duality results are established under invexity / generalized invexity, relating properly efficient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free boundary conditions are also presented.
17
Content available remote Pojęcie ekologicznych kosztów zewnętrznych
Graczyk A.
Ekonomia i Środowisko
|
2004
|
nr 2
7--29
PL
Oddziaływanie jednych podmiotów na inne za pośrednictwem środowiska ma cechy odpowiadające pojęciu kosztów zewnętrznych. Funkcja środowiska przyrodniczego w procesie powstawania kosztów zewnętrznych działalności gospodarczej nie jest jednak jednolicie określona. Zależności między podmiotami, w istnieniu których pośredniczy środowisko, można określić mianem ekologicznych kosztów zewnętrznych, pod warunkiem przedstawienia specyficznych cech ekologicznych kosztów zewnętrznych. Celem niniejszego artykułu jest określenie, czym są w istocie ekologiczne koszty zewnętrzne i jakie są charakterystyczne cechy ekologicznych kosztów zewnętrznych. Podstawą rozważań jest analiza kategorii efektów i kosztów zewnętrznych w ogólności oraz analiza miejsca i roli środowiska przyrodniczego w procesie powstawania kosztów zewnętrznych. Prowadzi to do roboczej definicji ekologicznych kosztów zewnętrznych. Następnie zostanie sformułowana hipoteza, polegająca na wyspecyfikowaniu głównych założeń dotyczących kosztów zewnętrznych. W odniesieniu do tych założeń, poprzez analizę i wnioskowanie przez analogię, możliwe będzie określenie specyfiki ekologicznych kosztów zewnętrznych i zakresu stosowalności oraz możliwości interpretacyjnych tego pojęcia.
EN
The paper presents an analysis of effects and external cost categories in general terms and the role of the environment in the creation of external costs. External environmental cost is an externa] technological cost created by means of the environment in a case when the objective function of the subject using the environment contains defined environmental goods. In the narrow approach it is required to describe property rights to environmental goods. However, the broad approach requires that theses goods be available at a level where it is proper for the realization of subjects' goals and not derogate their position in relationship to other subjects.
18
Content available remote Evolutionary Multi-Objective Pareto Optimisation of Diagnostic State Observers
Kowalczuk Z., Suchomski P., Białaszewski T.
International Journal of Applied Mathematics and Computer Science
|
1999
|
Vol. 9, no 3
689-709
EN
A multi-objective Pareto-optimisation procedure for the design of residual generators which constitute a primary instrument for model-based fault detection and isolation (FDI) in systems of plant monitoring and control is considered. An evolutionary approach to the underlying multi-objective optimisation problem is utilised. The resulting robust observer detector allows for FDI, taking into account the issue of false alarms.
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