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1
Content available remote

Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

100%
Boţ R., Hodrea I., Wanka G.
Open Mathematics
|
2008
|
tom 6
|
nr 3
453-468
EN
We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.
2
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Decentralized job scheduling in the cloud based on a spatially generalized Prisoner's Dilemma game

88%
Gąsior J., Seredyński F.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 4
737-751
EN
We present in this paper a novel distributed solution to a security-aware job scheduling problem in cloud computing infrastructures. We assume that the assignment of the available resources is governed exclusively by the specialized brokers assigned to individual users submitting their jobs to the system. The goal of this scheme is allocating a limited quantity of resources to a specific number of jobs minimizing their execution failure probability and total completion time. Our approach is based on the Pareto dominance relationship and implemented at an individual user level. To select the best scheduling strategies from the resulting Pareto frontiers and construct a global scheduling solution, we developed a decision-making mechanism based on the game-theoretic model of Spatial Prisoner's Dilemma, realized by selfish agents operating in the two-dimensional cellular automata space. Their behavior is conditioned by the objectives of the various entities involved in the scheduling process and driven towards a Nash equilibrium solution by the employed social welfare criteria. The performance of the scheduler applied is verified by a number of numerical experiments. The related results show the effectiveness and scalability of the scheme in the presence of a large number of jobs and resources involved in the scheduling process.
3
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A multivariable multiobjective predictive controller

75%
Ben Aicha F., Bouani F., Ksouri M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 1
35-45
EN
Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the NonDominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA.
4
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On a book Game Theory and Its Applications by Akio Matsumoto and Ferenc Szidarovszky

39%
Radzik T., Szajowski K. J.
Mathematica Applicanda
|
2017
|
tom 45
|
nr 2
PL
Prezentowana książka to wykład z teorii gier i jej zastosowań napisany przystępnie, z pokazaniem wykorzystania nowych narzędzi informatycznych do rozwiązywania szerokiej rozumianych problemów powstających przy modelowaniu metodami teorii gier. Zawiera szeroki wachlarz aplikacji do modelowania gier w wielu różnych dziedzinach. Autorzy skupili się na integracji podstaw, metodologii i głównych dziedzin zastosowań gier kooperacyjnych i niekooperacyjnych, w tym  antagonistycznych. Tematy omawiane w książce to gry dyskretne i ciągłe, w tym gry w postaci rozwiniętej, gry macierzowe i dwumacierzowe, koncepcje rozwiązań kooperacyjnych, gry w warunkach niepewności, gry dynamiczne i antagonistyczne. Metodologię ilustrują starannie wyselekcjonowane przykłady zastosowań modeli teorii gier, wybrane zagadnienia z ekonomii, nauk społecznych, inżynierii, bezpieczeństwa oraz modele militarne. Można książkę polecić czytelnikom, którzy są zainteresowani pogłębieniem metodologii oraz matematycznej teorii modelowania konfliktów i koncepcji rozwiązań dla takich zagadnień. Jest skierowany do uczestników studiów interdyscyplinarnych na poziomie magisterskim i doktorów prowadzących badania interdyscyplinarne. 
EN
The book under review presents the serious theoretical development of the game models in an easy-to-follow style and provides computer methodology to solve a broad class of problems. It includes a wide range of game modeling applications in many different areas. The authors have focused on integration the fundamentals, methodology, and major application fields of non-cooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games under uncertainty; dynamic games and conflict resolution. The methodology is illustrated by carefully chosen examples, applications and case studies which are selected from economics, social sciences, engineering, the military and homeland security. This book is highly recommended to readers who are interested in the in-depth and up-to-date integration of the theory and ever-expanding application areas of game theory. It is addressed to interdisciplinary graduate/ undergraduate students and to interdisciplinary young researchers.
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