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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
Content available remote Interactive multiobjective optimization with the Pareto memetic algorithm
100%
Jaszkiewicz A.
|
2007
|
tom Vol. 32, No. 1
15-31
EN
The paper describes an interactive multiobjective memetic algorithm. During the run of the method the DM is periodically asked to compare a pair of generated solutions. The comparisons are used to focus the search in the promising region of the nondorninated set. The algorithm is evaluated on the multiobjective traveling salesperson problem with four, five and six objectives. It is also compared to an interactive evolutionary metaheuristic proposed by Phelps and Koksalan. The results of the computational experiment indicate that the interactive algorithm can efficiently find high quality solutions even in the case of multidimensional objective space.
3
Content available remote Variational principles for set-valued mappings with applications to multiobjective optimization
100%
Bao T. Q. , Mordukhovich B. S.
|
2007
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tom Vol. 36, no 3
531-562
EN
This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which-being certainly of independent interest-are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang, formulated via an appropriate subdifferential notion for set-valued mappings with values in partially ordered spaces. Based on these variational principles and corresponding tools of generalized differentiation, we derive new conditions of the coercivity and Palais-Smale types ensuring the existence of optimal solutions to set-valued optimization problems with noncompact feasible sets in infinite dimensions and then obtain necessary optimality and suboptimality conditions for nonsmooth multiobjective optimization problems with general constraints, which are new in both finite-dimensional and infinite-dimensional settings.
4
Content available remote An improved method for deriving final ranking from a fuzzy preference relation via multiobjective optimization
100%
Fernandez E. , Olmedo R.
|
2003
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tom Vol. 28, No. 3
143-157
EN
Methods for deriving final ranking from a fuzzy preference relation do not perform well in presence of irrelevant alternatives or in case of complex graphs with numerous circuits. Recently some approaches based on the idea of reducing differences between a global model of preferences and a final ranking via multiobjective optimization with an evolutionary algorithm have been proposed. In this work a new method is presented based on similar ideas but improving them. The multiobjective optimization problem is separated into two steps and solved with a better model of preferences, also using an evolutionary algorithm simpler than the former. These improvements allow us to obtain better compromise solutions in a simpler way than the previous proposals.
5
Content available remote Multiobjective identification of boundary temperature using energy minimization method coupled with Boundary Element Method
100%
Jasiński M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2008
|
tom Vol. 7, nr 1
63-70
EN
The inverse problem consisting in an identification of boundary temperature is discussed. As the identification method the Pareto approach with two criteria connected with domain and boundary has been used. In order to solve the problem the energy minimization method connected with boundary element method for steady state problem has been employed. The theoretical considerations are supplemented by the examples of computations verifying the correctness of the algorithm proposed.
6
Content available remote The use of importance measures for the optimization of multi-state systems
100%
Zio E. , Podofillini L.
|
2006
|
tom nr 2
33-36
EN
In this paper we propose an approach to the multiobjective optimization of a multi-state system (MSS) design, based on incorporating information from importance measures (IMs). More specifically, IMs come into play at the objective functions level in order to drive the search towards a MSS which, besides being optimal from the points of view of economics and safety, is also 'balanced' in the sense that all components have similar IMs values, without bottlenecks or unnecessarily high-performing components.
7
Content available remote Weak sharp minima in multiobjective optimization
100%
Studniarski M.
|
2007
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tom Vol. 36, no 4
925-937
EN
We extend some necessary and sufficient conditions for strict local Pareto minima of order m obtained by Jiménez (2002) to the case of weak ψ-sharp local Pareto minima, i.e., to the case when the local solution is not necessarily unique.
8
Content available THE METHOD OF SUPPORTING DECISIONS UNDER RISK BASED ON MULTIOBJECTIVE OPTIMIZATION
100%
Łodziński A.
Metody Ilościowe w Badaniach Ekonomicznych
|
2013
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tom 14
|
nr 2
39-50
EN
The method of supporting decisions under risk was presented in this paper. Making decision under risk takes place when a result of a given decision is not explicit and depends on the condition of the environment. A decision-making process based on multiobjective optimization has been presented in this paper. Methods of multiobjective optimization do not give one unique solution, but a whole set of them. A decision making relies on interactive conducting of the decision making process. Selection of given decision is made by way of solving a problem with parameters defining aspirations of a decision maker and the evaluation of obtained results. A decision maker defines a parameter, for which a solution is indicated. Then he or she evaluates the received solution by either accepting or rejecting it. In the second case a decision maker provides a new parameter value and a problem is solved again for the new parameter.39-50
9
Content available remote Multiobjective simulated annealing - a metaheuristic technique for multiobjective optimization of a constrained problem
88%
Suman B.
|
2002
|
tom Vol. 27, No. 3
171-191
EN
The paper presents a multiobjective metaheuristic procedure - Weight based Multiobjective Simulated Annealing (WMOSA). The aim is to produce a set of potentially Pareto-optimal solutions of a constrained multiobjective optimization problem in a short time. In this method, the weight vector depends on the number of constraints to be satisfied by the solution vector and by the objective function vector, and the number of constraints of the problem. The weight vector is used in the acceptance criterion to handle constraints. Solution explores its neighborhood in a way similar to that of Classical Simulated Annealing. A computational experiment shows that WMOSA algorithm produces Pareto-optimal solutions of better quality than Suppapitanrm Multiobjective Simulated Annealing (SMOSA) with a penalty function approach at a lower computational cost.
10
Content available 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
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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.
11
Content available Multiobjective fuzzy approach to the vehicle routing problem with time windows
75%
Wesołek P. , Kubiak M.
|
2006
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tom nr 2(38)
21-24
EN
The paper presents a model of the vehicle routing problem with flexible (fuzzy) constraints. This kind of model allows a decision maker to explore a set of alternatives with diverse cost and constraint satisfaction levels. The model is tested on well-known instances of the vehicle routing problem with time windows adjusted to the fuzzy case. They are solved by a multiobjective Pareto Memetic Algorithm. The obtained results indicate that the introduction of fuzzy constraints leads to exploration of new alternatives which may be interesting to a decision maker.
PL
Artykuł prezentuje model problemu planowania tras z elastycznymi (rozmytymi) ograniczeniami. Model takiego rodzaju pozwala decydentowi na wybór rozwiązania spośród zbioru alternatyw ze zróżnicowanym kosztem i stopniem spełnienia ograniczeń. Ten model został przetestowany na klasycznym zestawie instancji problemu planowania tras z oknami czasowymi dostosowanych do przypadku rozmytych ograniczeń. Rozwiązania są uzyskiwane przez użycie wielokryterialnego algorytmu memetycznego. Uzyskane wyniki wskazują na to, że wprowadzenie elastycznych ograniczeń prowadzi do odkrycia rozwiązań, które mogą być interesujące z punktu widzenia decydenta
12
Content available remote Modele matematyczne do polioptymalizacji parametrycznej operacji z kolejno równoczesną pracą narzędzi
75%
Szwabowski J.
|
2003
|
tom Vol. 23, Nr 2
87-96
PL
W artykule zaprezentowano wyznaczenie ogólnej postaci modeli matematycznych niezbędnych do polioptymalizacji parametrycznej operacji wielonarzędziowych z kolejno równoczesną pracą narzędzi. Dla tokarek CNC z kilkoma suportami narzędziowymi i głowicami rewolwerowymi oraz z napędzanymi narzędziami obrotowymi opracowano ogólną strukturę czasową operacji i wyznaczono czas cyklu roboczego. Zaproponowano metodykę wyznaczania modeli matematycznych czasu, kosztu i ceny jednostkowej operacji. Wyznaczone modele dotyczą przypadków, gdy wielkości występujące w funkcjach celu i ograniczeniach są traktowane jako deterministyczne.
EN
The work presents the methodology of determining mathematical models for multiobjective optimization of the multitools operation with successive and simultaneous work of tools. The general time structure for operations on CNC-lathes, with a few tool slides and the turrets and with driven revolving tools, is presented. The time of a working cycle has been defined. The methodology of determining mathematical models for the time, the unit cost and unit price of the operation is proposed. The defined models apply to the cases of treating the quantities occurring in objective functions and constraints as deterministic.
13
Content available remote 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.
14
Content available remote A new multiobjective simulated annealing based fuzzy clustering technique: application to automatic pixel classification in remote sensing imagery
63%
Saha S. , Bandyopadhyay S.
|
2009
|
tom Vol. 34, No. 3
209-229
EN
An important approach for landcover classification in remote sensing images is by clustering the pixels in the spectral domain into several fuzzy partitions. In this article the problem of fuzzy partitioning the satellite images is posed as one of searching for some suitable number of cluster centers so that some measures of validity of the obtained partitions should be optimized. Thus the problem is posed as one of multiobjective optimization. A recently developed multiobjective simulated annealing based technique, AMOSA (archived multiobjective simulated annealing technique), is used to perform clustering, taking two validity measures as two objective functions. Center based encoding is used. The membership values of points to different clusters are computed based on the newly developed point symmetry based distance rather than the Euclidean distance. Two fuzzy cluster validity functions namely, Euclidean distance based well-known XB-index and the newly developed point symmetry based FSym-index are optimized simultaneously to automatically evolve the appropriate number of clusters present in an image. The proposed algorithm provides a set of final non-dominated solutions. A new method of selecting a single solution from this final Pareto optimal front is also developed subsequently. The effectiveness of this proposed clustering technique in comparison with the existing Fuzzy C-means clustering is shown for automatically classifying one artificially generated, three remote sensing satellite images of the parts of the cities of Kolkata and Mumbai.
15
Content available remote Multiobjective evolutionary optimization of MEMS structures
51%
Długosz A.
|
|
tom Vol. 17, no. 1
41-50
EN
The paper is devoted to the shape optimization of piezoelectric and electro-thermo-mechanical devices by the use of multiobjective evolutionary algorithm. In this paper, special implementation of multiobjective evolutionary algorithm is applied (MOOPTIM). Several test problems are solved in order to test efficiency of the algorithm. The results are compared with the Non-Dominated Sorting Genetic Algorithm (NSGA-II). The objective function values are calculated for each chromosome in every generation by solving a boundary value problem for the piezoelectricity and electro-thermal-mechanical analysis. In order to solve the boundary value problems, the finite element method is used. Different functionals based on the results derived from coupled field analyses are formulated. The aim of the multiobjective problem is to determine the specific dimensions of the optimized structures. Numerical examples for multiobjective shape optimization are enclosed.
16
Content available remote Wpływ probabilistycznych cech trwałości ostrza i chropowatości powierzchni na wyniki polioptymalizacji parametrycznej. Część I. Badania empiryczne i wyznaczanie optimum Pareto
51%
Szwabowski J. , Chmielewski K.
|
2001
|
tom Vol. 21, Nr 2
56-66
PL
Całość pracy dotyczy metod postępowania i różnic w efektach polioptymalizacji parametrycz-nej, gdy wielkości występujące w funkcjach celu i ograniczeniach mogą być traktowane jako deterministyczne lub probabilistyczne. W części pierwszej zamieszczono wyniki badań prowadzo-nych w warunkach produkcyjnych. Na podstawie pomiarów zużycia ostrza narzędzia przedstawio-no metodykę wyznaczania parametrów rozkładu logarytmo-normalnego trwałości ostrza. Wyko-rzystując pomiary wytwarzanych przedmiotów, oszacowano parametry i typ rozkładu gęstości prawdopodobieństwa chropowatości powierzchni jako zmiennej losowej. Podano przykład wyzna-czenia optimum Pareto dla jednonarzędziowej operacji tokarskiej przy podejściu deterministycznym.
EN
The work - as a whole - discusses procedures and differences in the results of parametric multiobjective optimization for the cases of treating quantities, used in objective functions and constraints, as deterministic or probabilistic. Part I of the work contains results of the investigations, carried out under the manufacturing conditions. The methodology of determining the parameters of the log-normal distribution of tool life is presented. The measurements of the manu-factured work pieces were used to estimate the parameters and the type of the probability density distribution of the surface roughness treated as a random variable. The example of determining Pareto optimum of a single-tool turning operation using deterministic approaches is presented.
17
Content available remote Wpływ probabilistycznych cech trwałości ostrza i chropowatości powierzchni na wyniki polioptymalizacji parametrycznej. Część II. Polioptymalizacja z uwzględnieniem cech probabilistycznych
51%
Szwabowski J. , Chmielewski K.
|
2001
|
tom Vol. 21, Nr 2
67-76
PL
Całość pracy dotyczy metod postępowania i różnic w efektach polioptymalizacji parametrycznej, gdy wielkości występujące w funkcjach celu i ograniczeniach mogą być traktowane jako deterministyczne lub probabilistyczne. W części drugiej podano przykłady polioptymalizacji para-metrycznej dla jednonarzędziowej operacji tokarskiej przy podejściu probabilistycznym. Pokazano wpływ zmian niezawodnego okresu trwałości ostrza na czas i koszt jednostkowy. Wykazano wpływ chropowatości powierzchni jako zmiennej losowej (będącej wskaźnikiem jakości przed-miotu obrobionego) na zmiany czasu głównego oraz czasu i kosztu jednostkowego w stosunku do wartości optymalnych wyznaczonych przy podejściu deterministycznym.
EN
The work - as a whole - discusses procedures and differences in the results of parametric multiobjective optimization for the cases of treating quantities, used in objective functions and constraints, as deterministic or probabilistic. Part II of the work presents examples of the paramet-ric multiobjective optimization for a single-tool turning operation using probabilistic approaches. There has been presented the effect of changes in the reliable tool life on the unit time and cost. There has been also presented the effect of surface roughness as a random variable (which is a workpiece quality index) on changes in the productive time and the unit time and cost in relation to the values determined using a deterministic approach.
18
Use of genetic algorithms in parametric multiobjective optimization of multi-tool operations with simultaneously active tools.
51%
Szwabowski J. , Zasada M.
|
1999
|
tom Vol. 23, nr 2
71-97
EN
The paper presents a methodology of parametric multiobjective optimization of multi -tool machining operations with simultaneously active tools. The optimum in Pareto sense is determined making use of the minimum unit cost and time criteria. In order to provide the desired production profitability, a minimum unit criterion is used for selecting one solution in the second stage of the multiobjective optimization. This criterion is based on the unit time and cost criteria and the amount of the profit required. Presented is a potental for the use of genetic algorithms in selecting multiobjective optimum values of the cutting parameters. On the example of the operation of boring holes it was shown the way of determining the optimum values of the cutting parameters in particular cuts, taking into account the feasibl solution domain constraints.
PL
Przedstawiono metodykę polioptymalizacji parametrycznej wielonarzędziowych operacji obróbki wiórowej z jednoczesną pracą narzędzi. W celu określenia optimum w sensie Pareto wykorzystano kryteria minimalnego kosztu i czasu jednostkowego. Dla zapewnienia pożądanej rentowności produkcji zastosowano - do wyboru jednego rozwiązania w drugim etapie polioptymalizacji - kryterium minimalnej ceny jednostkowej, oparte na kryteriach czasu i kosztu jednostkowego oraz wielkości wymaganego zysku. Przedstawiono możliwości wykorzystania algorytmów genetycznych do doboru polioptymalnych wartości parametrów skrawania. Na przykładzie operacji wytaczania otworów pokazano sposób wyznaczenia optymalnych wartości parametrów skrawania w zabiegach, z uwzględnieniem ograniczeń obszaru rozwiązań dopuszczalnych.
19
Use of genetic algorithms in parametric multiobjective optimization of multi-tool operations with simultaneously active tools.
51%
Szwabowski J. , Zasada M.
|
1999
|
tom Vol. 23, nr 2
71-97
EN
The paper presents a methodology of parametric multiobjective optimization of multi-tool machining operations with simultaneously active tools. The optimum in Pareto sense is determined making use of minimum unit cost and time criteria. In order to provide the desired production profitability, a minimum unit price criterion is used for selecting one solutions in the second stage of the multiobjective optimization. This criterion is based on the unit time and cost criteria and the amount of the profit required. It is presented a potential for the use of genetic algorithms in selecting multiobjective optimum values of the cutting parameters. On an example of the operation of boring holes shown is the way of determining the optimum values of the cutting parameters in particular cuts, taking into account the feasible solution domain constraints.
PL
Przedstawiono metodykę polioptymalizacji parametrycznej wielonarzędziowych operacji obróbki wiórowej z jednoczesną pracą narzędzi. W celu określenia optimum w sensie Pareto wykorzystano kryteria minimalnego kosztu i czasu jednostkowego. Dla zapewnienia pożądanej rentowności produkcji zastosowano - do wyboru jednego rozwiązania w drugim etapie polioptymalizacji - kryterium minimalnej ceny jednostkowej, oparte na kryteriach czasu i kosztu jednostkowego oraz wielkości wymaganego zysku. Przedstawiono możliwość wykorzystania algorytmów genetycznych do doboru polioptymalnych wartości parametrów skrawania. Na przykładzie operacji wytaczania otworów pokazano sposób wyznaczania optymalnych wartości parametrów skrawania w zabiegach, z uwzględnieniem ograniczeń obszaru rozwiązań dopuszczalnych.
20
Content available On a book Game Theory and Its Applications by Akio Matsumoto and Ferenc Szidarovszky
38%
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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