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1

Network Dimensioning with Maximum Revenue Efficiency for the Fairness Index

Zalewski G., Ogryczak W.

Journal of Telecommunications and Information Technology

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2016

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nr 4

15--21

EN

Network dimensioning is a specific kind of the resource allocation problem. One of the tasks in the network optimization is to maximize the total flow on given pairs of nodes (so-called demands or paths between source and target). The task can be more complicated when different revenue/profit gained from each unit of traffic stream allocated on each demand is taken into account. When the total revenue is maximized the problem of starvation of less attractive paths can appear. Therefore, it is important to include some fairness criteria to preserve connections between all the demands on a given degree of quality, also for the least attractive paths. In this paper, a new bicriteria ratio optimization method which takes into account both, the revenue and the fairness is proposed. Mathematical model is built in a form of linear programming. The solutions are analyzed with some statistical measures to evaluate their quality, with respect to fairness and efficiency. In particular, the Gini’s coefficient is used for this purpose.

2

Comparison of Selected Fair-optimization Methods for Flow Maximization between Given Pairs of Nodes in Telecommunications Network

Zalewski G., Ogryczak W.

Journal of Telecommunications and Information Technology

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2016

|

nr 3

18--24

EN

Dimensioning of telecommunications networks requires the allocation of the ows (bandwidth) to given trac demands for the source-destination pairs of nodes. Unit ow allocated to the given demand is associated with revenue that may vary for dierent demands. Problem the decision-making basic algorithms to maximize the total revenue may lead to the solutions that are unacceptable, due to "starvation" or "locking" of some demand paths less attractive with respect to the total revenue. Therefore, the fair optimization approaches must be applied. In this paper, two fair optimization methods are analyzed: the method of ordered weighted average (OWA) and the reference point method (RPM). The study assumes that ows can be bifurcated thus realized in multiple path schemes. To implement optimization model the AMPL was used with general-purpose linear programming solvers. As an example of the data, the Polish backbone network was used.

3

On MILP Models for the OWA Optimization

Ogryczak W., Olender P.

Journal of Telecommunications and Information Technology

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2012

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nr 2

5-12

EN

The problem of aggregating multiple outcomes to form overall objective functions is of considerable importance in many applications. The ordered weighted averaging (OWA) aggregation uses the weights assigned to the ordered values (i.e., to the largest value, the second largest and so on) rather than to the specific coordinates. It allows to evaluate solutions impartially, when distribution of outcomes is more important than assignments these outcomes to the specific criteria. This applies to systems with multiple independent users or agents, whose objectives correspond to the criteria. The ordering operator causes that the OWA optimization problem is nonlinear. Several MILP models have been developed for the OWA optimization. They are built with different numbers of binary variables and auxiliary constraints. In this paper we analyze and compare computational performances of the different MILP model formulations.

4

Path Diversity Protection in Two-Layer Networks

Dzida M., Śliwiński T., Zagożdżon M., Ogryczak W., Pióro M.

Journal of Telecommunications and Information Technology

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2009

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nr 3

14-19

EN

The paper addresses an optimization problem related to dimensioning links in a resilient two-layer network. A particular version of the problem which assumes that links of the upper layer are supported by unique paths in the lower layer is considered. Two mixed-integer programming formulations of this problem are presented and discussed. Direct resolving of these formulations requirespre-selection of "good" candidate paths in the upper layer of the network. Thus, the paper presents an alternative approach which is based on decomposing the resolution process into two phases, resolved iteratively. The first phase subproblem is related to designing lower layer path flows that provide the capacities for the logical links of the upper layer. The second phase is related to designing the flow patterns in the upper layer with protection assured through diversity of paths. In this phase we take into account the failures of the logical links that result from the failures of the lower layer links (so called shared risk link groups).

5

Decision Support under Risk by Optimization of Scenario Importance Weighted OWA Aggregations

Ogryczak W., Śliwiński T.

Journal of Telecommunications and Information Technology

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2009

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nr 3

5-13

EN

The problem of evaluation outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e., to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective functions related to decisions under risk. Linear programming formulations are introduced for optimization of theWOWA objective representing risk averse preferences. Their computational efficiency is demonstrated.

6

Reference Point Method with Importance Weighted Partial Achievements

Ogryczak W.

Journal of Telecommunications and Information Technology

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2008

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nr 4

17-25

EN

The reference point method (RPM) is based on the so-called augmented max-min aggregation where the worst individual achievement maximization process is additionally regularized with the average achievement. In order to avoid inconsistencies caused by the regularization, we replace it with the ordered weighted average (OWA) which combines all the individual achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further following the concept of the weighted OWA (WOWA) we incorporate the importance weighting of several achievements into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows us to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities.

7

Reference distribution based decision support platform

Breja K., Ogryczak W.

Journal of Telecommunications and Information Technology

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2008

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nr 3

5-14

EN

There many decision problems where numerous partial achievement functions are considered impartially which makes the distribution of achievements more important than the assignment of several achievements to the specific criteria. Such models are generally related to the evaluation and optimization of various systems which serve many users where quality of service for every individual user defines the criteria. This applies to various technical systems, like to telecommunication ones among others, as well as to social systems. An example arises in location theory, where the clients of a system are entitled to equal treatment according to some community regulations. This paper presents an implementation of decision support framework for such problems. This platform is designed for multiple criteria problems analyzed with the reference distribution approach. Reference distribution approach is an extension of the reference point method.

8

Multicriteria models for fair resource allocation

Ogryczak W.

Control and Cybernetics

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2007

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Vol. 36, no 2

303-332

EN

Resource allocation problems are concerned with the allocation of limited resources among competing activities so as to achieve the best performances. However, in systems which serve many users there is a need to respect some fairness rules while looking for the overall efficiency. The so-called Max-Min Fairness is widely used to meet these goals. However, allocating the resource to optimize the worst performance may cause dramatic worsening of the overall system efficiency. Therefore, several other fair allocation schemes are being considered and analyzed. In this paper we show how the concepts of multiple criteria equitable optimization can effectively be used to generate various fair and efficient allocation schemes. First, we demonstrate how the scalar inequality measures can be consistently used in bicriteria models to search for fair and efficient allocations. Further, two alternative multiple criteria models equivalent to equitable optimization are introduced, thus allowing to generate a larger variety of fair and efficient resource allocation schemes.

9

Obszary badań Instytutu Automatyki i Informatyki Stosowanej

Zieliński C., Malinowski K., Tatjewski P., Ogryczak W., Pacut A., Toczyłowski E., Sacha K., Kasprzak W.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2006

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nr 10

289-292

PL

Przedstawiono w sposób ogólny badania prowadzone w Instytucie Automatyki i Informatyki Stosowanej. Obejmują one zagadnienia związane ze: sterowaniem, symulacją i optymalizacją systemów złożonych, biometrią uczeniem maszynowym, robotyką, rozpoznawaniem obrazów i sygnałów mowy, sterowaniem układów nieliniowych, metodami wytwarzania oprogramowania oraz oceny jego jakości, wspomaganiem decyzji, badaniami operacyjnymi, harmonogramowaniem oraz bazami danych. Przedstawiono zarówno dokonania teoretyczne jak i aplikacyjne w tym zakresie.

EN

The paper presents in generał the research conducted at the Institute of Control and Computation Engineering. This research encompasses: control, simulation and optimization of complex systems, biometrics, machine leaming, robotics, pattern and speech recognition, nonlinear control, methods of software engineering and evaluation of its quality, decision support, operations research, scheduling and data bases. Both the obtained theoretical results and application of those results have been presented.

10

Telecommunications network design and max-min optimization problem

Ogryczak W., Pióro M., Tomaszewski A.

Journal of Telecommunications and Information Technology

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2005

|

nr 3

43-56

EN

Telecommunications networks are facing increasing demand for Internet services. Therefore, the problem of telecommunications network design with the objective to maximize service data flows and provide fair treatment of all services is very up-to-date. In this application, the so-called max-min fair (MMF) solution concept is widely used to formulate the resource allocation scheme. It assumes that the worst service performance is maximized and the solution is additionally regularized with the lexicographic maximization of the second worst performance, the third one, etc. In this paper we discuss solution algorithms for MMF problems related to telecommunications network design. Due to lexicographic maximization of ordered quantities, the MMF solution concept cannot be tackled by the standard optimization model (mathematical programme). However, one can formulate a sequential lexicographic optimization procedure. The basic procedure is applicable only for convex models, thus it allows to deal with basic design problems but fails if practical discrete restrictions commonly arriving in telecommunications network design are to be taken into account. Then, however, alternative sequential approaches allowing to solve non-convex MMF problems can be used.

11

On multi-criteria approaches to bandwidth allocation

Ogryczak W., Wierzbicki A.

Control and Cybernetics

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2004

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Vol. 33, no 3

427-448

EN

Modern telecommunication networks face an increasing demand for services. Among these, an increasing number are services that can adapt to available bandwidth, and are therefore referred to as elastic traffic. Nominal network design for elastic traffic becomes increasingly significant. Typical resource allocation methods are concerned with the allocation of limited resources among competing activities so as to achieve the best overall performance of the system. In the network dimensioning problem for elastic traffic, one needs to allocate bandwidth to maximize service flows and simultaneously to reach a fair treatment of all the elastic services. Thus, both the overall efficiency (throughput) and the fairness (equity) among various services are important. In such applications, the so-called Max-Min Fairness (MMF) solution concept is widely used to formulate the resource allocation scheme. This approach guarantees fairness but may lead to significant losses in the overall throughput of the network. In this paper we show how the concepts of multiple criteria equitable optimization can be effectively used to generate various fair resource allocation schemes. We introduce a multiple criteria model ecluivalent to equitable optimization and we develop a corresponding reference point procedure to generate fair efficient bandwidth allocations. The procedure is tested on a sample network dimensioning problem and its abilities to model various preferences are demonstrated.

12

Fair resource allocation schemes and network dimensioning problems

Ogryczak W., Śliwiński T., Wierzbicki A.

Journal of Telecommunications and Information Technology

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2003

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nr 3

34-42

EN

Resource allocation problems are concerned with the allocation of limited resources among competing activities so as to achieve the best overall performances of the system but providing fair treatment of all the competitors. Telecommunication networks are facing the increasing demand for Internet services. Therefore, a problem of network dimensioning with elastic traffic arises which requires to allocate bandwidth to maximize service flows with fair treatment of all the services. In such applications, the so-called max-min fairness (MMF) solution concept is widely used to formulate the resource allocation scheme. This guarantees the fairness but may lead to significant losses in the overall throughput of the network. In this paper we show how multiple criteria optimization concepts can be used to generate various fair resource allocation schemes. The solution concepts are tested on the network dimensioning problem and their abilities to model various preferences are demonstrated.

13

Zadania lokalizacyjne z kryterium minimalizacji najgorszej średniej warunkowej

Ogryczak W., Zawadzki M.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2002

|

z. 136

167-177

PL

Praca dotyczy zagadnień lokalizacyjnych z kryterium minimalizacji najgorszej średniej warunkowej. Kryterium to stanowi parametryczne uogólnienie minimalizacji maksymalnej odległości biorące pod uwagę wielkość zapotrzebowania odpowiadającego największym odległościom. Dla ustalonego poziomu tolerancji reprezentującego część (procent) sumarycznego zapotrzebowania bierzemy pod uwagę odpowiednią porcję (kwantyl) największych odległości i minimalizujemy ich średnią. W pracy pokazano, że rozważane kryterium może być implementowane za pomocą dodatkowego układu prostych nierówności liniowych.

EN

Classical approaches to location problems are based on the minimization of the average distance or the minimization of the maximum distance to service facilities. In this paper we investigate a parametric solution concept based on the minimization of the conditional mean distance which allows us to take into account the portion of demand related to the largest distances. Namely, for a specified portion (quantile) of demand we focus on the group of the corresponding largest distances and we minimize their average. It is shown that such an objective may be modeled with a number of simple linear inequalities.

14

On equitable approaches to resource allocation problems: the conditional minimax solutions

Ogryczak W., Śliwiński T.

Journal of Telecommunications and Information Technology

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2002

|

nr 3

40-48

EN

In this paper we introduce and analyze a solution concept of the conditional minimax as a generalization of the minimax solution concept extended to take into account the number of services (the portion of demand) related to the worst performances. Namely, for a specified portion of demand we take into account the corresponding portion of the maximum results and we consider their average as the worst conditional mean to be minimized. We show that, similar to the standard minimax approach, the minimization of the worst conditional mean can be defined by a linear objective and a number of auxiliary linear inequalities. We report some results of initial computational experience with the new solution concept.

15

Multiple criteria optimization and decisions under risk

Ogryczak W.

Control and Cybernetics

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2002

|

Vol. 31, no 4

975-1003

EN

The mathematical background of multiple criteria optimization (MCO) is closely related to the theory of decisions under uncertainty. Most of the classical solution concepts commonly used in the MCO methodology have their origins in some approaches to handling uncertainty in decision analysis. Nevertheless, the MCO as a separate discipline has developed several advanced tools of interactive analysis leading to effective decision support techniques with successful applications. Progress made in the MCO tools raises a question of possible feedback to the decision making under risk. The paper shows how decisions under risk, and specifically the risk aversion preferences, can be modeled within the MCO methodology. This provides a methodological basis allowing for taking advantage of the interactive multiple criteria techniques for decision support under risk.

PL

Podstawy matematyczne optymalizacji wielokryterialnej są blisko związane z teorią podejmowania decyzji w warunkach ryzyka. Większość klasycznych koncepcji rozwiązań zazwyczaj wykorzystywanych w metodach optymalizacji wielokryterialnej pochodzi z pewnych podejść uwzględniania niepewności w analizie decyzji. Jednakże, należy podkreślić, że optymalizacja wielokryterialna, jako niezależna dyscyplina, rozwinęła szereg zaawansowanych narzędzi analizy interaktywnej, prowadzących do efektywnych technik wspomagania decyzji, znajdujących rzeczywiste zastosowania. Postęp, jaki się dokonał w zakresie narzędzi wielokryterialnego podejmowania decyzji, stawia pytanie o ewentualne sprzężenie zwrotne w kierunku podejmowania decyzji w warunkach ryzyka. W artykule pokazano, jak decyzje z ryzykiem, a szczególnie preferencje co do unikania ryzyka, mogą być modelowane przy użyciu metodyki optymalizacji wielokryterialnej. W ten sposób stworzono podstawę metodyczną pozwalającą korzystać z interaktywnych technik wielokryterialnych we wspomaganiu decyzji z ryzykiem.

16

Wielokryterialne podejście do zadań lokalizacyjnych

Ogryczak W.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

|

2000

|

z. 131

111-120

PL

Dyskretny problem lokalizacyjny może być rozpatrywany jako zagadnienie wielokryterialne, gdzie kryteria mierzą poziom satysfakcji (odległości) poszczególnych klientów. Rozkład wartości ocen (odległości od klientów) jest na ogół istotnym czynnikiem wyboru rozwiązania. Podstawowe koncepcje rozwiązań zadań lokalizacyjnych (optymalizacja średniej lub najgorszej oceny) wykorzystują proste techniki agregacji wielu ocen. Uwzględnienie całego rozkładu wymaga zastosowania odpowiednich modeli optymalizacji wielokryterialnej.

EN

Location problems can be considered as multiple criteria models where for each client (spatial unit) there is defined an individual objective function, which measures the effect of a location pattern with respect to the client satisfaction. This results in a multiple criteria model taking into account the entire distribution of individual effects (distances). Our analysis of the multiple criteria problem focuses on the symmetrically efficient solutions which comply with minimization of distances as well as with impartial consideration of the clients.

17

A recursive procedure for selecting optimal portfolio according to the MAD model

Michałowski W., Ogryczak W.

Control and Cybernetics

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1999

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Vol. 28, no 4

725-738

EN

The mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. Im a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we poesent a recursive procedure which allows to identify optimal portfolio of the MAD model depending on investor's downside risk aversion.

18

Location problems from the multiple criteria perspective: efficient solutions

Ogryczak W.

Archives of Control Sciences

|

1998

|

Vol. 7, no. 3/4

161-180

EN

Location problems can be considered as multiple criteria models where for each client (spatial unit) there is defined an individual objective function, which measures quality of a location pattern with respect to the client satisfaction (e.g. it expresses the distance or travel time between the client and the assigned facility). The individual objective functions are usually conflicting when optimized. Therefore, the decision maker or planner needs to select some compromise solution for implementation. In this paper we analyze various approaches to discrete multiple facility location problems (various solution concepts) from the perspective of the multiple criteria models. We focus our analysis on two aspects of the solution concepts: if a generated solution is an efficient (Pareto-optimal) solution to the multiple criteria problem, and if the solution concept provides some control parameters allowing the decision maker to select every efficient solution of the multiple criteria problem. That means, we analyze if a solution concept complies with the optimality principle for the multiple criteria model as well as if it allows to take into account various preferences of the decision maker.