Meta-heuristic approach to proportional fairness

Köppen, Mario; Yoshida, Kaori; Ohnishi, Kouhei; Tsuru, Masato

doi:10.1007/s12065-012-0084-5

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…Some of them may have been stated in different application contexts. (For instance in [21] a detailed discussion on the properties of proportional fair solutions is presented.) However, to the best of our knowledge, they have not been previously formalized for a general multi-agent problem without any assumption on the utility sets.…”

Section: General Resultsmentioning

confidence: 99%

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Price of Fairness for allocating a bounded resource

Nicosia

Pacifici

Pferschy

2017

European Journal of Operational Research

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In this paper we study the problem of allocating a scarce resource among several players (or agents). A central decision maker wants to maximize the total utility of all agents. However, such a solution may be unfair for one or more agents in the sense that it can be achieved through a very unbalanced allocation of the resource. On the other hand fair/balanced allocations may be far from optimal from a central point of view. So, in this paper we are interested in assessing the quality of fair solutions, i.e. in measuring the system efficiency loss under a fair allocation compared to the one that maximizes the sum of agents utilities. This indicator is usually called the Price of Fairness and we study it under three different definitions of fairness, namely maximin, Kalai-Smorodinski and proportional fairness.Our results are of two different types. We first formalize a number of properties holding for any general multi-agent problem without any special assumption on the agents utilities. Then we introduce an allocation problem, where each agent can consume the resource in given discrete quantities (items). In this case the maximization of the total utility is given by a Subset Sum Problem. For the resulting Fair Subset Sum Problem, in the case of two agents, we provide upper and lower bounds on the Price of Fairness as functions of an upper bound on the items size.

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Section: General Resultsmentioning

confidence: 99%

“…Therefore, in the right-hand side of ( 21) it must be a(x * ) â > b(x * ) b . This means that to fulfill (21) we also must have a…”

Section: Separate Item Setsmentioning

confidence: 99%

Price of Fairness for allocating a bounded resource

Nicosia

Pacifici

Pferschy

2017

European Journal of Operational Research

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“…An allocation y is proportionally fair if for any other feasible allocation y , the total proportional change ( i∈I (y i − y i )/y i ) is zero or negative when all outcomes are nonnegative. The proportional fairness concept can be advocated from a game theoretic point of view as a proportionally fair allocation is also the Nash bargaining solution, satisfying certain axioms of fairness (Bertsimas et al, 2011;Crowcroft & Oechslin, 1998;Kelly, Maulloo, & Tan, 1998;Morell et al, 2008;Bonald et al, 2006;Kelly, Massoulié, & Walton, 2009;Walton, 2011); see also Köppen (2013), Köppen, Yoshida, Ohnishi, and Tsuru (2012) for a discussion of proportional fairness within a relational framework and a symmetric version of this concept, -rank-ordered proportional fairness). Proportional fairness is a specific case of a more general fairness scheme called α − f airness, which maximize the following parametric class of utility functions for α ≥ 0 ) (see also Verloop, Ayesta, and Borst (2010) for a discussion of α − f airness in multi-class queuing systems):…”

Section: Definition 3 a Function F Is Strictly Schur-concave (Schur-mentioning

confidence: 99%

Inequity averse optimization in operational research

Karsu

Morton

2015

European Journal of Operational Research

138

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a b s t r a c tThere are many applications across a broad range of business problem domains in which equity is a concern and many well-known operational research (OR) problems such as knapsack, scheduling or assignment problems have been considered from an equity perspective. This shows that equity is both a technically interesting concept and a substantial practical concern. In this paper we review the operational research literature on inequity averse optimization. We focus on the cases where there is a tradeoff between efficiency and equity.We discuss two equity related concerns, namely equitability and balance. Equitability concerns are distinguished from balance concerns depending on whether an underlying anonymity assumption holds. From a modeling point of view, we classify three main approaches to handle equitability concerns: the first approach is based on a Rawlsian principle. The second approach uses an explicit inequality index in the mathematical model. The third approach uses equitable aggregation functions that can represent the DM's preferences, which take into account both efficiency and equity concerns. We also discuss the two main approaches to handle balance: the first approach is based on imbalance indicators, which measure deviation from a reference balanced solution. The second approach is based on scaling the distributions such that balance concerns turn into equitability concerns in the resulting distributions and then one of the approaches to handle equitability concerns can be applied.We briefly describe these approaches and provide a discussion of their advantages and disadvantages. We discuss future research directions focussing on decision support and robustness.

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“…Therefore, there is an emerging need to develop approximate or heuristic algorithms for such problems. Early results in this area show that several communication network problems with PF or OWA fairness criteria can be effectively handled by meta-heuristic approaches [80,106,151].…”

Section: Complexity Issuesmentioning

confidence: 99%

Fair Optimization and Networks: A Survey

Ogryczak

Luss

Pióro

et al. 2014

Journal of Applied Mathematics

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Optimization models related to designing and operating complex systems are mainly focused on some efficiency metrics such as response time, queue length, throughput, and cost. However, in systems which serve many entities there is also a need for respecting fairness: each system entity ought to be provided with an adequate share of the system’s services. Still, due to system operations-dependant constraints, fair treatment of the entities does not directly imply that each of them is assigned equal amount of the services. That leads to concepts of fair optimization expressed by the equitable models that represent inequality averse optimization rather than strict inequality minimization; a particular widely applied example of that concept is the so-called lexicographic maximin optimization (max-min fairness). The fair optimization methodology delivers a variety of techniques to generate fair and efficient solutions. This paper reviews fair optimization models and methods applied to systems that are based on some kind of network of connections and dependencies, especially, fair optimization methods for the location problems and for the resource allocation problems in communication networks.

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Meta-heuristic approach to proportional fairness

Cited by 6 publications

References 22 publications

Price of Fairness for allocating a bounded resource

Price of Fairness for allocating a bounded resource

Inequity averse optimization in operational research

Fair Optimization and Networks: A Survey

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