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Efficient Approximation Methods for Lexicographic Max-Min Optimization

Śliwiński Tomasz

Journal of Telecommunications and Information Technology

2024

nr 1

46--53

Lexicographic max-min (LMM) optimization is of considerable importance in many fairness-oriented applications. LMM problems can be reformulated in a way that allows to solve them by applying the standard lexicographic maximization algorithm. However, the reformulation introduces a large number of auxiliary variables and linear constraints, making the process computationally complex. In this paper, two approximation schemes for such a reformulation are presented, resulting in problem size reduction and significant performance gains. Their influence on the quality of the solution is shown in a series of computational experiments concerned with the fair network dimensioning and bandwidth allocation problem.

Fair resource allocation schemes and network dimensioning problems

Ogryczak W., Śliwiński T., Wierzbicki A.

Journal of Telecommunications and Information Technology

2003

nr 3

34-42

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.