Solving Nonlinear Covering Problems Arising in WLAN Design

Abstract

Wireless Local Area Networks (WLANs) are widely used for cable replacement and wireless Internet access. Since the medium access control (MAC) scheme of WLANs has a strong influence on network performance, it should be accounted for in WLAN design. This paper presents AP location models that optimize a network performance measure specific for the MAC scheme of WLANs, which represents the efficiency in sharing the wireless medium. For these models, we propose a solution framework based on an effective integer-linear programming Dantzig-Wolfe reformulation. This framework is applicable to any nonlinear covering problem where the objective function is a sum of contributions over the groundset elements (users in WLANs). Extensive computational results show that our solution strategy quickly yields optimal or near-optimal solutions for WLAN design instances of realistic size.

Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations

“…Fractional binary optimizations arise naturally in many contexts that involve optimization of efficiency measures (e.g., maximizing the ratio of return/investment or profit/time and minimizing the ratio of cost/time, see [10,27,32,34]), averages, probabilities and percentages, among others. Fractional optimization models can be found in diverse application areas including problems in data mining (such as feature selection [17,26] and biclustering [12,37]), scheduling [31], retail assortment [13,25,35], set covering [2,3], facility location [36], stochastic service systems [15], finding alternative solutions to binary linear programs [38], clinical trials [7], and so on. For an overview of applications and solution methods for FPs we refer to a recent survey in [10].…”

“…In order to attain (ii), in Sect. 3 we show how to use binary expansions (emanated from MILPs) in MICQP formulations; and how to use conic strengthening (originally proposed in the context of CEF) and polymatroid cuts (originated from CF P ) to strengthen the formulations. More importantly, we show how to incorporate binary expansions and polymatroid strengthening in a single (either MILP or MICQP) formulation.…”

“…For our test instances, we generate the data as in the assortment optimization problem considered in [33]. Specifically, the product prices are the same across the customer classes, i.e., r i j = r j for all i ∈ I and drawn from a U [1,3] distribution. Moreover, the preferences μ i j are drawn from a U [0, 1] distribution, and μ i0 = 5 for all i ∈ I .…”

On Robust Fractional 0-1 Programming

“…Many diverse applications can be readily formulated as FP. Such applications encompass scheduling (Saipe 1975), retail assortment (Subramanian and Sherali 2010, Davis et al 2014, Méndez-Díaz et al 2014, set covering (Amaldi et al 2011(Amaldi et al , 2012, facility location (Tawarmalani et al 2002), stochastic service systems (Elhedhli 2005, Han et al 2013, biclustering (Busygin et al 2005, Trapp et al 2010, finding diverse solutions to binary linear programs (Trapp and Konrad 2015), cell formation problems (Bychkov et al 2014, Pinheiro et al 2018, and clinical trials (Bertsimas et al 2019). Additionally, specialized techniques have been proposed for special cases of FP, including the minimum fractional spanning tree problem (Ursulenko et al 2013), the minimum cost-to-time cycle problem (Dasdan et al 1999), the maximum mean cut problem (McCormick and Ervolina 1994), the minimum fractional assignment problem (Shigeno et al 1995), and the maximum clique ratio problem (Moeini 2015, Sethuraman andButenko 2015).…”

AP Deployment Research Based on Physical Distance and Channel Isolation

“…Aiming at AP channel interference problems, there have been some research results, most of which are mainly through the graph coloring [1], integer linear programming [2], and heuristic method [3] for allocating channels for APs in ISM (industrial, scientific, medical) band to make the whole interference minimum. Reference [4] uses the cognitive radio technology, combined with the service condition of the primary users' band, to allocate accessible primary users' channels for AP.…”