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Distributed optimization in wireless sensor networks: an island-model framework

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Abstract

Wireless sensor networks (WSNs) is an emerging technology in several application domains, ranging from urban surveillance to environmental and structural monitoring. Computational intelligence (CI) techniques are particularly suitable for enhancing these systems. However, when embedding CI into wireless sensors, severe hardware limitations must be taken into account. In this paper we investigate the possibility to perform an online, distributed optimization process within a WSN. Such a system might be used, for example, to implement advanced network features like distributed modelling, self-optimizing protocols, and anomaly detection, to name a few. The proposed approach, called DOWSN (distributed optimization for WSN) is an island-model infrastructure in which each node executes a simple, computationally cheap (both in terms of CPU and memory) optimization algorithm, and shares promising solutions with its neighbors. We perform extensive tests of different DOWSN configurations on a benchmark made up of 15 continuous optimization problems; we analyze the influence of the network parameters (number of nodes, inter-node communication period and probability of accepting incoming solutions) on the optimization performance. Finally, we profile energy and memory consumption of DOWSN to show the efficient usage of the limited hardware resources available on the sensor nodes.

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Notes

  1. The Q16.16 notation indicates that 16 digits are used for the fractional part and 16 for the integer part of the number. The representable range is \([-32768.0,32767.999985],\) with a precision of \(1/65536=0.000015.\) libfixmath provides an overflow detection mechanism which allows developers to check the correctness of operations.

  2. It should be noted that the packet structure used by the RIME protocol stack imposes an upper bound of 128 bytes for the payload, which in turns limits the maximum amount of information that can be exchanged among nodes. Considering this limit, a maximum number of \(128/4=32\) Q16.16 fixed-point values can be reliably transferred over RIME. Since each packet exchanged in DOWSN contains an n-dimensional array encoding an individual and its fitness (also in Q16.16 format), the upper limit for problem dimension in DOWSN is 31. To overcome this limitation and handle solutions of higher dimensional optimization problems, an application-level protocol should be implemented on top of RIME.

  3. COOJA is a cross-level simulator for Contiki which allows for simultaneous simulation at network, OS and machine code level. It includes several post-processing plugins, e.g. to estimate the power consumption on each node based on a simple energetic model.

  4. In a real WSN deployment, these data might be collected on the data flash memory on the motes and then analyzed for post-processing. Another option would be a “sink” node connected to a PC: in this scenario, the sink would listen periodically to broadcast packets in order to provide the user, in real-time, the global output.

  5. Recalling that the standard error of the mean of a n-dimensional sample whose variance is \(\sigma \) is \(\sigma /\!\sqrt{n},\) and applying the central limit theorem to approximate the sample mean with a normal distribution, it follows that a sample size \(n=16\sigma ^2/ W^2\) guarantees a 95 % confidence interval of width \(W.\)

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Acknowledgments

INCAS\(^{3}\) is co-funded by the Province of Drenthe, the Municipality of Assen, the European Fund for Regional Development and the Ministry of Economic Affairs, Peaks in the Delta.

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  1. INCAS3, Innovation Centre for Advanced Sensors and Sensor Systems, P. O. Box 797, 9400 AT , Assen, The Netherlands

    Giovanni Iacca

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Correspondence to Giovanni Iacca.

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Communicated by G. Acampora.

Appendix: Test problems

Appendix: Test problems

The test problems listed in Table 14 have been considered in this study. For each problem, the decision space was set to \(\mathbf{D}=\left[ -2.0,2.0\right] ^{n}\), where \(n\) is the problem dimensionality. As shown in Table 14, the testbed is composed of \(15\) fitness functions with different properties in terms of modality and separability.

Table 14 Test problems
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Iacca, G. Distributed optimization in wireless sensor networks: an island-model framework. Soft Comput 17, 2257–2277 (2013). https://doi.org/10.1007/s00500-013-1091-x

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