The deployments of Environmental Sensor Networks (ESN) is an interesting research area in which a particular algorithm (spatial samplingmethod) is used to obtain optimal placements of nodes within the RoI. As already mentioned in the previous chapter (Chapter 2, Section 2.1), a number of techniques have been investigated to address this problem, and yet, no optimal method is applicable and appropriate in all circumstances. Therefore, a new spatial- sampling technique is utilised based on Evolutionary Algorithm (EA) in this dissertation to build a near-optimal ESN [10]. EA mimics the procedure of the biological mechanism such as reproduce, cross over, mutation, recombination, and elitism, that maximise or minimise a user-definedfitness functionin order to reach a near-optimal solution.
3.2.1
Problem Statement
Distinct types of static sensor nodes are denoted as: SNi={sni,1,sni,2,· · ·,sni,n,· · ·,sni,N}
withi=item={hive,f ood,water,corner}to represent bee hive, food source, water source, and weather stations located at the map’s corners (top-left, top-right, bottom-left, and bottom- right) respectively. We can also denote nodes within entire networks usingSN={sn:sn∈ SNhive∪SNf ood∪SNwater∪SNcorner}.
Furthermore, for the purpose of this work, a constraint is being introduced for the optimisation algorithm so that the sensor nodes placements to be optimised (SNhive) are
located within the ‘convex hull’ generated bySNf ood∪SNwater (Figure 3.7). This assumption is made in order to concentrate the bee hives in the middle-part of the RoI and to reduce the probability of insects flying around the map’s border. Therefore, a solution will be invalid if one or more optimised sensor nodes (hives) is located outside of the convex hull (a grey area in Figure 3.7).
Fig. 3.7 Illustration of the ‘convex hull’ generated bySNf ood∪SNwater (white area), in which theSNhive is allowed to be optimised within. The squares are: weather stations at the map’s corners (brown), food (green) and water (blue) sources respectively; whilst the triangle denotes the locations of bee hives to be optimised.
3.2 Optimisation Algorithm - ESN Deployments 37
3.2.2
Chromosome Design
Chromosome (also called an ‘individual’ in EA) design is an important step in the develop- ment of any optimisation EA technique in order to represent a single solution so that it is assessable for quality evaluation using the so-called f itnessfunction.
Fig. 3.8 A chromosome encoding and decoding example that consists of only the hive nodes which are to be optimised.
LetSNchrom={sn:sn∈SNhive}be a set of sensor node locations encoded as a chromo- some for optimisation purposes. It stores a list of integers with theN=N(SNchrom)elements, where each item ranges from 0 to 15250 (a total of 101×151=15251 grids/cells through- out the RoI). In order to obtain the exact spatial location (x and y) within the landscape (chromosome decoding), we use the following:
loc(csn) = x=snnmod 151 y=snn÷151 (3.1)
An example is shown in Figure 3.8 to illustrate the procedure. Then, a f itnessfunction is used for quality assessment of a single chromosome in the following sub-section.
3.2.3
Fitness Function
The main motivation of the fitness function calculation is based on the fact that spatial interpolation is often criticised for an inability to estimate extreme values [84]. For example, within a mountainous region, if we only deploy the sensor nodes within the lower ground of the landscape (the foothills in this case), no interpolation method is capable of estimating the temperature values on the mountain’s peak. Thus, the main objectives of the fitness function are focusing on the following:
• To capture therepresentativenodes within the RoI, such that extreme low and high values are represented. Here, ‘representativeness’ is defined as the ability of an interpolator to best estimate the condition of a particular environmental parameter of the RoI at a later stage (given a pre-defined number of nodes for optimisation).
38 Methodology
• To minimiseredundantnodes. The term ‘redundant’ in this case refers to those points that are able to be estimated by the interpolation method with less statistical error (e.g. RMSE);
• Create asparselydistributed network of sensor nodes. In addition to the objectives given above, a dispersed sensor network design is also preferred.
A statistical error measurement method is exploited; Leave-One-Out Cross-Validation (LOCCV), in conjunction with spatial interpolation method to obtain the critical points over the landscape. The ‘critical’ points are defined as the representative sensor nodes placed in such a way that each node’s observation is unable to be restored (estimated) using a conventional interpolation technique; In other words, the absence of any node would degrade the representativeness of the entire sensor network:
LOCCV(fˆ) = s 1 N N
∑
n=1 (ychrom,n−fˆ(−n)(x chrom,n))2 (3.2)where ˆf is a particular interpolation technique;Nis the total number of nodes withinSNchrom; ynis the observed value atSNchrom,n; and ˆf(−n)(xchrom,n)is the estimated value of xchrom,n
using ˆf method using the sensor nodes of food sources, water source, and the hives (nodes to be optimised) withnth node absent (i.e.(SNf ood∪SNwater∪SNhive)\SNhive,n). Also, note
that theLOOCV is only calculated fromSNchrom.
The f itnessfunction within the optimisation process is calculated by maximising the following equation:
f itness = LOCCV(fˆ)×sparsity
= LOOCV(fˆ)×min{pdist(SNf ood∪SNwater∪SNchrom)} (3.3) where the network’s sparseness is estimated by obtaining the minimal pairwise distance (pdist) between the sensor nodes: SNf ood∪SNwater∪SNchrom.