CONTROLADOR DE CARGA

The neural network components within the hybrid solution to the British Airways cargo consignment problem consisted of three standard Back-propagation neural networks [92], one each for Auckland, Melbourne and Sydney destinations. The network simulator used to build these networks was described in Chapter 5. The neural networks were used to learn the mapping between previous cargo consignment details and the final decision of the cargo acceptance officers. The networks were used to build a profile of cargo acceptance and rejection for a particular route, so that they could be used to make decisions about new requests based on previous trends.

6.10.1. Data Preparation, Scaling, and Network Topology

Much of the success of neural networks has been due to their ability to learn from raw data. The importance of pre-processing the raw data is often forgotten but can make the difference between a network that trains in five days and performs quite well and a network that trains in five minutes and performs very well.

As explained earlier, the British Airways data had insufficient information per flight to build profiles or forecasts of demand or build up a picture of how space is utilised for each individual flight before departure. This meant that neural networks had to be trained at the destination level, not the more detailed flight level. Therefore the aim was to train three neural networks on the previous cargo acceptance/rejection characteristics of the three most popular routes (Auckland, Melbourne and Sydney).

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From the original BA data three data sets for Auckland, Melbourne and Sydney were separated. These data sets were constructed because each destination may have individual characteristics. These were pre-processed to remove duplicates and any outliers in the data. From these data sets the training and validation sets were chosen for each neural network. The training set contained representative members and the actual output to be trained upon for all possible decision classes (i.e. representatives of accepts and rejects). Within each class an adequate variation was included. The validation set is also drawn from the same population as the training set but is not used for training but for validating the results of training. Due to the small number of rejects in each route, the training and validation sets were small (ideally they should be larger). The Auckland network training data consisted of 100 training requests and 22 for validation, the Melbourne network consisted of 74 training and 21 validation and the Sydney network had 96 training and 21 validation requests. For all destinations, the training and validation sets consisted of 50% accepts and 50% rejects.

Both the training and validation sets were scaled because the desired output must be within a range realisable by the activation function used within the Back-propagation network. As the logistic activation function f ( x ) =--- — is used in the feedforward

1 + g

neural networks, output activation limits should be 0.9 and 0.1 respectively. In theory the inputs need not be scaled, but stability of the network is improved by using comparable limits. Also uniform scaling will also equalise the importance of input variables. A linear scaling was used to map the variable’s (input and desired output) practical extremes to the networks practical extremes (0.1 to 0.9). To scale a variable V to a value A, the simple formula below was used [641:

= r V + (A„i„

where r = —^ ---— and and the maximum and minimum values of input

% nax % nin

variables and the Aj^j^ the practical limits of the neural network (0.9 and 0.1 ) respectively. The validation set was also scaled using the same values for

the training set. This was done to achieve a uniform input range for the networks. This scaling was also performed within the rules of the expert system (for each route network), so that cargo consignment inputs could be passed to the networks appropriately scaled.

The topology of the network (i.e. the number of input, hidden and output nodes) was determined by the input variables, the number of decision classes and monitoring the

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training and validation errors in the case of hidden nodes. The input layer contained 6 nodes, one for each of the following inputs: available weight, available volume, consignment weight, consignment volume, rate difference (consignment rate - standard rate) and the days until the flight. As the output decision is a binary classification of Accept or Reject there is only one output node. Where an activation of 0.9 represents Accept and 0.1 represents Reject.

The selection of hidden nodes is an important aspect of the design of a neural network. The activity patterns in the hidden nodes or “leamed-feature detectors” [111] is an encoding of what the network determines are significant features of the data. With too many hidden nodes, a network can simply memorise the correct response to each pattern in its training set, instead of learning a general solution. By limiting the size of the hidden layers, the network is forced to develop appropriate feature detectors to efficiently classify large sets of input patterns. These general-purpose feature detectors are more likely to correctly classify new inputs, and therefore the network would perform better.

There are many “rules of thumb” and trail by error procedures for determining the required number of hidden layers [40, 111, 64]. The procedure used was one of starting with a small number of hidden nodes and evaluating the performance against the validation set. Then adding one more node and re-evaluating the performance until no improvement could be made. This is the procedure recommend by Masters [64] to find the best number of hidden nodes. The final number of nodes that gave the best performance was 5 hidden nodes. The final network topology was 6 input nodes, 5 hidden node and 1 output node.

The networks were then trained using the supervised back-propagation learning algorithm, with the initial weights set between -0.5 and +0.5, learning rate set to 0.1 and momentum set to 0.9. These parameters were not experimented with but were chosen from the results of other researchers [92] who found they produced good results for back- propagation networks.

Table 6.3 shows the final results of the percentage of correct classification for the training and validation set for the three route networks.

Chapter 6 Hybrid Applications 107 Percentage Correct on Training Set Percentage Correct on Validation Set Auckland Network 97% 81.81% Melbourne Network 95% 69% Sydney Network 96% 72.6%

Table 6.3 — Final results showing the performance of the three route networks. As an experiment to see if the different routes had different cargo acceptance characteristics, the test set for the Auckland network was tested on the Melbourne and the Sydney networks. The Auckland test data on the Melbourne network scored 67% where as on the Sydney network, it scored only 60% correct. These results showed a marked drop in performance from the normal score for the network, which could point to there being route specific characteristics for accepting and rejecting cargo requests.