This paper derives key equations for the determination of optimal control strategies in an important engineering application. A train travels from one station to the next along a track with continuously varying gradient. The journey must be completed within a given time and it is desirable to minimise fuel consumption. We assume that only certain discrete throttle settings are possible and that each setting determines a constant rate of fuel supply. This assumption is based on the control mechanism for a typical diesel-electric locomotive. For each setting the power developed by the locomotive is directly proportional to the rate of fuel supply. We assume a single level of braking acceleration. For each fixed finite sequence of control settings we show that fuel consumption is minimised only if the settings are changed when certain key equations are satisfied. The strategy determined by these equations is called a strategy of optimal type. We show that the equations can be derived using an intuitive limit procedure applied to corresponding equations obtained by Howlett [9,10] in the case of a piecewise constant gradient. The equations will also be derived directly by extending the methods used by Howlett. We discuss a basic solution procedure for the key equations and apply the procedure to find a strategy of optimal type in appropriate specific examples.
A train travels from a station to the next along tracks with gradient and speed limits. The journey must be completed within a given time, and it is desirable to minimise energy consumption. In this paper, we use the fuel consumption model and pay attention to different algorithms with some numerical examples.
Protein–protein interactions (PPIs) play key roles in most cellular processes, such as cell metabolism, immune response, endocrine function, DNA replication, and transcription regulation. PPI prediction is one of the most challenging problems in functional genomics. Although PPI data have been increasing because of the development of high-throughput technologies and computational methods, many problems are still far from being solved. In this study, a novel predictor was designed by using the Random Forest (RF) algorithm with the ensemble coding (EC) method. To reduce computational time, a feature selection method (DX) was adopted to rank the features and search the optimal feature combination. The DXEC method integrates many features and physicochemical/biochemical properties to predict PPIs. On the Gold Yeast dataset, the DXEC method achieves 67.2% overall precision, 80.74% recall, and 70.67% accuracy. On the Silver Yeast dataset, the DXEC method achieves 76.93% precision, 77.98% recall, and 77.27% accuracy. On the human dataset, the prediction accuracy reaches 80% for the DXEC-RF method. We extended the experiment to a bigger and more realistic dataset that maintains 50% recall on the Yeast All dataset and 80% recall on the Human All dataset. These results show that the DXEC method is suitable for performing PPI prediction. The prediction service of the DXEC-RF classifier is available at .
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