Dynamic Programming as a Scheduling Tool in Multiprogrammed Computing Systems

<p>A potentially parallel iterative algorithm for the solution of the unconstrained N-stage decision problem of Dynamic Programming is developed. This new solution method, known as Variable Metric Dynamic Programming, is based on the use of variable metric minimisation techniques to develop quadratic approximations to the optimal cost function for each stage. The algorithm is applied to various test problems, and a comparison with an existing similar algorithm proves favourable. The Variable Metric Dynamic Programming solution method is used in the implementation of an adaptive highlevel scheduling mechanism on a multiprogrammed computer in a university environment. This demonstrates a practical application of the new algorithm. More importantly, the application of Variable Metric Dynamic Programming to a scheduling problem illustrates how Mathematical Programming may be used in complex computer scheduling problems to provide in a natural way the required dynamic feedback mechanisms.</p>

Dynamic Programming as a Scheduling Tool in Multiprogrammed Computing Systems

<p>A potentially parallel iterative algorithm for the solution of the unconstrained N-stage decision problem of Dynamic Programming is developed. This new solution method, known as Variable Metric Dynamic Programming, is based on the use of variable metric minimisation techniques to develop quadratic approximations to the optimal cost function for each stage. The algorithm is applied to various test problems, and a comparison with an existing similar algorithm proves favourable. The Variable Metric Dynamic Programming solution method is used in the implementation of an adaptive highlevel scheduling mechanism on a multiprogrammed computer in a university environment. This demonstrates a practical application of the new algorithm. More importantly, the application of Variable Metric Dynamic Programming to a scheduling problem illustrates how Mathematical Programming may be used in complex computer scheduling problems to provide in a natural way the required dynamic feedback mechanisms.</p>

Shipping pattern may be altered according to available refining capacity

Alternate optimal solutions in the mathematical programming solution of a real-world problem are rare, unless there are multiple objective functions. In a recent application of 2 mathematical programming solvers to a problem of crude oil logistics, I obtained 2 different optimal solutions. The almost optimal solutions obtained from the convex combinations of the 2 optimal solutions, are feasible as real transportation choices, if the optimal solutions cannot be implemented. It was observed that the 2 solutions led to different capacity utilization at the refineries downstream, and so do the many solution alternatives. This is useful information for the petroleum company during downtime for maintenance or capacity expansion.

Estimation of aerator air demand by an embedded multi-gene genetic programming

A spillway discharging a high-speed flow is susceptible to cavitation damages. As a countermeasure, an aerator is often used to artificially entrain air into the flow. Its air demand is of relevance to cavitation reduction and requires accurate estimations. The main contribution of this study is to establish an embedded multi-gene genetic programming (EMGGP) model for improved prediction of air demand. It is an MGGP-based framework coupled with the gene expression programming acting as a pre-processing technique for input determination and the Pareto front serving as a post-processing measure for solution optimization. Experimental data from a spillway aerator are used to develop and validate the proposed technique. Its performance is statistically evaluated by the coefficient of determination (CD), Nash–Sutcliffe coefficient (NSC), root-mean-square error (RMSE) and mean absolute error (MAE). Satisfactory predictions are yielded with CD = 0.95, NSC = 0.94, RMSE = 0.17 m3/s and MAE = 0.12 m3/s. Compared with the best empirical formula, the EMGGP approach enhances the fitness (CD and NSC) by 23% and reduces the errors (RMSE and MAE) by 48%. It also exhibits higher prediction accuracy and a simpler expressional form than the genetic programming solution. This study provides a procedure for the establishment of parameter relationships for similar hydraulic issues.