No abstract

The traditional dimensionality reduction methods can be generally classified into Feature Extraction (FE) and Feature Selection (FS) approaches. The classical FE algorithms are generally classified into linear and nonlinear algorithms. Linear algorithms such as Principal Component Analysis (PCA) aim to project high dimensional data to a lower-dimensional space by linear transformations according to certain criteria. The central idea of PCA is to reduce the dimensionality of the data set consisting of a large number of variables. In this paper, PCA was used to reduce the dimension of flow shop scheduling problems. This mathematical procedure transforms a number of (possibly) correlated jobs into a smaller number of uncorrelated jobs called principal components, which are the linear combinations of the original jobs. These jobs are carefully determined so that from the solution of the reduced problem multiple solutions of the original high dimensional problem can readily be obtained, or completely characterized, without actually listing the optimal solution(s). The results show that by fixing only some critical jobs at the beginnings and ends of the sequence using Johnson's method, the remaining jobs could be arranged in an arbitrary order in the remaining gap without violating the optimality condition that also guarantees minimum completion time. In this regard, Johnson's method was relaxed by terminating the listing of jobs at the first/last available positions when the job with minimum processing time on either machine attains the highest processing time on the other machine for the first time. By terminating Johnson's algorithm at an early stage, the method minimizes the time needed for sequencing those jobs that could be left arbitrarily. By allowing these jobs to be arranged in arbitrary order it gives job sequencing freedom for job operators without affecting minimum completion time. The results of the study were originally obtained for deterministic scheduling problems but they are more relevant on test problems randomly generated from uniform distribution  with lower bound  and upper bound  and normal distribution  with mean  and standard deviation .

Reservoir operation studies purely based on the storage level, inflow, and release decisions during dry periods only fail to serve the optimal reservoir operation policy design because of the fact that the release decision during this period is highly dependent on wet season water conservation and flood risk management operations. Imperatively, the operation logic in the two seasons are quite different. If the two operations are not sufficiently coordinated, they may produce poor responses to the system dynamics. There are high levels of uncertainties on the model parameters, values and how they are logically operated by human or automated systems. Soft computing methods represent the system as an artificial neural network (ANN) in which the input- output relations take the form of fuzzy numbers, fuzzy arithmetic and fuzzy logic (FL). Neuro-Fuzzy System (NFS) soft computing combine the approaches of FL and ANN for single purpose reservoir operation. Thus, this study proposes a Bi-Level Neuro-Fuzzy System (BL-NFS) soft computing methodology for short and long term operation policies for a newly inaugurated irrigation project in Gidabo Watershed of Main Ethiopian Rift Valley Basin. Keywords: Bankruptcy rule, BL-NFS, Reservoir operation, Sensitivity analysis, Soft computing, Water conservation.