Optimal design of an in-situ bioremediation system using support vector machine and particle swarm optimization

A methodology based on support vector machine and particle swarm optimization techniques (SVM-PSO) was used in this study to determine an optimal pumping rate and well location to achieve an optimal cost of an in-situ bioremediation system. In the first stage of the two stage methodology suggested for optimal in-situ bioremediation design, the optimal number of wells and their locations was determined from preselected candidate well locations. The pumping rate and well location in the first stage were subsequently optimized in the second stage of the methodology. The highly nonlinear system of equations governing in-situ bioremediation comprises the equations of flow and solute transport coupled with relevant biodegradation kinetics. A finite difference model was developed to simulate the process of in-situ bioremediation using an Alternate-Direction Implicit technique. This developed model (BIOFDM) yields the spatial and temporal distribution of contaminant concentration for predefined initial and boundary conditions. BIOFDM was later validated by comparing the simulated results with those obtained using BIOPLUME III for the case study of Shieh and Peralta (2005). The results were found to be in close agreement. Moreover, since the solution of the highly nonlinear equation otherwise requires significant computational effort, the computational burden in this study was managed within a practical time frame by replacing the BIOFDM model with a trained SVM model. Support Vector Machine which generates fast solutions in real time was considered to be a universal function approximator in the study. Apart from reducing the computational burden, this technique generates a set of near optimal solutions (instead of a single optimal solution) and creates a re-usable data base that could be used to address many other management problems. Besides this, the search for an optimal pumping pattern was directed by a simple PSO technique and a penalty parameter approach was adopted to handle the constraints in the PSO. The results showed that the costs involved in the proposed management solution were consistent with that resulting from other nontraditional optimization techniques which use embedded/linked bioremediation simulation models. Moreover, an optimal transient pumping strategy resulted in an overall reduction in pumping cost by almost 20% when compared to cases where a steady state pumping strategy was adopted. A considerable reduction in the number of simulations was achieved using the SVM approach.