Optimizing Selection of Technologies in a Multiple Stage, Multiple Objective Wastewater Treatment System

In this paper, a multiple stage wastewater treatment system (WTS) is solved for the selection of technological options at each stage to minimize (economic cost, size, odour emissions) and to maximize (nutrient recovery, robustness, global desirability). Stages in the wastewater treatment system are the levels of treatment. There are 17 levels of treatment, where the first 11 levels are for the liquid treatment and the last 6 levels are for the solid treatment. This results in a 20-dimensional, continuous-state, 17-stage, 6-objective, stochastic optimization problem. The resulting multiple stage, multiple objective (MSMO) WTS is solved using the three-phase methodology in conjunction with the multiple objective version of high-dimensional, continuous-state, stochastic dynamic programming (SDP). The three-phase methodology comprises the input phase, the matrix generation phase and the weighting phase. The primary goal of three-phase methodology is to obtain weight vectors at each stage of the WTS utilizing expert's opinions in the input phase, computing pairwise comparison matrices at each stage using the geometric mean-based methods in the matrix generation phase, and then calculating weight vectors at each stage using the eigenvector method in the weighting phase. The weight vectors are then used to scalarize the vector optimization problem, which is solved using the high-dimensional, continuous-state SDP augmented for handling multiple objectives at each stage. The results obtained are practical as evidenced by the selection of new technologies in levels 1 and 5 thereby validating expert's decision to include them in the evaluation process. In addition to encouraging reviews from WTS experts, the implementation results satisfy a set of external constraints in the form of interstage dependencies between technological options in the WTS. Furthermore, the solution technique presented here utilizes expert's opinions in the solution development process, and is quite general in its application to a variety of large-scale MSMO problems.