Using a Genetic Algorithm to Solve a Bi-Objective WWTP Process Optimization

When modeling an activated sludge system of a wastewater treatment plant (WWTP), several conflicting objectives may arise. The proposed formulation is a highly constrained bi-objective problem where the minimization of the investment and operation costs and the maximization of the quality of the effluent are simultaneously optimized. These two conflicting objectives give rise to a set of Pareto optimal solutions, reflecting different compromises between the objectives. Population based algorithms are particularly suitable to tackle multi-objective problems since they can, in principle, find multiple widely different approximations to the Pareto-optimal solutions in a single run. In this work, the formulated problem is solved through an elitist multi-objective genetic algorithm coupled with a constrained tournament technique. Several trade-offs between objectives are obtained through the optimization process. The direct visualization of the trade-offs through a Pareto curve assists the decision maker in the selection of crucial design and operation variables. The experimental results are promising, with physical meaning and highlight the advantages of using a multi-objective approach. 1 Multi-objective Optimization We apply the Multi-objective Elitist Genetic Algorithm (MEGA), described in [3] to the WWTP multi-objective optimization problem. This approach, in contrast to other algorithms, does not require any differentiability or convexity conditions of the search space. Moreover, since it works with a population of points, it can find, Lino Costa · Isabel A. C. P. Espı́rito-Santo · Edite M. G. P. Fernandes Department of Production and Systems, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal e-mail: {lac,iapinho,emgpf}@dps.uminho.pt Roman Denysiuk Algoritmi R&D Center, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal email: [email protected]