Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

Abstract

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Pöyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to speed up the iterations of the NIMBUS method. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original wastewater treatment problem. With the mixed integer surrogate problem, the time required from the decision maker is comparatively short. In addition, a new IND-NIMBUS ® PAINT module is developed to allow the smooth interoperability of the NIMBUS method and the PAINT method.

Multiplicity of solutions in model-based multiobjective optimization of wastewater treatment plants

“…For instance, Fu et al [20] compared the results of the optimization or urban wastewater systems using NSGA-II and ParEGO, a surrogate model-based multi-objective optimization algorithm [30]. More recently, Hartikainen et al [24] implemented the approximation method PAINT within an interactive optimization platform to construct computationally inexpensive surrogate problems for the original wastewater treatment problem.…”

“…This approach is related to the concepts introduced by Lewis et al [31] that explore the idea of dynamic s-Pareto frontiers and preferences, or by Vallerio et al [47], which consider operational risks and uncertainties as additional objectives to solve multi-objective optimization problems of nonlinear dynamic processes. The idea of simulating possible realistic scenarios in a multiobjective formulation could be compatible with the interactive optimization platforms to analyze WWTP optimization problems proposed in recent years [22,24].…”

Interactive decision support and trade-off analysis for sustainable forest landscape planning under deep uncertainty

“…Interactive methods save computation resources and reduce cognitive load by focusing only on solutions that are interesting to the DM. Interactive methods have proved their potential for multiobjective decision support in different environmental and forest management 3 1 INTRODUCTION applications (e.g., Tecle et al, 1994;Hartikainen et al, 2015Hartikainen et al, , 2016Eyvindson et al, 2018;Saccani et al, 2020).…”

Agent assisted interactive algorithm for computationally demanding multiobjective optimization problems

“…The solution process was carried out with the implementations of agents, NIMBUS and PAINT contained in the IND-NIMBUS software framework where the DM used a graphical user interface. For further implementation details of the two methods, see [11,8], respectively.…”

“…These problem include optimal control of a continuous casting of steel [4,5], intensity modulated radiotherapy treatment planning [6], optimizing congurations of an oxyfuel power plant process [7], operating wastewater treatment plant [8,9], optimal design and control of a paper mill [10], among others. For more examples of use of interactive methods in various elds see [11] and references therein.…”