Demonstrating the Applicability of PAINT to Computationally Expensive Real-life Multiobjective Optimization

Abstract

We demonstrate the applicability of a new PAINT method to speed up iterations of interactive methods in multiobjective optimization. As our test case, we solve a computationally expensive non-linear, five-objective problem of designing and operating a wastewater treatment plant. 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 problem. We develop an IND-NIMBUS(R) PAINT module to combine the interactive NIMBUS method and the PAINT method and to find a preferred solution to the original problem. With the PAINT method, the solution process with the NIMBUS method take a comparatively short time even though the original problem is computationally expensive.