Optimizing both investment and operational costs of a water treatment network: that is the goal of the challenge. This industrial concern implies solving a particularly complicated Mixed-Integer Nonlinear Program (MINLP).
The solution proposed by Artelys uses Xpress-Optimizer and Artelys Knitro as solvers and is modelled in AMPL. It exploits relaxations of bilinear constraints and consists of an iterative algorithm where these relaxations are refined at each step where necessary. This method provides very good solutions in short computation time on most of the instances, leading Artelys to the 1st place of the competition.
The solution developed by Artelys solves instances made of up to 15 process/treatment units, 10 water sources/destination and 10 contaminants (~10k variables in total) in less than an hour.
The figure shows a toy-model network made of 1 water source, 2 industrial process units and 2 treatment units. The goal is to define the optimal routing of water pipelines within the plant, and schedule continuous and batch water processing operations over a cyclic time horizon.