A Genetic Algorithm tweak for result improvement in inverse optimization problems

Abstract

The decrease of global greenhouse gas (GHG) emissions is one of the ways to contain global warming. Through Anaerobic Digestion (AD) organic effluents are transformed into biomass and, in the process, biogas (methane and carbon dioxide) is released. Methane, with a higher GHG potential than CO2, is an important contributor to climate change. Therefore, the controlled use of microbes to synthetize organic material and minimize the methane release to the atmosphere with the subsequent methane capture and reutilization is one attractive choice in industries with large organic waste production. Different models were developed to simulate AD. The most common are nonlinear dynamic systems composed of a set of ordinary differential equations. They differ in the number of processes considered. In order to have a valid model, so it can be used for control purposes, for example, the dynamical model parameters require an estimation. For that reason, an Inverse Optimization (IO) must be performed. Due to the simplicity, flexibility and global search efficiency of Genetic Algorithms (GA) they are largely used in different research areas. However, the conventional implementation of Genetic Algorithms, called here Basic Genetic Algorithms (BGA), faces some difficulties in solving this kind of IO problem. To deal with these problems, a tweak to the BGA is proposed, the Neighbored Genetic Algorithm (NGA). In the newly proposed NGA method, one or more subjects within the population are selected for use in an inner loop of the algorithm. In this loop, those subjects will randomly generate a subpopulation, with a specific number of individuals, from a normal distribution (or other), whose mean is the value of the selected subject. The best subject of this subpopulation will replace the one that generated him, if he is fitter. This will, in principle, enhance the chances of getting new subpopulations closer to the solution. To validate and test the proposed model, a benchmark function (Goldstein-Price) was used. In this case, the NGA method converged in 99% of the runs, while the BGA method only converged in 38% of the cases. Finally, simulated data for methane production were used in the calibration of the AD model. In this IO problem, both BGA and NGA were run 100 times in order to compare their performance. After 10 000 iterations, the cost function values for the BGA and NGA models were 8×10-3 and 1×10-4, respectively. Even though the new approach has proved to be computationally more expensive per iteration, a lower cost function value with less computational time was consistently found in the 100 tests performed when the NGA method was used.