Experimental Comparisons of Metaheuristic Algorithms in Solving Combined Economic Emission Dispatch Problem Using Parametric and Non-Parametric Tests

Abstract

In this paper, the parametric and non-parametric statistical tests are applied for comparisons of metaheuristic algorithms’ (MAs) behavior in solving Combined Economic Emission Dispatch (CEED) problem. In the last years, in many published papers, a large number of MAs have been proposed to solve CEED problem of different dimensions consisting of different objective functions. In this paper, the statistical tests are applied over samples of results obtained for eight objective functions of CEED problem using the four MAs: Firefly Algorithm, Moth Swarm Algorithm, Adaptive Wind Driven Optimization and Particle Swarm Optimization-Gravitational Search Algorithm. The standard IEEE 30-bus six-generator test system is used. The statistical tests are applied over results obtained for each function and over results obtained for all eight functions simultaneously. The analysis of the results of statistical tests over a single function shows that one MA statistically behaves differently for different functions and one MA is not the best for each function of CEED problem. Therefore, more MAs are more acceptable than one MA for solving a specified CEED problem. However, the analysis of the results of statistical tests over all functions simultaneously shows that all four MAs statistically behave in the same way.