Modified Differential Evolution Algorithm Applied to Economic Load Dispatch Problems

Abstract

This paper proposes a modification of the Differential Evolution (DE) algorithm to solve the problem of Economic Load Dispatch (ELD). DE is an algorithm based on the theory of natural selection of species, where the fittest are more likely to survive. In the original DE, each possible solution to the target problem composes an initial population. This population evolved through genetic operators of mutation, selection, and crossover of individuals. In each iteration of the DE, the newly generated population replaces and discards the old population input. At the end of execution, the DE should return the best solution found. The Modification of the Differential Evolution (MDE) present in this paper considers that, in the selection stage, the ablest individual will replace the old one in the current population instead of being inserted in the new sample. To verify the performance of the MDE about the original DE, we solve a set of test functions to obtain the global minimum and different instances of the ELD. Both algorithms were effective in minimizing the three least-dimensional functions. Our results showed that DE proved more effective than MDE in minimizing the set of higher dimensional test functions, presenting a solution up to 99.99% better. However, none of the algorithms managed to obtain the optimal solution. In the ELD resolution, where it is to find the production level of each thermoelectric generating unit, satisfying the total system demand at the lowest cost, MDE was more effective than DE in all cases, finding a solution up to 1.10% better, solving the constraints of the problem. In addition, the computation time reduction of MDE concerning DE was up to 95.98%. Therefore, we confirm the efficiency of the proposed modification over the original DE version.