A nondominated sorting genetic algorithm III with three crossover strategies for the combined heat and power dynamic economic emission dispatch with or without prohibited operating zones

This paper presents a nondominated sorting genetic algorithm III with three crossover strategies (NSGA-III-TCS) for the combined heat and power dynamic economic emission dispatch (CHPDEED) problems with or without prohibited operating zones. The first strategy updates the individuals of the first nondomination rank by a modified improvisation of the harmony search algorithm, which accelerates the information exchanges of the elite individuals. The second strategy regulates the individuals of the last nondomination rank according to a modified single-point crossover of the genetic algorithm, which strengthens the convergence of the population. The third strategy adjusts the remaining individuals in terms of a modified DE/rand-to-best/1 mutation of the differential evolution algorithm, and it guides these individuals to move towards the ones which have at least one minimum objective function value, which is beneficial for expanding the distribution range of the population. NSGA-III-TCS obtains the largest average hypervolumes and shows a desirable convergence for six CHPDEED problems. NSGA-III-TCS achieves relatively high coverage rates in most cases, indicating the dominance of the Pareto sets of NSGA-III-TCS over those of the other algorithms. Also, it has relatively low average spacings for all problems, suggesting the good evenness of the Pareto sets.