L-SHADE optimization algorithms with population-wide inertia

Numerous Differential Evolution algorithms (DE) have been proposed during last twenty years for numerical optimization problems. Recently a number of successful history-based adaptive DE variants with linear population size reduction (L-SHADE) have been considered among the most efficient Evolutionary Algorithms. Various L-SHADE algorithms become the winners of numerous IEEE CEC competitions. In this study we show that the performance of L-SHADE variants may be improved by adding a population-wide inertia term (PWI) to the mutation strategies. The PWI term represent an averaged direction and size of moves that were successful in the previous generation. Hence, by introducing PWI into mutation strategy we boost the moves of L-SHADE individuals in the direction that on average led to the improvement in the previous generation. The PWI term is implemented into four L-SHADE variants proposed during 2014-2018 period. Empirical tests are performed on 60 artificial benchmark problems from IEEE CEC'2014 and IEEE CEC'2017 test sets, and on 22 real-world problems from IEEE CEC'2011. For each considered test set every L-SHADE variant performs better with PWI term than without it. Finally, four PWI-based L-SHADE variants are compared against 16 different metaheuristics. For each among three sets of problems PWI-based L-SHADE algorithms win the comparison, and only two among 16 other metaheuristics may be considered competitive on some sets of problems.