A partition cum unification based genetic- firefly algorithm for single objective optimization

Firefly algorithm is one of the most promising population-based meta-heuristic algorithms. It has been successfully applied in many optimization problems. Several modifications have been proposed to the original algorithm to boost the performance in terms of accuracy and speed of convergence. This work proposes a partition cum unification based genetic firefly algorithm to explore the benefits of both the algorithms in a novel way. With this, the initial population is partitioned into two compartments based on a weight factor. An improved firefly algorithm runs in the first compartment, whereas, the genetic operators like selection, crossover, and mutation are applied on the relatively inferior fireflies in the second compartment giving added exploration abilities to the weaker solutions. Finally, unification is applied on the subsets of fireflies of the two compartments before going to the next iterative cycle. The new algorithm in three variants of weightage factor have been compared with the two constituents i.e. standard firefly algorithm and genetic algorithm, additionally with some state-of-the-art meta-heuristics namely particle swarm optimization, cuckoo search, flower pollination algorithm, pathfinder algorithm and bio-geography based optimization on 19 benchmark objective functions covering different dimensionality of the problems viz. 2-D, 16-D, and 32-D. The new algorithm is also tested on two classical engineering optimization problems namely tension-compression spring and three bar truss problem and the results are compared with all the other algorithms. Non-parametric statistical tests, namely Wilcoxon rank-sum tests are conducted to check any significant deviations in the repeated independent trials with each algorithm. Multi criteria decision making tool is applied to statistically determine the best performing algorithm given the different test scenarios. The results show that the new algorithm produces the best objective function value for almost all the functions including the engineering problems and it is way much faster than the standard firefly algorithm.