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.

Firefly 算法是最有前途的基于种群的元启发式算法之一。它已成功应用于许多优化问题。已经对原始算法提出了一些修改，以提高准确性和收敛速度方面的性能。这项工作提出了一种基于分区兼统一的遗传萤火虫算法，以一种新颖的方式探索这两种算法的优点。这样，初始种群根据权重因子分为两个部分。改进的萤火虫算法在第一个隔间运行，而选择、交叉和变异等遗传算子应用于第二个隔间中相对较差的萤火虫，为较弱的解决方案增加了探索能力。最后，在进入下一个迭代循环之前，统一应用于两个隔间的萤火虫子集。将权重因子的三种变体中的新算法与标准萤火虫算法和遗传算法这两个组成部分进行了比较，此外还与一些最先进的元启发式算法进行了比较，即粒子群优化、布谷鸟搜索、花授粉算法、探路者基于算法和生物地理学优化 19 个基准目标函数，覆盖问题的不同维度，即。2-D、16-D 和 32-D。新算法还在两个经典的工程优化问题上进行了测试，即拉压弹簧和三杆桁架问题，并将结果与​​所有其他算法进行了比较。非参数统计检验，即进行 Wilcoxon 秩和检验以检查每个算法在重复独立试验中的任何显着偏差。应用多准则决策工具以统计确定给定不同测试场景的最佳性能算法。结果表明，新算法对包括工程问题在内的几乎所有函数都产生了最佳目标函数值，并且比标准萤火虫算法快得多。