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Artificial bee colony is a powerful optimization method, which has strong search abilities to solve many optimization problems. However, some studies proved that ABC has poor exploitation abilities in complex optimization problems. To overcome this issue, an improved ABC variant based on elite strategy and dimension learning (called ABC-ESDL) is proposed in this paper. The elite strategy selects better solutions to accelerate the search of ABC. The dimension learning uses the differences between two random dimensions to generate a large jump. In the experiments, a classical benchmark set and the 2013 IEEE Congress on Evolutionary (CEC 2013) benchmark set are tested. Computational results show the proposed ABC-ESDL achieves more accurate solutions than ABC and five other improved ABC variants.

In the optimization process of multi-objective firefly algorithm, population is easy to fall into local optimum, which leads to poor population distribution and convergence. In order to solve this problem, this article proposes a multi-objective firefly algorithm with multi-strategy integration (MOFA-MSI). First, in order to improve the distribution of population, MOFA-MSI proposes a cloning strategy, which calculates the distribution degree of individuals in population, clones them according to their distribution degree, and local mutation in the cloned individual produce a new population with good distribution. Then, in order to maintain the convergence of population, a position updating strategy based on non-dominated sorting is proposed. The new population after local mutation are performed by non-dominated sorting, and the fireflies with higher rank guide the fireflies with lower rank to fly, and then new population are generated by global mutation after position updated. Finally, the greedy strategy is adopted to select solutions with better distribution and convergence and store them in external files. In the experimental part, different types of test problems are used to test the performance of each algorithm, and MOFA-MSI is compared with three classical and four new multi-objective evolutionary algorithms. The results show that MOFA-MSI is superior to other seven algorithms in terms of the distribution and convergence of population.

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