An improved mixed-coded hybrid firefly algorithm for the mixed-discrete SSCGR problem

Reducers play a particularly important role in mechanical transmission field, and even a slight reduction in the material consumption would bring considerable economic and social benefits. With the goal of the minimum volume of consumables, a general mathematical model for the widely used single-stage cylindrical gear reducer (SSCGR), is established. When some real and discrete parameters are selected as the design variables, the SSCGR problem becomes a mixed-discrete SSCGR problem. To minimize the mixed-discrete SSCGR problem and make discrete design variables always satisfy discrete constraints, an improved mixed-coded hybrid firefly algorithm (IMCHFA) is proposed. The proposed approach uses new mixed-coded method to encode the position structure, and uses sorting group selection to select paired fireflies for position update, then uses combinatorial mutation to accelerate convergence of the algorithm. Meanwhile, the rounding technique is adopted to make the position structure meet the coding rules. 28 modified CEC 2017 mixed-discrete problems and two practical mixed-discrete engineering optimization problems are tested by the IMCHFA and other improved algorithms. The results show that the solution quality of IMCHFA is significantly better than other improved algorithms examined in this study. Finally, the proposed IMCHFA is applied to optimize the mixed-discrete SSCGR problem. Compared to the solution quality of other improved algorithms examined in this study, the proposed IMCHFA can obtain more efficient and economic solutions.