Abstract: A constrained discrete optimization problem is transformed into an equivalent constrained integer programming problem (CIPP) and a discrete differential evolution (DDE) algorithm is employed to solve this problem. The concept of component consistency at the dimensional level is proposed to analysis a population of DDE algorithm. It is revealed that if components at the dimensional level in a population are in a consistent status, it will cause evolutionary stagnation of the population. The simulation results of numerical examples confirm the validity of theoretical analysis. The diversity metricΓ of a population is introduced to depict quantitatively the diversity for a population of DDE algorithm. On this basis, the study presents a maintenance strategy for population diversity based on monitoring the continuous generations of evolutionary stagnation and diversity metricΓ to overcome the stagnant evolutionary defect of a population caused by a component consistency at the dimensional level, and furthermore to enhance the global optimization performance of the algorithm. Thus this work embeds the diversity maintenance strategies in DDE algorithm, adopts feasibility rules to handle constraints, and forms to a DDE algorithm with the diversity maintenance strategy (DMDDE) for solving CIPPs. A constrained discrete optimization model is constructed to formulate the optimal design problem on the minimum volume for a two-stage helical cylindrical gear transmission in a flight conveyer, and DMDDE algorithm is utilized to approach this problem. Numerical experiments indicate that DMDDE algorithm has better performance than four compared algorithms in terms of the robustness and convergence accuracy. Moreover, the obtained result is better than one of the original design scheme and the corresponding volume has decreased by 40.8% compared with that scheme.

Key words: cylindrical gear transmission, differential evolution algorithm, diversity maintenance strategy, population diversity metric, constrained discrete optimization