基于合作博弈的多部件设备非完美维修策略优化

非完美维修是设备维修资源受限条件下广泛采用的维修方式，然而设备非完美维修中各部件维修等级的确定随着部件数量或非完美维修等级的增加而变得困难。本文针对多部件设备非完美维修策略优化问题，以设备可靠性为基础，选择各部件的非完美维修等级为优化变量，以维修时间及任务可靠性为约束条件，以设备总维修费用最低为目标建立了设备维修策略优化问题数学模型；进而选择各部件的负责人为参与者，构建相应的合作博弈场景，提出基于合作博弈的设备非完美维修策略优化方法，通过设置每轮博弈中各参与者的策略空间构造、收益及博弈规则，能够使每轮博弈中设备维修方案的更新是朝着优化目标的方向进行；从而通过动态博弈过程获得多部件设备最优的非完美维修策略。通过仿真算例分析及与遗传算法等对比，验证了所提方法的优化结果整体上明显优于遗传算法和粒子群算法的优化结果、且能够显著提高非完美维修策略优化过程的计算效率。本研究为当前有限资源下的设备维修策略优化提供了新思路。

Imperfect Maintenance Strategy Optimization of Multi-parts Equipment Based on the Cooperative Game

Imperfect maintenance policy is always required and carried out on the equipment parts under limited maintenance resources. The maintenance strategy optimization of the imperfect maintenance level for each equipment part becomes difficult for large parts number or high imperfect maintenance levels. To solve the imperfect maintenance strategy optimization problem of equipment with multiple parts and maintenance levels, a repeated cooperative game theory based optimization algorithm is proposed in this research. Considering the imperfect maintenance level of each equipment part as the optimization variable and maintenance cost minimization as the optimization objective, a mathematical model of imperfect maintenance of equipment with multiple parts connected in series is fabricated under the constraints of limited maintenance time and minimal required reliability. Further, considering the administrators corresponding to each equipment part as the game players, the equipment imperfect maintenance model is mapped into a cooperative game scenario. Via constructing the strategy space, setting the payoff in each round of the cooperative game, the updated maintenance plan in each round will move towards the global optimum via repeated game. Moreover, the performance of the proposed method is tested via case and parameter studies, and compared with traditional optimization methods including genetic algorithm method. The analysis results show that the proposed cooperative game algorithm provides overall more accurate optimization results, and enhances the optimization efficiency. The research could provide more practical guidelines for imperfect maintenance strategy optimization of equipment in engineering applications.