路灯维护总费用随机优化模型及其概率分布拉格朗日松弛方法

Stochastic model for total cost optimization in street lamp maintenance and its probabilistic Lagrangian relaxation method

中文关键词  维修  总费用  多部件  联合更换  随机策略优化  概率分布拉格朗日松弛

英文关键词  maintenance  total cost  multi-component  joint replacement  stochastic policy optimization  probabilistic Lagrangian relaxation

中文摘要

      针对一般故障特性的部件, 优化其有限阶段内更换策略尚无相关模型及有效的解决办法. 本文为路灯维修问题建立了联合更换部件的多阶段随机策略优化模型. 策略优化难点在于部件更换的相互耦合, 且其耦合约束为难以处理的随机约束. 不同于现有的基于情境松弛随机耦合约束的方法, 本文通过引入与决策概率分布相关的乘子松弛约束, 给出概率分布拉格朗日松弛方法(PLR), 其乘子数目与指数增长的情境数目无关. 本文通过给出了联合更换分段策略的求解方法及其充分条件, 进一步解除各阶段决策之间由于故障率非时齐带来的耦合关系. 在实际问题的数值测试中, PLR同时得到了最优解下界及近优解, 可大幅降低当前实际费用; 同时验证了该模型及PLR在大 规模策略优化中的有效性.

英文摘要

      Optimization models and algorithms for the maintenance policy of components with general failure modes in a finite horizon still remain a challenge. This paper provides a multi-stage stochastic model to optimize the joint replacement policy for street lamp components of general failure modes. The major difficulty arises from the stochastic coupling constraints on different component replacement decisions. Instead of relaxing those constraints based on scenarios as in existing methods, we propose the probability Lagrangian relaxation method(PLR) by introducing multipliers ssociated with the probability distributions of decisions, where the number of multipliers is independent of the exponentially increasing scenarios. A solution method and its sufficient conditions are also provided for a phase-wise policy structure to decouple the correlation among stages due to the time-variant failure rates. In numerical testing with real data, the PLR obtains the lower bound of the optimal solution and a suboptimal solution. The results lead to a significant reduction in the current maintenance cost, and demonstrate the efficiency of the model and PLR in solving practical problems.