基于子集模拟的建设工程项目多资源均衡优化算法

王家 刘可心 张学清 陈涛

摘要：为高效、稳定地求解建设工程项目管理过程中的多资源均衡问题，提出一种基于子集模拟的优化算法.多资源均衡问题中，如直接采用工序计划开始时间作为决策变量，在优化算法的实现时易违反工序间的逻辑关系.为避免该问题，本文采用工序计划开始时间的间隔率变量表示（在二者的映射中考虑工序间的逻辑关系），并据此建立间隔率变量表示的建设工程项目多资源均衡优化模型，以简化基于子集模拟的优化算法的操作流程.通过算例验证，与目前应用较广的遗传算法相比，本文提出的优化算法在最优解的获取稳定性上有較大改进.

关键词：资源均衡问题；子集模拟；马尔科夫链蒙特卡罗；间隔率；遗传算法

中图分类号：TU722文献标志码：A

基金项目：中国博士后科学基金资助项目（2017M622575），China Postdoctoral Science Foundation（2017M622575）

Optimization Algorithm for Resource Leveling of Construction Projects with Multiple Resources Based on Subset Simulation

WANG Jia1，2，LIU Kexin1，ZHANG Xueqing3，CHEN Tao4

（1. College of Civil Engineering，Hunan University，Changsha 410082，China；2. National Center for International Research Collaboration in Building Safety and Environment，Hunan University，Changsha 410082，China；3. Department of Civil and Environmental Engineering，Hong Kong University of Science and Technology，Hong Kong 999077，China；4. Changsha Midea Real Estate Development Co Ltd，Changsha 410082，China）

Abstract：In this paper，an efficient optimization algorithm based on subset simulation is proposed for solving the resource leveling problem of construction projects with multiple resources. In the resource leveling problem，if the de-cision variables are chosen to be the scheduled starting time for the involved activities，the logical relationship be-tween the activities may be violated during the implementation of the optimization algorithm. In order to avoid this problem，the interval rate variables are introduced to substitute the scheduled starting time in modeling the resource leveling problem of construction projects with multiple resources so as to simplify the procedures of the proposed opti-mization algorithm based on subset simulation. As shown in the illustrative example，compared with the widely used genetic algorithm，the proposed optimization algorithm can obtain higher improvement in the stability of achieving the optimal solution.

Key words：resource levelling problem；subset simulation；Markov chain Monte Carlo simulation；interval rate；genetic algorithm

建设项目的施工过程需消耗大量的人工、材料、机械等资源.如果建设项目实施过程中的资源计划（劳动力计划、材料进场计划、机械排班等）安排不合理，会引起建设项目工期内资源消耗量的过大波动（表现为施工人员的窝工或少工、材料和机械的过度使用或空置等），最终影响建设工程的生产效率、成本节约和项目管理质量[1].作为资源调度优化的手段之一，资源均衡问题（Resource Leveling Problem，RLP）旨在通过调整项目中非关键工序的计划开始时间，在不延长项目工期和不违反各工序间逻辑关系的前提下，降低项目工期内资源消耗量……