启发式列生成算法求解带恶化效应的同构并行机调度问题  

Heuristic column generation algorithm for identical parallel machine scheduling problem with deterioration effect

作　　者：孙鑫伟 钱斌[1,2] 胡蓉[1,2] 张森 于乃康 SUN Xin-wei;QIAN Bin;HU Rong;ZHANG Sen;YU Nai-kang(Faculty of Information Engineering and Automation,Kunming University of Science and Technology,Kunming 650500,China;Yunnan Key Laboratory of Artificial Intelligence,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学信息工程与自动化学院,昆明650500 [2]昆明理工大学云南省人工智能重点实验室,昆明650500

出　　处：《控制与决策》2024年第5期1636-1644,共9页Control and Decision

基　　金：国家自然科学基金项目(62173169,61963022);云南省基础研究重点项目(202201AS070030)。

摘　　要：针对实际生产中广泛存在的一类带恶化效应的同构并行机调度问题,以最小化最大完工时间为优化目标,构建该问题的整数规划模型,并提出一种启发式列生成算法(HCGA)进行求解.在HCGA中,首先,利用Dantzig-Wolfe分解方法,将原问题分解为一个主问题(MP)和多个子问题;然后,设计启发式算法获得初始列,其中每列为一台机器上的一个调度方案,基于初始列构建限制主问题(RMP)模型;接着,设计快速有效的动态规划算法求解子问题,以得到需添加至RMP的列集,同时,考虑传统列生成算法收敛速度较慢,设计一系列方法来加速列生成过程;最后,基于所获取的MP线性松弛解,设计深潜启发式算法确定原问题的整数解. HCGA与商用求解器GUROBI的对比实验结果表明, HCGA可在较短时间内获得更优的解.An integer programming model is built to minimize the maximum completion time and a heuristic column generation algorithm(HCGA)is proposed for a class of identical parallel machine scheduling problem with deterioration effect that widely exist in practical production.In the HCGA,first,the original problem is decomposed into a master problem(MP)and multiple subproblems by using the Dantzig-Wolfe decomposition method.Secondly,a heuristic algorithm is designed to obtain initial columns,where each column represents a schedule on one machine.Based on the initial columns,a restricted MP(RMP)model is constructed.Then,a fast and effective dynamic programming algorithm is designed to solve each subproblem to obtain the column set to be added to the RMP.At the same time,considering that the convergence speed of traditional column generation algorithms is slow,a series of methods are designed to accelerate the column generation process.Finally,based on the obtained linear relaxation solution of the MP,a diving heuristic algorithm is designed to determine the integer solution of the original problem.According to the comparative experimental results of the HCGA and commercial solver GUROBI,the HCGA can obtain better solutions in a shorter time.

关 键 词：并行机 恶化效应 最大完工时间 列生成 动态规划 深潜启发式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]