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
孙鑫伟 1钱斌 2胡蓉 2张森 1于乃康1
作者信息
- 1. 昆明理工大学信息工程与自动化学院,昆明 650500
- 2. 昆明理工大学信息工程与自动化学院,昆明 650500;昆明理工大学云南省人工智能重点实验室,昆明 650500
- 折叠
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GUROB1的对比实验结果表明,HCGA可在较短时间内获得更优的解.
Abstract
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Key words
parallel machine/deterioration effect/maximum completion time/column generation/dynamic programming/diving heuristic引用本文复制引用
基金项目
国家自然科学基金(62173169)
国家自然科学基金(61963022)
云南省基础研究重点项目(202201AS070030)
出版年
2024
NETL
NSTL
万方数据