Heuristic algorithms for scheduling on uniform parallel machines with heads and tails

This paper considers the uniform parallel machine scheduling problem with unequal release dates and delivery times to minimize the maximum completion time.For this NP-hard problem,the largest sum of release date,processing time and delivery time first rule is designed to determine a certain machine for each job,and the largest difference between delivery time and release date first rule is designed to sequence the jobs scheduled on the same machine,and then a novel algorithm for the scheduling problem is built.To evaluate the performance of the proposed algorithm,a lower bound for the problem is proposed.The accuracy of the proposed algorithm is tested based on the data with problem size varying from 200 jobs to 600 jobs.The computational results indicate that the average relative error between the proposed algorithm and the lower bound is only 0.667%,therefore the solutions obtained by the proposed algorithm are very accurate.

On-Line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

Online algorithms for scheduling with machine activation cost on two uniform machines

In this paper we investigate a variant of the scheduling problem on two uniform machines with speeds 1 and s. For this problem, we are given two potential uniform machines to process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed, the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and the machine activation cost. We design optimal online algorithms with competitive ratio of (2s+1)/(s+1) for every s≥1.

Better Algorithm for Order On-Line Scheduling on Uniform Machines

In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. An algorithm with competitive ratio of 7.4641 is addressed, which is better than the best existing result of 12.

A Scheduling Strategy of Light Supplement in Agricultural Greenhouse Based on the Displacement of Light Source Group

LED can effectively promote the growth of crops and improve the yield of crops. In order to make the crops grow evenly in the agricultural greenhouse, the uniformity of illumination is very important. Because of the importance of illumination uniformity to the growth of crops, this paper intends to establish the illuminance model of light source without considering the influence factors such as the difference of each light source group and air scattering. On this basis, the reasonable layout of each light source position in the light source group is considered. Therefore, a light replenishment scheduling strategy based on the displacement of light source group is proposed in this paper Improve the uniformity of illumination in agricultural greenhouse and reduce its operation cost. Experiments show that the strategy is effective.

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （PART I：EQUAL TIMES AND COSTS）

Abstract Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by reallocating resources. In this paper, authors consider a machine scheduling problem with controllable processing times. In the first part of this paper, a special case where the processing times and compression costs are uniform among jobs is discussed. Theoretical results are derived that aid in developing an O(n 2) algorithm to slove the problem optimally. In the second part of this paper, authors generalize the discussion to general case. An effective heuristic to the general problem will be presented.

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS ： PROOF OF THEOREMS

Abstract This report is virtually the appendix part of the author's previous paper which includes the proofs for the theorems and lemmas.

基于改进遗传算法的柔性作业车间调度研究

针对柔性作业车间的多目标调度问题,文章建立以最大完工时间、能耗为目标的数学模型,提出一种多目标的改进遗传算法的求解方法。首先,在交叉算子中使用均匀交叉法,采用了基于邻域的变异算子。其次,针对交叉变异算子进行了非均匀改进,旨在增加算法搜索能力。通过动态调整非均匀交叉和非均匀变异的概率,提高搜索空间覆盖率,避免陷入局部最优解。最后,采用基准算例Kacem测试集进行测试。实验证明,该改进算法有效地解决了同时考虑最大完工时间和能耗的多目标调度问题,取得了显著的改善效果。

共享制造环境下的同类机排序问题

考虑了共享制造环境下的同类机排序问题.在共享制造环境中,每个工件Jj都有一个可以加工的机器集Mj,Jj可以被分别给Mj的某一台机器加工,也可以一定服务成本分配给其他剩余机器进行加工.该文的目标是最小化工件的最大完工时间加总服务成本.对于机器台数是固定常数情况,该文对经典加工模型和简单退化加工模型分别提出了基于程序划分的全多项式时间近似方案.对总服务成本不超过给定上界的限制下最小化最大完工时间问题,给出了其整数规划模型.

An Optimal Online Algorithm for Fractional Scheduling on Uniform Machines with Three Hierarchies

This paper is concerned with the fractional version of online hierarchical scheduling problem on uniform machines.In the problem,the jobs and machines have several different hierarchies and each job can be arbitrarily split between the machines with hierarchies not above the hierarchy of the job.The objective is to minimize the makespan.The authors present an optimal algorithm for the problem with three hierarchies.

ON-LINE SCHEDULING OF UNIT TIME JOBS WITH REJECTION ON UNIFORM MACHINES

The authors consider the problem of on-line scheduling of unit execution time jobs on uniform machines with rejection penalty. The jobs arrive one by one and can be either accepted and scheduled, or be rejected. The objective is to minimize the total completion time of the accepted jobs and the total penalty of the rejection jobs. The authors propose an on-line algorithm and prove that the competitive ratio is 1/2 （2 W √3） ≈ 1.86602.

PARAMETRIC BOUNDS FOR LPT SCHEDULING ON UNIFORM PROCESSORS

The nonpreemptive assignment of independent tasks to a system of m uniform processors isexamined with the objective of minimizing the makespan. Using r_m, the ratio of the fasest speed tothe slowest speed of the system, as a parameter, we assess the performance of LPT (largestprocessing time) schedule with respect to optimal schedules. It is shown thet the worst-case boundfor the ratio of the two schedule lengths is between

Uniform Parallel-Machine Scheduling with Time Dependent Processing Times

We consider several uniform parallel-machine scheduling problems in which the processing time of a job is a linear increasing function of its starting time.The objectives are to minimize the total completion time of all jobs and the total load on all machines.We show that the problems are polynomially solvable when the increasing rates are identical for all jobs;we propose a fully polynomial-time approximation scheme for the standard linear deteriorating function,where the objective function is to minimize the total load on all machines.We also consider the problem in which the processing time of a job is a simple linear increasing function of its starting time and each job has a delivery time.The objective is to find a schedule which minimizes the time by which all jobs are delivered,and we propose a fully polynomial-time approximation scheme to solve this problem.

Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

We study an online(over time)scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and v(0<≤1),respectively,to minimize the makespan.We first show that no online algorithm can have a competitive ratio less than 1+αL,whereαL=(√5−1)/2≈0.618 if 0≤1/2,andαL=α2(v)is the positive root ofα^(3)+3α^(2)+(3−1/v)α−1/v=0 if1/2≤1.This lower bound is still valid when all jobs have the same processing times.Then,we provide an online algorithm with a competitive ratio at most min{(√5+1)/2,√2/v}.When the jobs have the same processing times,we present the best possible online algorithm with a competitive ratio 1+αL.

Optimal Preemptive Online Algorithms for Scheduling with Known Largest Size on Two Uniform Machines

In this paper, we consider the seml-online preemptive scheduling problem with known largest job sizes on two uniform machines. Our goal is to maximize the continuous period of time （starting from time zero） when both machines are busy, which is equivalent to maximizing the minimum machine completion time if idle time is not introduced. We design optimal deterministic semi-online algorithms for every machine speed ratio s ∈ [1, ∞）, and show that idle time is required to achieve the optimality during the assignment procedure of the algorithm for any s 〉 （s^2 ＋ 3s ＋ 1）/（s^2 ＋ 2s ＋ 1）. The competitive ratio of the algorithms is （s^2 ＋ 3s ＋ 1）/（s^2 ＋ 2s ＋ 1）, which matches the randomized lower bound for every s ≥ 1. Hence randomization does not help for the discussed preemptive scheduling problem.

ON-LINE PREEMPTIVE SCHEDULING ON UNIFORM MACHINES

We address the problem of preemptively schedule on-line jobs on arbitrary m uniformly related machines with the objective of minimizing the schedule length. We provide the first on-line algorithm for this general problem, and show that the algorithm has a competitive ratio of 1 ± σ, where a (m - 1)s1/(si +…+ sm), S1 S2 Sm being the speeds of the m machines.

UNIFORM MACHINE SCHEDULING WITH MACHINE AVAILABLE CONSTRAINTS

In this paper, we consider a uniform machine scheduling problem with nonsimultaneous available times. We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3). We tighten this bound when the machine speed ratio is small or m=2. Furthermore, we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.

非均匀分布下无线传感器网络节点调度机制

针对传统依赖精确位置信息的计算复杂和无位置信息部署受限性等弊端,从理论上对节点部署方式进行分析,提出一种非均匀分布下的无线传感器网络节点调度NDNS(non-uniform distribution node scheduling)机制,该机制利用节点与邻居节点的距离信息,对节点覆盖冗余进行判别,适应于任意分布下的网络部署方式。通过实验对机制进行了性能分析和验证,结果表明该方案在保证网络覆盖的前提下,有效地延长了网络生存时间。

柔性车间调度的新型初始机制遗传算法

为了提高柔性作业车间调度求解遗传算法(GA-Ⅰ)的初始种群质量,提出一种基于短用时和设备均衡策略的机器链优化初始方法.运用均匀设计原理对每道工序的具有最短加工时间的可选机器进行均匀组合,形成机器分配链优化遗传算法(GA-Ⅱ)的初始群体;采用均匀设计法构造不同权值,形成机器总负荷和机器负荷方差的不同加权组合以构造机器链优化的适应度函数;通过GA-Ⅱ计算产生定量优化的机器分配链群体.将上述机器分配链优化群体作为柔性作业车间调度问题遗传算法(GA-Ⅰ)的机器链初始群体,并利用混合方式的交叉与变异在工件和工序级尺度上进行遗传操作,实现了FJSP的高效求解算法.通过典型算例验证了该方法的可行性和有效性.

同类机环境下不同尺寸工件的分批调度问题

为了有效地利用批处理机,提高生产效率,提出了同类机加工环境下具有不同尺寸工件的批处理机调度问题并进行了求解。由于该问题是NP难解的,给出了一个下界以衡量近似算法的性能,并证明了该下界的有效性。提出了批的隐性加工时间的概念,并以此为基础给出了一种新的局部优化算法,对最大最小蚁群算法进行了改进。使用启发式算法最终对同类机环境下分批调度问题进行求解。通过仿真实验将该蚁群算法与遗传算法、微粒群优化算法及BFLPT等进行比较和性能分析。