A Cooperated Imperialist Competitive Algorithm for Unrelated Parallel Batch Machine Scheduling Problem

This study focuses on the scheduling problem of unrelated parallel batch processing machines(BPM)with release times,a scenario derived from the moulding process in a foundry.In this process,a batch is initially formed,placed in a sandbox,and then the sandbox is positioned on a BPM formoulding.The complexity of the scheduling problem increases due to the consideration of BPM capacity and sandbox volume.To minimize the makespan,a new cooperated imperialist competitive algorithm(CICA)is introduced.In CICA,the number of empires is not a parameter,and four empires aremaintained throughout the search process.Two types of assimilations are achieved:The strongest and weakest empires cooperate in their assimilation,while the remaining two empires,having a close normalization total cost,combine in their assimilation.A new form of imperialist competition is proposed to prevent insufficient competition,and the unique features of the problem are effectively utilized.Computational experiments are conducted across several instances,and a significant amount of experimental results show that the newstrategies of CICAare effective,indicating promising advantages for the considered BPMscheduling problems.

Hierarchical On-line Scheduling of Multiproduct Batch Plants with a Combined Approach of Mathematical Programming and Genetic Algorithm

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.

On-line Scheduling Algorithm for Penicillin Fed-batch Fermentation

An on-line scheduling algorithm to maximize gross profit of penicillin fed-batch fermentation is proposed. According to the on-line classification method, fed-batch fermentation batches are classified into three categories. Using the scheduling strategy, the optimal termination sequence of batches is obtained. Pseudo on-line simulations for testing the proposed algorithm with the data from industrial scale penicillin fermentation are carried out.

Performance Prediction Based Workload Scheduling in Co-Located Cluster

Cloud service providers generally co-locate online services and batch jobs onto the same computer cluster,where the resources can be pooled in order to maximize data center resource utilization.Due to resource competition between batch jobs and online services,co-location frequently impairs the performance of online services.This study presents a quality of service(QoS)prediction-based schedulingmodel(QPSM)for co-locatedworkloads.The performance prediction of QPSM consists of two parts:the prediction of an online service’s QoS anomaly based on XGBoost and the prediction of the completion time of an offline batch job based on randomforest.On-line service QoS anomaly prediction is used to evaluate the influence of batch jobmix on on-line service performance,and batch job completion time prediction is utilized to reduce the total waiting time of batch jobs.When the same number of batch jobs are scheduled in experiments using typical test sets such as CloudSuite,the scheduling time required by QPSM is reduced by about 6 h on average compared with the first-come,first-served strategy and by about 11 h compared with the random scheduling strategy.Compared with the non-co-located situation,QPSM can improve CPU resource utilization by 12.15% and memory resource utilization by 5.7% on average.Experiments show that the QPSM scheduling strategy proposed in this study can effectively guarantee the quality of online services and further improve cluster resource utilization.

Research on Flexible Job Shop Scheduling Based on Improved Two-Layer Optimization Algorithm

To improve the productivity,the resource utilization and reduce the production cost of flexible job shops,this paper designs an improved two-layer optimization algorithm for the dual-resource scheduling optimization problem of flexible job shop considering workpiece batching.Firstly,a mathematical model is established to minimize the maximum completion time.Secondly,an improved two-layer optimization algorithm is designed:the outer layer algorithm uses an improved PSO(Particle Swarm Optimization)to solve the workpiece batching problem,and the inner layer algorithm uses an improved GA(Genetic Algorithm)to solve the dual-resource scheduling problem.Then,a rescheduling method is designed to solve the task disturbance problem,represented by machine failures,occurring in the workshop production process.Finally,the superiority and effectiveness of the improved two-layer optimization algorithm are verified by two typical cases.The case results show that the improved two-layer optimization algorithm increases the average productivity by 7.44% compared to the ordinary two-layer optimization algorithm.By setting the different numbers of AGVs(Automated Guided Vehicles)and analyzing the impact on the production cycle of the whole order,this paper uses two indicators,the maximum completion time decreasing rate and the average AGV load time,to obtain the optimal number of AGVs,which saves the cost of production while ensuring the production efficiency.This research combines the solved problem with the real production process,which improves the productivity and reduces the production cost of the flexible job shop,and provides new ideas for the subsequent research.

Research on Optimization of Dual-Resource Batch Scheduling in Flexible Job Shop

With the rapid development of intelligent manufacturing and the changes in market demand,the current manufacturing industry presents the characteristics of multi-varieties,small batches,customization,and a short production cycle,with the whole production process having certain flexibility.In this paper,a mathematical model is established with the minimum production cycle as the optimization objective for the dual-resource batch scheduling of the flexible job shop,and an improved nested optimization algorithm is designed to solve the problem.The outer layer batch optimization problem is solved by the improved simulated annealing algorithm.The inner double resource scheduling problem is solved by the improved adaptive genetic algorithm,the double coding scheme,and the decoding scheme of Automated Guided Vehicle(AGV)scheduling based on the scheduling rules.The time consumption of collision-free paths is solved with the path planning algorithm which uses the Dijkstra algorithm based on a time window.Finally,the effectiveness of the algorithm is verified by actual cases,and the influence of AGV with different configurations on workshop production efficiency is analyzed.

Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines

The paper investigates a semi on-line scheduling problem wherein the largest processing time of jobs done by three uniform machines M1, M2, M3 is known in advance. A speed si (s1=1, s2=r, s3=s, 1≤r≤s) is associated with machine Mi. Our goal is to maximize Cmin?the minimum workload of the three machines. We present a min3 algorithm and prove its competitive ratio is max{r+1,(3s+r+1)/(1+r+s)}, with the lower bound being at least max{2,r}. We also claim the competitive ratio of min3 algo- rithm cannot be improved and is the best possible for 1≤s≤2, r=1.

Semi On-line Scheduling Problem for Maximizing the Minimum Machine Completion Time on mIdentical Machines

In this paper, a semi on-line version on m ide ntical machines M 1, M 2, …,M m(m≥3) was considered, where th e processing time of the largest job is known in advance. Our goal is to maximiz e the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m-1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2m-1)p max where p max is the largest job' s processing time, then the worst-case ratio is 2-1/m.

Modeling and Optimization for Scheduling of Chemical Batch Processes

Chemical batch processes have become significant in chemical manufacturing. In these processes, large numbers of chemical products are produced to satisfy human demands in daily life. Recently, economy globalization has resulted, in growing worldwide competitions in tradi.tional chemical .process industry. In order to keep competitive in the global marketplace, each company must optimize its production management and set up a reactive system for market fluctuation. Scheduling is the core of production management in chemical processes. The goal of this paper is to review the recent developments in this challenging area. Classifications of batch scheduling problems and optimization methods are introduced. A comparison of six typical models is shown in a general benchmark example from the literature. Finally, challenges and applications in future research are discussed.

A Genetic Algorithm-based Approach to Scheduling of Batch Production with Maximum Profit

The optimal scheduling of multi-product batch process is studied and a new mathematics model targeting the maximum profit is proposed, which can be solved by the modified genetic algorithm (MGA) with mixed coding (sequence coding and decimal coding) developed by us. In which, the partially matched cross over (PMX) and reverse mutation are used for the sequence coding, whereas the arithmetic crossover and heteropic mutation are used for the decimal coding. In addition, the relationship between production scale and production cost is analyzed and the maximum profit is always a trade-off of the production scale and production cost. Two examples are solved to demonstrate the effectiveness of the method.

On-line Monitoring for Phosphorus Removal Process and Bacterial Community in Sequencing Batch Reactor

For efficient energy consumption and control of effluent quality, the cycle duration for a sequencing batch reactor (SBR) needs to be adjusted by real-time control according to the characteristics and loading of waste-water. In this study, an on-line information system for phosphorus removal processes was established. Based on the analysis for four systems with different ecological community structures and two operation modes, anaerobic-aerobic process and anaerobic-anaerobic process, the characteristic patterns of oxidation-reduction potential (ORP) and pH were related to phosphorous dynamics in the anaerobic, anoxic and aerobic phases, for determination of the end of phosphorous removal. In the operation mode of anaerobic-aerobic process, the pH profile in the anaerobic phase was used to estimate the relative amount of phosphorous accumulating organisms (PAOs) and glycogen accumulat-ing organisms (GAOs), which is beneficial to early detection of ecology community shifts. The on-line sensor val-ues of pH and ORP may be used as the parameters to adjust the duration for phosphorous removal and community shifts to cope with influent variations and maintain appropriate operation conditions.

Synthesis and Scheduling of Optimal Batch Water-recycle Networks

This work develops an optimization-based methodology for the design and scheduling of batch water recycle networks. This task requires the identification of network configuration, fresh-water usage, recycle assignments from sources to sinks, wastewater discharge, and a scheduling scheme. A new source-tank-sink representation is developed to allow for storage and dispatch tanks. The problem is solved in stages by first eliminating scheduling constraints and determining minimum usage of fresh water and wastewater discharge. An iterative procedure is formulated to minimize the total annual cost of the system by trading off capital versus operating costs. The work overcomes limitations in previous literature work including restricted recycle within the same cycle, lumped balances that may not lead to feasible solutions, and unrealistic objective functions. A case study is solved to illustrate the usefulness of the devised procedure.

An improved multi-objective optimization algorithm for solving flexible job shop scheduling problem with variable batches

In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.

The Single Machine Parallel Batch Scheduling Problem with Job Compatibility Constraints

The single machine parallel batch problem with job compatibility is considered to minimize makespan, where the job compatibility constraints are represented by a graph G. This problem is proved to be NP-hard. And when the graph G is limited to be a general bipartite, a complete bipartite and a complete m-partite graph, these problems are solved in polynomial time respectively.

ON-LINE PROBLEMS OF MINIMIZING MAKESPAN ON A SINGLE BATCH PROCESSING MACHINE WITH NONIDENTICAL JOB SIZES

The on-line problem of scheduling on a batch processing machine with nonidentical job sizes to minimize makespan is considered. The batch processing machine can process a number of jobs simultaneously as long as the total size of these jobs being processed does not exceed the machine capacity. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. The paper deals with two variants： the case only with two distinct arrival times and the general case. For the first case, an on-line algorithm with competitive ratio 119/44 is given. For the latter one, a simple algorithm with competitive ratio 3 is given. For both variants the better ratios can be obtained if the problem satisfies proportional assumption.

A two-stage flexible flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage

This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a （j∈N）, and the processing time of job Jj is bj（j∈N） on a batch processorM. We take makespan （Cmax） as our minimization objective. In this paper, for the problem of FSMP-BI （m identical parallel machines on the first stage and a batch processor on the second stage）, based on the algorithm given by Sung and Choung for the problem of 1 ｜ri, BI｜Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O（nlogn）, O（nB）} time. A max {O（nlogn） , O（nB）}time symmetric Algorithm H2 is given then for the problem of BI-FSMP （a batch processor on the first stage and m identical parallel machines on the second stage）.

Bicriteria Scheduling on a Series-Batching Machine to Minimize Makespan and Total Weighted Completion Time with Equal Length Job

It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted completion time with equal length job simultaneously. A batching machine can handle up to b jobs in a batch, where b is called the batch capacity of the machine. We study the unbounded model with b ≥ n, where n denotes the number of jobs. A dynamic programming algorithm is proposed to solve the unbounded model, which can find all Pareto optimal schedules in O(n3) time.

Genetic algorithm for short-term scheduling of make-and-pack batch production process

This paper considers a scheduling problem in industrial make-and-pack batch production process. This process equips with sequence-dependent changeover time, multipurpose storage units with limited capacity, storage time, batch splitting, partial equipment connectivity and transfer time. The objective is to make a production plan to satisfy all constraints while meeting demand requirement of packed products from various product families. This problem is NP-hard and the problem size is exponentially large for a realistic-sized problem. Therefore,we propose a genetic algorithm to handle this problem. Solutions to the problems are represented by chromosomes of product family sequences. These sequences are decoded to assign the resource for producing packed products according to forward assignment strategy and resource selection rules. These techniques greatly reduce unnecessary search space and improve search speed. In addition, design of experiment is carefully utilized to determine appropriate parameter settings. Ant colony optimization and Tabu search are also implemented for comparison. At the end of each heuristics, local search is applied for the packed product sequence to improve makespan. In an experimental analysis, all heuristics show the capability to solve large instances within reasonable computational time. In all problem instances, genetic algorithm averagely outperforms ant colony optimization and Tabu search with slightly longer computational time.

Genetic Algorithm for Scheduling Problem of Chemical Batch Process with Due Date Constraints

The intense competition in the current marketplace ha s forced firms to reexamine their methods of doing business, using superior manu facturing practices in the form of just-in-time (JIT), production with JIT pra ctices pursue completion on time and zero inventory, which is often instruct ed according to the custom’s demand or the sale contract. Earliness and tardine ss are undesirable because both of them will bring the extra cost, cost will als o be increased by some factors such as operation condition, intermediate storage , clean method, etc, to minimize the total cost is often the main scheduling objective, but sometime it is most important for factories to eliminate the tar diness cost in order to maintain the commercial credit and to avoid penalty, the refore, minimum of tardiness cost becomes the first objective. It is more import ant to select a reasonable objective by the actual condition during scheduli ng. In this paper scheduling problem of chemical batch process with due date is studied, two different intermediate storage policies and two different productio n modes are also discussed, production scheduling with different intermediate st orage policy and different production mode is proposed and the result is compare d. In order to complete all products within the due date, not only earliness and tardiness but also holding problem is considered, the objective is to selec t a proper intermediate storage policy and production mode and to minimize the c ost resulted by the earliness and tardiness, even the cost result by the interme diate storage. Scheduling with multiple stage and multiple machine is known as a NP-hard problem, mathematical program (MP) method, such as branch-and-bound (BAB), mixed integer linear program (MILP), etc, is often used to solve the sche duling problem. But as is well known, MP method is not good for combination opti mization, especially for large scale and complex optimal problem, whereas geneti c algorithm (GA) can overcome the MP method’s shortcoming and is fit for solvin g such scheduling problem. In this paper a modified genetic algorithm with speci al crossover operator and mutation operator is presented to solve this schedulin g problem. The results show such problem can be solved effectively with the pres ented method.

A Note on DP Algorithm for Batching Scheduling to Minimize Maximum Lateness

In parallel-batching machine scheduling, all jobs in a batch start and complete at the same time, and the processing time of the batch is the maximum processing time of any job in it. For the unbounded parallel-batching machine scheduling problem of minimizing the maximum lateness, denoted 1|p-batch|L_(max), a dynamic programming algorithm with time complexity O(n^2) is well known in the literature.Later, this algorithm is improved to be an O(n log n) algorithm. In this note, we present another O(n log n) algorithm with simplifications on data structure and implementation details.