An improved meta-heuristic for makespan minimization of a single batch machine with non-identical job sizes

We consider the problem of minimizing the makespan on a single batch machine with non-identical job sizes, where several jobs can be simultaneously processed as a batch. We formulate makespan minimization as a problem of minimizing the wasted space. Applying a candidate set strategy to narrow the search space, combined with a wasted-space-based heuristic to update the pheromone information, an improved max–min ant system algorithm is presented. A specific local search method is incorporated to gain better performance. Appropriate parameter settings in the proposed algorithm are determined by extensive experiments. The experimental results show that the proposed algorithm outperforms several previously studied algorithms.     

差异工件平行机批调度问题的SAGA*

为了求解差异工件平行机批调度问题,提出了一种模拟退火遗传算法 (simulated annealing genetic algorithm,SAGA)。将模拟退火算法（simulated annealing,SA）的状态转移操作引入基于最优保留的遗传算法(genetic algorithm,GA)中,作为局部搜索算子,以避免算法陷入局部最优,也有效地发挥了SA和GA在局部搜索与全局搜索能力方面的优势。为了解决GA迭代后期适应函数难以区分一些适应度接近的个体这个问题,SAGA分两阶段标定适应函数,在进化后期     

A branch and price algorithm to minimize makespan on a single batch processing machine with non-identical job sizes

In this paper, we consider the scheduling problem on a single batch processing machine with non-identical job sizes; in which the machine has a limited capacity and can process a group of jobs simultaneously as a batch. The processing time of a batch is the longest processing time of all jobs in the batch. The objective is to minimize the makespan. We formulate the problem using Dantzig–Wolfe decomposition as a set partitioning problem. Based on the set partitioning formulation, we present a tight lower bound using column generation method. A heuristic algorithm is also developed to generate the basic solution in the column generation method. A branch and price algorithm which combines the column generation technique with branch and bound method is then presented to obtain the optimal solution of the problem. The efficiency of the proposed branch and price algorithm is ultimately compared to the branch and bound algorithm from the literature, based on the generated sample problems.     

Constrained binary artificial bee colony to minimize the makespan for single machine batch processing with non-identical job sizes

This paper proposes an artificial bee colony approach to minimize the makespan for a single batch-processing machine. The single batch-processing problem is characterized by discontinuity in the objective function and having integer variables. Since the problem under study is NP-hard, an artificial bee colony approach is proposed. The penalty function method is used to convert the constrained problem to unconstrained problem, which is then solved by the ABC algorithm. A procedure to generate initial solutions is presented, which is based on filling partially filled batches first. The analysis in the article shows that the colony size, the value of the penalty parameter, the penalty function iteration, the ABC iteration, and maximum trials per food source all have a significant effect on the performance of the ABC algorithm; however, no pattern can be established.     

An ACO algorithm for makespan minimization in parallel batch machines with non-identical job sizes and incompatible job families

We study the problem of scheduling a set of N jobs with non-identical job sizes from F different families on a set of M parallel batch machines; the objective is to minimize the makespan. The problem is known to be NP-hard. A meta-heuristic based on Max–Min Ant System (MMAS) is presented. The performance of the algorithm is compared with several previously studied algorithms by computational experiments. According to our results, the average distance between the solutions found by our proposed algorithm and the lower bounds is about 4% less than that of the best of all the compared algorithms, demonstrating that our algorithm outperforms the previously studied algorithms.     

基于自由搜索算法求解单机差异工件批调度问题*

采用自由搜索（free search,FS）算法对单机差异工件批调度问题的制作跨度进行优化。针对该问题的离散优化特征以及自由搜索算法的不足,将自由搜索算法与实数编码遗传算法相结合,在标准FS算法的基础上引入两种杂交算子和精英保留策略,提出混合自由搜索（hybrid free search,HFS）算法。仿真实验结果表明,该算法表现出良好的鲁棒性和收敛性,与标准FS、FFLPT以及BFLPT算法相比,HFS算法提高了寻优精度。     

Minimising makespan for two batch-processing machines with non-identical job sizes in job shop

In this article, the job shop scheduling problem with two batch-processing machines is considered. The machines have limited capacity and the jobs have non-identical job sizes. The jobs are processed in batches and the total size of each batch cannot exceed the machine capacity. The processing times of a job on the two machines are proportional. We show the problem of minimising makespan is NP-hard in the strong sense. Then we provide an approximation algorithm with worst-case ratio no more than 4, and the running time of the algorithm is O(n?log?n). Finally, the performance of the proposed algorithm is tested by different levels of instances. Computational results demonstrate the effectiveness of the algorithm for all the instances.     

不同容量平行机下差异工件尺寸的批调度算法

在容量不同的平行批处理机环境下, 针对工件带有不同尺寸和机器适用限制的最小化制造跨度的批调度问题, 提出一种有效的蚁群优化算法. 该算法基于解的浪费空间定义启发式信息, 针对机器容量约束提出两种用于构建解的候选集, 从而有效缩小搜索空间, 并引入局部优化方法提高解的质量. 仿真实验结果表明, 所提出算法具有较好的性能, 并且优于已有的其他算法.

     

Scheduling unrelated parallel batch processing machines with non-identical job sizes

Scheduling unrelated parallel batch processing machines to minimize makespan is studied in this paper. Jobs with non-identical sizes are scheduled on batch processing machines that can process several jobs as a batch as long as the machine capacity is not violated. Several heuristics based on best fit longest processing time (BFLPT) in two groups are proposed to solve the problem. A lower bound is also proved to evaluate the quality of the heuristics. Computational experiments were undertaken. These showed that J_SC-BFLPT, considering both load balance of machines and job processing times, was robust and outperformed other heuristics for most of the problem categories.     

An effective hybrid multi-objective genetic algorithm for bi-criteria scheduling on a single batch processing machine with non-identical job sizes

This paper addresses the problem of scheduling jobs with non-identical sizes on a single batch processing machine. A batch processing machine is one which can process multiple jobs simultaneously as a batch as long as the total size of jobs being processed does not exceed the machine capacity. The batch processing time is equal to the longest processing time among all jobs in the batch. For the simultaneous minimization of the bi-criteria of makespan and maximum tardiness, we propose two different multi-objective genetic algorithms based on different representation schemes. While the first algorithm do search via generating sequences of jobs using genetic operators and then batching jobs keeping their order in the sequence, the second algorithm uses the idea of generating batches of jobs directly using genetic operators and ensures feasibility through using heuristic procedures. The type of representation used in the second algorithm allows introducing heuristics with the ability of biasing the search towards each objective and also allows hybridization with a local search heuristic that gives the ability of finding Pareto-optimal or locally efficient Pareto-solutions. Computational results show that the non-dominated solutions obtained by the latter algorithm are very superior in closeness to the true Pareto-optimal solutions and to keep diversity in the obtained Pareto-set, as the problem size increases.     

Enhanced grouping league championship and optics inspired optimization algorithms for scheduling a batch processing machine with job conflicts and non-identical job sizes

This research aims to address scheduling of a single batch processing machine, where jobs are in different sizes and have a conflicting nature with each other, in the sense that two conflicting jobs cannot share the same batch and hence, cannot be processed simultaneously by the machine. The problem is referred to as SBMC. After formulating the problem, a strong lower bound procedure is developed by transforming a relaxed version of the scheduling problem to the multiple bottleneck transportation problem (MTP) with conflicts. An efficient Lagrangian relaxation procedure is proposed, which takes advantage of decomposable nature of the relaxed problem, to attain a lower bound for MTP which in essence is a lower bound for SBMC. To solve the problem, two metaheuristic algorithms, namely the League Championship Algorithm (LCA) and Optic Inspired Optimization (OIO), are adapted and fundamentally modified to match the problem unique structure (i.e., the grouping structure) and accordingly the grouping version of these algorithms is developed. The effectiveness of the lower bound procedure, as well as algorithms, are evaluated through extensive computational experiments. To show they perform efficiently in running times and effective in finding near-optimal bounds for most of the problem instances, we generate 20 different classes of problems according to variability in job sizes, number of jobs and density of incompatibility matrix. Then, we make comparison with two of extensively used algorithms from literature, SA and GA. Our proposed algorithms obtain solutions with objective values less than 6% gap from the lower bound and outperform SA and GA algorithms, especially for large instances. Moreover, values of the lower bound procedure lie within less than 4% of objective values provided by CPLEX.     

求解差异工件批调度问题的改进型蚁群算法

针对最小化制造跨度的差异工件尺寸单批处理机调度问题,通过将其转化为最小化浪费空间的问题,采用候选集策略构建分批以减少搜索空间,利用基于浪费空间的启发式更新信息素,提出一种改进的最大最小蚁群算法。此外,在算法中还引入了一种局部优化策略,以进一步提高算法的性能。仿真实验结果表明,所提出的算法优于其他几种已有算法,验证了所提出算法的有效性和鲁棒性。     

模糊环境下多目标差异作业单机批调度问题研究

针对现实生产制造系统中存在的时间参数模糊化问题,采用梯形模糊数表征时间参数,给出一种具有模糊交货期和模糊加工时间,以最小化提前/拖期惩罚、制造跨度以及加工费用为目标的多目标差异作业单机批调度问题模型.在对该问题进行求解方面,针对基本粒子群算法容易陷入局部最优的问题,引入混沌局部搜索策略,给出了一种基于混沌优化技术的混合粒子群算法.仿真实验验证了所提出算法的可行性和有效性.     

模糊环境下的差异作业单机批调度优化问题的研究*

针对现实生产制造系统中存在的时间参数模糊化问题,本文用梯形模糊数表征时间参数,给出了一种具有模糊加工时间和模糊批次间隔的、以最小化制造跨度为目标的模糊差异作业单机批调度问题模型。在对模糊差异作业单机批调度问题进行有效求解方面,针对基本粒子群算法容易陷入局部最优的问题,本文给出了一种基于遗传操作的混合粒子群算法,利用遗传算法思想对粒子进行交叉、变异操作,增强了算法跳出局部最优的能力。仿真实验验证了该算法具有可行性和有效性。     

Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times

This research analyzes the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch processing machines so as to minimize the makespan. Unrelated parallel machine is a generalization of the identical parallel processing machines and is closer to real-world production systems. Each machine can accommodate and process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch. Motivated by the computational complexity and the practical relevance of the problem, we present several heuristics based on first-fit and best-fit earliest job ready time rules. We also present a mixed integer programming model for the problem and a lower bound to evaluate the quality of the heuristics. The small computational effort of deterministic heuristics, which is valuable in some practical applications, is also one of the reasons that motivates this study. The results show that the heuristic proposed in this paper has a superior performance compared to the heuristics based on ideas proposed in the literature.     

Minimizing total weighted tardiness on a single batch process machine with incompatible job families

The diffusion step in semiconductor wafer fabrication is very time consuming, compared to other steps in the process, and performance in this area has a significant impact on overall factory performance. Diffusion furnaces are able to process multiple lots of similar wafers at a time, and are therefore appropriately modeled as batch processing machines with incompatible job families. Due to the importance of on-time delivery in semiconductor manufacturing, we focus on minimizing the total weighted tardiness in this environment. The resulting problem is NP-Hard, and we decompose it into two sequential decision problems: assigning lots to batches followed by sequencing the batches. We develop several heuristics for these subproblems and test their performance.     

Scheduling a single batch-processing machine with non-identical job sizes in fuzzy environment using an improved ant colony optimization

In this paper, we introduce the fuzzy model of the makespan on a single batch-processing machine with non-identical job sizes. The uncertainty of the jobs and the machine in the processing is denoted using fuzzy logic. Then an improved ant colony optimization (ACO) method is proposed and the Metropolis criterion is used to select the paths of ants to overcome the immature convergence of the algorithm. In the experiment, we adopt the random instances and the results of the fuzzy makespan demonstrate that the proposed algorithm outperforms GA and SA in all instances.     

Minimizing makespan on a single burn-in oven with job families and dynamic job arrivals

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine and each batch processing time is represented by the largest processing time among those of all the jobs contained in the batch. Each job belongs to one of the given number of families. Moreover, the release times of the jobs are different from one another. The objective measure of the problem is the maximum completion time (makespan) of all jobs. A dynamic programming algorithm is proposed in the order of polynomial time complexity for a situation where the number of job families is given (fixed). A computational experiment is performed to compare the time complexity of the proposed algorithm with that of another exact algorithm evaluating all possible job sequences based on batching-dynamic programming (BDP). The results of the experiment show that the proposed algorithm is superior to the other.Scope and purposeThis paper considers a scheduling problem on the burn-in operation in a semiconductor manufacturing process. The burn-in operation is a bottleneck process in the final testing process which is one of four major steps including wafer fabrication, wafer probe, assembly, and final testing steps. Thus, its scheduling is very important to improve the productivity of the whole manufacturing line. The objective of this paper is to find a solution technique that will find the optimal schedule that minimizes makespan for problems which are found in the semiconductor manufacturing industry.