###### Abstract  
The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming.  
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A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot  
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Evolutionary & Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot  
separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference.  
In addition to expanding the single objective FJSP lot streaming to a multi-objective one and customizing the two-stage genetic algorithm to solve it, an added contribution of this paper is its provision of many numerical studies. At the outset of the numerical studies, all the ten objective function terms are illustrated using a small prototype problem. The importance of multi-objective optimization in small versus large size problems is examined and contrasted. The capability of the two-stage genetic algorithm to jointly optimize all the objective function terms is evaluated. The need to optimize both the maximum and the total of a performance measure (such as flowtime) is examined.  
The relevance of two newly proposed objective function terms (sublot finish-time separation and maximum workload difference) in providing better solution quality is assessed. The quality of the initial population and the convergence behavior of the two-stage genetic algorithm is contrasted against the regular genetic algorithm with respect to each of the objective function terms. Further algorithm enhancement through high-performance parallel computation is considered. Algorithm components and parameters are empirically studied. In particular, three different selection operators are examined, and an Analysis of Variance (ANOVA) on mutation and crossover probabilities is conducted.  
The remainder of this article is organized as follows. In Section 2, recent articles in lot streaming are reviewed. The proposed multi-objective FJSP lot streaming model is presented in Section 3. The adaptation of the two-stage genetic algorithm to solve the multi-objective lot streaming model is detailed in Section 4. Section 5 provides extensive numerical studies. Our conclusions, discussion, and future research are in Section 6.