This paper presents a genetic algorithm (GA) approach to cost-optimal task scheduling in a production line. The system consists of a set of serial processing tasks, each with a given duration, unit execution cost, and precedence constraints, which must be assigned to an unlimited number of stations subject to a per-station duration bound. The objective is to minimize the total production cost, modeled as a station-wise function of task costs and the duration bound, while strictly satisfying all prerequisite and capacity constraints. Two chromosome encoding strategies are investigated: a station-based representation implemented using the JGAP library with SuperGene validity checks, and a task-based representation in which genes encode station assignments directly. For each encoding, standard GA operators (crossover, mutation, selection, and replacement) are adapted to preserve feasibility and drive the population toward lower-cost schedules. Experimental results on three classes of precedence structures-tightly coupled, loosely coupled, and uncoupled-demonstrate that the task-based encoding yields smoother convergence and more reliable cost minimization than the station-based encoding, particularly when the number of valid schedules is large. The study highlights the advantages of GA over gradient-based and analytical methods for combinatorial scheduling problems, especially in the presence of complex constraints and non-differentiable cost landscapes.

翻译：本文提出一种遗传算法（GA）方法，用于实现生产线中成本最优的任务调度。该系统由一系列串行处理任务组成，每个任务具有给定的持续时间、单位执行成本及前驱约束，且必须分配给无限数量的工位，同时满足每个工位的持续时间上限。目标是最小化总生产成本，该成本被建模为任务成本与持续时间上限的工位函数，且严格满足所有先决条件与容量约束。本文研究了两种染色体编码策略：一种是基于工位的表示法，采用JGAP库并配合SuperGene有效性检查实现；另一种是基于任务的表示法，其基因直接编码工位分配。针对每种编码方式，标准遗传算法算子（交叉、变异、选择与替换）均经过调整，以保持解的可行性并引导种群向更低成本的调度方案进化。在三种前驱结构类型——紧密耦合、松散耦合及非耦合——上的实验结果表明，与基于工位的编码相比，基于任务的编码能够实现更平滑的收敛过程及更可靠的成本最小化效果，尤其在有效调度方案数量较多时更为显著。本研究凸显了遗传算法在处理组合调度问题时相较于基于梯度的方法与解析方法的优势，特别是在存在复杂约束及不可微成本函数的情况下。