Abstract: For the Flexible Job-shop Scheduling Problem (FJSP) with machine flexibility and machine tool depreciation, in order to reduce the energy consumption in the production process, a mathematical model with the minimization of weighted sum of maximum completion time and total energy consumption as the scheduling objective was established, and an Improved Genetic Algorithm (IGA) was proposed. Firstly, according to strong randomness of Genetic Algorithm (GA), the principle of balanced dispersion of orthogonal test was introduced to generate initial population, which was used to improve the search performance in global range. Secondly, in order to overcome genetic conflict after crossover operation, the coding mode of three-dimensional real numbers and the arithmetic crossover of double individuals were used for chromosome crossover, which reduced the steps of conflict detection and improved the solving speed. Finally, the dynamic step length was adopted to perform genetic mutation in mutation operation stage, which guaranteed local search ability in global range. By testing on the 8 Brandimarte examples and comparing with 3 improved heuristic algorithms in recent years, the calculation results show that the proposed algorithm is effective and feasible to solve the FJSP.

Key words: green manufacturing, machine tool depreciation, Flexible Job-shop Scheduling Problem (FJSP), Improved Genetic Algorithm (IGA), three-dimensional real coding, principle of balanced dispersion

摘要： 针对具有机器柔性和机床折旧特性的柔性作业车间调度问题（FJSP），为了降低生产过程的能耗，建立了以最大完工时间和能耗加权的和最小为优化目标的数学模型，并提出了一种改进遗传算法（IGA）。首先，根据遗传算法（GA）随机性强的特点，引入正交试验的均衡分散原则生成初始种群，用于提高在全局范围的搜索性能；然后，为了克服交叉操作后的基因冲突，采用三维实数的编码方式并结合双个体算术交叉用于染色体交叉，减少了冲突检测步骤，提高了求解速度；最后，在变异操作阶段采用了动态步长的方式进行基因变异，保证了全局范围内的局部搜索能力。通过对8个Brandimarte算例进行仿真测试，并与近年来3个改进启发式算法进行对比，计算结果表明该算法求解FJSP的有效性和可行性。

关键词: 绿色制造, 机床折旧, 柔性车间调度问题, 改进遗传算法, 三维实数编码, 均衡分散原则