CAJ | 학술논문

惩罚函数法优化有约束换热网络时，罚因子的取值过大降低计算效率，过小降低优化精度，设置合适的罚因子值却不容易。基于微分进化算法优化连续变量的启发，采用罚因子协同进化机制，同步优化罚因子与解变量，应用于换热网络优化问题。协进化机制优化主要思想如下：建立两类种群，一类为罚因子种群，一类为换热面积种群。优化过程中，每一组换热面积种群用来评价每一个罚因子个体，逐个优化所有解种群，得到所有罚因子个体的评价值，再根据微分进化的思想，对罚因子执行变异、交叉、选择过程，进化罚因子。两类种群如此反复交替优化，直到满足终止条件。算例证明，协进化机制应用于换热网络优化能进一步提高优化效率与精度，也为混合算法选取合适的罚因子优化换热网络提供了一种新思路。
징벌함수법우화유약속환열망락시，벌인자적취치과대강저계산효솔，과소강저우화정도，설치합괄적벌인자치각불용역。기우미분진화산법우화련속변량적계발，채용벌인자협동진화궤제，동보우화벌인자여해변량，응용우환열망락우화문제。협진화궤제우화주요사상여하：건립량류충군，일류위벌인자충군，일류위환열면적충군。우화과정중，매일조환열면적충군용래평개매일개벌인자개체，축개우화소유해충군，득도소유벌인자개체적평개치，재근거미분진화적사상，대벌인자집행변이、교차、선택과정，진화벌인자。량류충군여차반복교체우화，직도만족종지조건。산예증명，협진화궤제응용우환열망락우화능진일보제고우화효솔여정도，야위혼합산법선취합괄적벌인자우화환열망락제공료일충신사로。
Penalty function methods are usually employed to convert constraint problems to unconstraint problems in heat exchanger networks (HENs) optimization. However, it is difficult to set proper penalty factors, since large penalty factors reduce compute efficiency and small ones decrease optimization accuracy. A cooperative mechanism, i.e. a differential evolution algorithm was developed to optimize penalty factor and HENs area variables simultaneously. Two populations are established: penalty factor population and HENs area variable population. Each penalty factor was evaluated by optimizing the corresponding HENs area variable population. The penalty factor was optimized through mutation, crossover, and selection process based on the differential evolution method. These two steps were repeated until the terminal conditions were satisfied. The results demonstrate that the cooperative differential evolution can further improve the optimization efficiency and accuracy, and also provides a new method to select appropriate penalty factors.