The job-shop scheduling problem (JSP) is NP hard, which has very important practical significance. Because of many uncontrollable factors, such as machine delay or human factors, it is difficult to use a single real-number to express the processing and completion time of the jobs. JSP with fuzzy processing time and completion time (FJSP) can model the scheduling more comprehensively, which benefits from the developments of fuzzy sets. Fuzzy relative entropy leads to a method that can evaluate the quality of a feasible solution following the comparison between the actual value and the ideal value (the due date). Therefore, the multiobjective FJSP can be transformed into a single-objective optimization problem and solved by a hybrid adaptive differential evolution (HADE) algorithm. The maximum completion time, the total delay time, and the total energy consumption of jobs will be considered. HADE adopts a mutation strategy based on DE-current-to-best. Its parameters (CR and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> ) are all made adaptive and normally distributed. The new individuals are selected according to the fitness value (FRE) obtained from a population consisting of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> parents and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> children in HADE. The algorithm is analyzed from different viewpoints. As the experimental results demonstrate, the performance of the HADE algorithm is better than those of some other state-of-the-art algorithms (namely, ant colony optimization, artificial bee colony, and particle swarm optimization).
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