The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.
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