In　the　vehicle　routing　problem,　the　uncertainty　of　delivery　time　and　customer　expectation　time　greatly　affects　the　selection　of　the　delivery　route　and　the　customer　service　level.　Therefore,　the　traditional　vehicle　routing　optimization　model　and　algorithm　with　time　windows　are　no　longer　applicable.　The　author　uses　the　travel　budget　time　formula　to　generate　a　grey　time　window　for　vehicle　distribution,　and　uses　a　probability　density　function　to　whiten　the　Grey　Delivery　Time,　uses　a　fuzzy　gradient　function　to　represent　customer　satisfaction,　and　builds　a　multi-depot　with　maximum　customer　satisfaction　and　minimum　cost　as　the　goal.　In　the　process　of　solving　the　model,　the　classical　quantum　evolutionary　algorithm　has　a　problem　of　a　large　amount　of　effective　information　being　lost　in　the　mapping　processing　between　the　quantum　domain,　the　binary　domain,　and　the　problem　domain.　The　author　puts　forward　the　concept　of　a　quantum　cell　body　and　operation　method　of　qubit　alignment　and　constructs　a　new　quantum　evolution　algorithm　to　solve　the　model.　The　author　conducts　experiments　through　specific　examples　to　verify　the　correctness　of　the　model　and　the　effectiveness　of　the　algorithm.