Deep　belief　network　(DBN)　is　an　effective　deep　learning　model,　which　can　learn　the　complex　data　by　extracting　features　hierarchically.　However,　the　successful　application　of　DBN　depends　on　the　suitable　size　of　the　structure　(the　number　of　hidden　neurons),　which　is　still　an　open　problem.　Currently,　the　network　structure　size　is　basically　determined　by　experience　with　a　time-consuming　process.　In　this　article,　a　complexity-based　structural　optimization　(CBSO)　algorithm,　based　on　multiobjective　ordinal　optimization　(MOO),　is　developed　for　designing　the　DBN　structure.　First,　the　problem　formulation　of　structural　optimization　of　DBN　is　given,　where　the　multiple　objectives　are　to　minimize　the　fitting　error　and　complexity.　Second,　the　lower　bound　for　alignment　probability　in　optimizing　DBN　structure　is　developed　according　to　MOO.　Finally,　an　effective　method　to　maximize　the　probability　of　correct　select　is　given　to　pursue　the　good　tradeoff　between　the　complexity　and　the　performance.　The　performance　of　proposed　CBSO　algorithm　is　demonstrated　via　predicting　and　controlling　water　quality　of　wastewater　treatment　process　(WWTP)　using　the　CBSO-DBN-based　model　predictive　control　(MPC)　strategy.　The　simulation　results　show　that　the　resulting　CBSO-DBN　can　find　the　better　structure　design　by　using　CBSO　algorithm　with　smaller　fitting　error　and　limited　computational　complexity,　and　thereby　achieve　the　better　performance　in　WWTP　than　its　peers.　Especially,　the　CBSO-DBN-MPC　improves　the　control　accuracy　by　76.16%　and　computational　complexity　by　50.45%,　respectively.　IEEE