When　evaluating　2-way　constrained　covering　arrays,　the　minimum　sizes　given　by　the　existing　methods　are　too　large　because　the　constraints　are　ignored.　In　order　to　obtain　more　accurate　minimum　sizes　of　2-way　constrained　covering　arrays　and　evaluate　the　2-way　constrained　covering　arrays　generated　by　existing　algorithms,　a　forbidden　edge　decomposing　method　was　proposed　to　promote　lower　bounds　of　the　minimum　sizes　of　2-way　constrained　covering　arrays　in　this　study.　The　graphs　that　describe　the　input　configurations　of　the　systems　under　test　were　decomposed　into　two　subgraphs.　Through　calculating　the　sizes　of　the　sub　constrained　covering　arrays　which　cover　all　the　vertices　in　the　two　subgraphs　and　the　number　of　the　remaining　value　combinations　to　be　covered,　the　minimum　sizes　of　the　2-way　constrained　covering　arrays　were　promoted　compared　with　the　number　of　the　value　combinations　to　be　covered.　The　lower　bounds　of　the　minimum　sizes　obtained　from　the　proposed　method　were　closer　to　the　real　values.　If　the　sizes　of　the　2-way　constrained　covering　arrays　are　less　than　the　lower　bounds　of　the　minimum　sizes,　then　it　is　impossible　for　them　to　exist.　The　proposed　experimental　method　applied　the　forbidden　edge　decomposing　method　to　the　existing　systems　under　test,　then　obtained　the　lower　bounds　of　the　minimum　sizes　of　2-way　constrained　covering　arrays,　and　compared　the　lower　bounds　of　the　minimum　sizes　with　the　sizes　of　the　2-way　constrained　covering　arrays　given　by　the　generation　algorithms.　The　experimental　results　show　that　the　lower　bounds　of　the　minimum　sizes　given　by　the　forbidden　edge　decomposing　method　can　be　used　to　evaluate　the　2-way　constrained　covering　arrays　generated　by　the　existing　algorithms,　and　are　helpful　to　determine　their　existence.　©　2020,　Editorial　Board　of　Journal　of　Harbin　Institute　of　Technology.　All　right　reserved.