Effectively　utilizing　biological　firing　rate　data　to　estimate　the　numerous　connection　weights　in　the　mouse　primary　visual　cortex　(V1)　model　from　the　Allen　Institute　is　a　challenging　task.　The　existing　iterative　grid-search　algorithm　cannot　enable　the　mouse　V1　model　to　better　fit　the　biological　firing　rate　data.　To　tackle　this　issue,　we　propose　an　excitation-inhibition　balanced　adaptive　sequential　neural　posterior　estimation　(E/I　balanced　ASNPE)　approach　to　accurately　infer　the　connection　weights　of　the　mouse　V1　model,　allowing　the　neurons＇　firing　rates　to　converge　to　the　given　biological　data.　This　method　fully　leverages　the　structural　information　of　the　mouse　V1　model,　reducing　the　dimensionality　of　the　weight　parameters　to　be　optimized.　Initially,　sampling　is　performed　in　the　prior　distribution　based　on　the　proposed　non-dominated　sorting　adaptive　genetic　algorithm　(NSAGA).　This　algorithm　optimizes　the　sorting,　crossover　and　mutation　processes　based　on　the　fitness　scores　of　the　current　samples　and　updates　the　proposal　distribution　based　on　these　samples,　increasing　the　likelihood　of　identifying　high　posterior　probability　regions　in　the　prior　distribution.　To　avoid　bad　simulations,　we　also　explore　the　E/I　balance　in　each　layer　of　the　mouse　V1　model,　adding　biological　constraints　during　weight　inference　with　Automatic　Posterior　Transformation　(APT).　Experimental　results　confirm　that　the　proposed　E/I　balanced　ASNPE　method　significantly　outperforms　the　baseline　in　all　five　firing　rate　fitness　scores　in　the　mouse　V1　model.　This　study　is　pioneering　in　applying　non-dominated　sorting　genetic　algorithms　combined　with　sequential　neural　posterior　estimation　to　optimize　connection　weights　in　large-scale　complex　biological　models.　©　2024　IEEE.