In this paper we propose a computational approach to empirical optimal taxation. We develop and estimate a microeconometric model that is run to simulate household labour supply decisions and the implied economic, fiscal and welfare effects. The microsimulation is embedded into a numerical optimization routine that identifies the tax-transfer rule that maximizes a social welfare function. We consider the class of tax-transfer rules where net available income is computed as a 4th degree polynomial transformation of taxable income plus a transfer. We present the results for six European countries: Germany, France, Italy, Luxembourg, Spain and the United Kingdom. For most values of the inequality aversion parameter k that characterizes the social welfare function, the optimized rules provide a higher social welfare than the current rule, with the exception of Luxembourg. The optimized tax-transfer rules are close to a Flat Tax plus a Universal Basic Income (or equivalently a Negative Income Tax).