Performance analysis and multi-objective optimization based on finite-time thermodynamics are conducted in this paper for an absorption heat pump operating between four temperature levels. The exergy-based ecological (E), the exergetic performance (EPC) and the thermo-economic (F) criteria were considered as the objective functions. The maxima of the three objective functions and the corresponding optimal conditions were obtained by applying the flowchart optimization methodology. The influences of some design factors such as the economic indicators, internal irreversibility parameters, heat-transfer coefficients of heat exchangers and the distribution ratio rate of the total heat-reject quantity between the absorber and the condenser on the maxima of the exergy-based ecological (E), the exergetic performance (EPC) and the thermo-economic (F) objective functions and the corresponding optimal parameters have been analyzed and discussed. The results show that: (i) Materials with a low heat-transfer coefficient significantly affect the performance of the system. (ii) The detrimental effects of internal irreversibilities depend on the order of magnitude of the optimal heat-transfer rates in the absorber and the condenser. Finally, (iii) the optimum performance has been obtained for certain values of the heat exchange surface area and the exergy input rate from an economic point of view.