On the basis of a four-heat-reservoir endoreversible absorption refrigeration cycle model, another linear heat transfer law [i.e., the heat-flux] is adopted, the fundamental optimal relation between the coefficient of performance (COP) and the cooling load, as well as the maximum cooling load and the corresponding COP of the cycle coupled to constant-temperature heat reservoirs are derived by using finite-time thermodynamics or thermodynamic optimization. The optimal distribution of the heat-transfer surface areas is also obtained. Moreover, the effects of the cycle parameters on the COP and the cooling load of the cycle are studied by detailed numerical examples. The results obtained herein are of importance to the optimal design and performance improvement of an absorption refrigeration cycle.