The cellular downlink power and rate control problems are considered in this thesis. Many studies have extensively examined this topic, but most of them have focused on single-objective (SO) approaches for resource allocation.
In a real-world scenario, multiple objectives naturally occur, and often conflict with one another. In such a case, the globally optimal solution may not exist. Therefore, the strategy is to provide the base station (BS) or service provider with several Pareto optimal solutions for power and rate assignment, and the BS can select one according to its own preference. To this end, a multi-objective (MO) approach is proposed in this study. For the downlink resource allocation, the BS desires the revenue obtained from the mobile stations (MSs) or users to be maximized, while keeping the total network utility as large as possible. However, the total power resource is constrained and the allocated data rates to MSs are upper bounded by the
channel capacity. In this thesis, the resource allocation problem is first formulated as a constrained MO problem (MOP), and then transformed into an MOP with only box constraints, which can be solved by the existing multiobjective evolutionary algorithms (MOEAs). A careful design is proposed to provide good initial setting for the employed MOEA. Related analysis has been carried out to examine some interesting properties of the problem, and
the numerical simulation has been given to verify the proposed MO approach.

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