To increase the efficiency of Concentrated Solar Power (CSP) plants, the use of optimization methods is a current topic of research. This paper focuses on applying an integrated optimization technology to a solar thermal application, more specifically for the optimization of a trapezoidal cavity absorber of an LFR (Linear Fresnel Reflector), also called a Linear Fresnel Collector (LFC), CSP plant. LFR technology has been developed since the 1960s, and while large improvements in efficiencies have been made, there is still room for improvement. Once such area is in the receiver design where the optimal cavity shape, coatings, insulation thickness, absorber pipe selection, layout and spacing always need to be determined for a specific application. This paper uses a commercial tool to find an optimal design for a set of operating conditions. The objective functions that are used to judge the performance of a 2-D cavity are the combined heat loss through convection, conduction and radiation, as well as a wind resistance area. In this paper the effect of absorbed irradiation is introduced in the form of an outer surface of pipe temperature. Seven geometrical parameters are used as design variables. Based on a sample set requiring 79 CFD simulations, a global utopia point is found that minimizes both objectives. The most sensitive parameters were found to be the top insulation thickness and the cavity depth. Based on the results, the Multi-Objective Genetic Algorithm (MOGA) as contained in ANSYS DesignXplorer is shown to be effective in finding candidate optimal designs as well as the utopia point.