The radio stripe (RS) system is a practical implementation of cell-free mMIMO, in which a set of multi-antenna access points (APs) serves at the same time-frequency resources the user equipment (UE) in the network. The APs are sequentially connected in a stripe, sharing the same fronthaul link to the central processing unit. This work considers an uplink power optimization problem that aims to enhance the network spectral efficiency (SE) by considering two metrics—the max–min fairness and the max–sum rate. We employ a meta-heuristic based on the differential evolution algorithm to solve the bi-objective optimization problem. The SE performances of the full power along with the single-objective and multiple-objective scenarios are analyzed and compared for the optimal sequential linear processing detection scheme. The bi-objective approach is able to unveil the trade-offs to identify solution balancing the SE distribution resulting from the optimization of the max–min fairness and the max–sum rate objective functions.