In the noisy intermediate-scale quantum (NISQ)-era, quantum computers (QC) are highly prone to noise-related errors and suffer from limited connectivity between their physical qubits. Circuit transformations must be made to abstract circuits to address the noise and hardware constraints of NISQ-era devices. Such transformations introduce additional gates to the original circuit, thereby reducing the circuit's overall fidelity. To address the aforementioned constraints of NISQ-era QCs, dynamic remapping procedures permute logical qubits about physical qubits of the device to increase the fidelity of operations and make operations hardware-compliant. The quantum layout problem (QLP) is the problem of mapping logical qubits of the circuit to physical qubits of the target QC in a way that maximizes circuit fidelity and satisfies all device connectivity constraints. This research effort seeks to use metaheuristic algorithms to find high-quality solutions to the QLP. In this work, the QLP is mathematically modeled, integrated into various optimization algorithm domains, and resultant algorithms evaluated for efficiency and effectiveness. Moreover, fitness landscape analysis is performed based on the devised representation, objective functions, and search operators.