In this work, we evaluate the application of four different metaheuristic optimisation algorithms for solving the channel assignment problem in a multi-radio multi-channel Wireless Mesh Network (WMN) using Dynamic Spectrum Access (DSA). The work advances a near optimal channel assignment in a WMN that uses DSA by applying soft computing methods. While CA in a WMN is wellstudied, and CA for secondary user cognitive radio networks has also been studied in the literature, CA for our specific scenario of an infrastructure DSA-WMN is novel. This scenario poses new challenges because nodes are spread out geographically and so may have different allowed channels and experience different levels of external interference in different channels. A solution must meet two conflicting requirements simultaneously: 1) to avoid interference within the network and with external interference sources, and 2) maintain connectivity within the network; all while staying within the radio interface constraint, i.e., only assigning as many channels to a node as it has radios. Our method is unique in that it is protocol-agnostic, being able to avoid interference from external sources that use different protocols and standards. We present a novel algorithm, used alongside the metaheuristic optimisation algorithms, which ensures the feasibility of solutions in the search space. Average Signal to Interference and Noise Ratio (SIN R) over the network is used as the performance measure, with the goal of optimisation being to find the highest average SIN R. This is a more realistic performance measure than the binary on/off conflict-based measures most common in the literature. Our energy-based method also has the unique advantage that it is protocol-agnostic, being able to avoid interference from external sources that use different protocols and standards. The algorithms that are compared in this work are Simulated Annealing (SA), the Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and Differential Evolution (DE). These algorithms were evaluated through the use of simulation in Network Simulator 3. Various parameters were experimented with for each of the employed algorithms. The resultant best set of parameters was used for the comparison of the four metaheuristic algorithms. It was found that the population-based algorithms (PSO, GA, and DE) all perform satisfactorily for this problem, although DE is superior to the others. SA can give acceptable solutions, but performs poorly in comparison to the population-based algorithms. The paper also considers the computational complexity of the methods. It is found that SA and DE perform well in this regard.