In this paper, the topic of constrained multiobjective in-core fuel management optimisation (MICFMO) using metaheuristics is considered. Several modern and state-of-the-art metaheuristics from different classes, including evolutionary algorithms, local search algorithms, swarm intelligence algorithms, a probabilistic model-based algorithm and a harmony search algorithm, are compared in order to determine which approach is the most suitable in the context of constrained MICFMO. A test suite of 16 optimisation problem instances, based on the SAFARI-1 nuclear research reactor, has been established for the comparative study. The suite is partitioned into three classes, each consisting of problem instances having a different number of objectives, but subject to the same stringent constraint set. The effectiveness of a multiplicative penalty function constraint handling technique is also compared with the constrained-domination technique from the literature. The different optimisation approaches are compared in a nonparametric statistical analysis. The analysis reveals that multiplicative penalty function constraint handling is a competitive alternative to constrained-domination, and seems to be particularly effective in the context of bi-objective optimisation problems. In terms of the metaheuristic solution comparison, it is found that the nondominated sorting genetic algorithm II (NSGA-II), the Pareto ant colony optimisation (P-ACO) algorithm and the multiobjective optimisation using cross-entropy method (MOOCEM) are generally the best-performing metaheuristics across all three problem classes, along with the multiobjective variable neighbourhood search (MOVNS) in the bi-objective problem class. Furthermore, the practical relevance of the metaheuristic results is demonstrated by comparing the solutions thus obtained to the current SAFARI-1 reload configuration design approach.