This paper explores using metaheuristic algorithms for single-criteria optimisation problems (SCOP) and multi-criteria optimisation problems (MCOP). It highlights the critical differences between these types, noting that SCOP focusses on a single objective while MCOP deals with conflicting goals. We applied metaheuristic algorithms inspired by natural phenomena to both problem types and provided a table comparing generic algorithms with problem-specific adaptations (PSAs), including their applications. A case study customised a contemporary algorithm for the Traveling Salesman Problem (TSP) using Genetic Algorithms (GA). At the same time, another examined the differences between generic algorithms and PSAs in a multi-criteria context with the Multi-Objective Knapsack Problem, utilising Multi-Objective Genetic Algorithms (MOGA) and Multi-Objective Particle Swarm Optimisation (MOPSO) alongside their tailored versions. The results indicate that PSAs outperform generic algorithms in SCOPs. The GA for TSP reduced the total journey distance over the generations, indicating progress towards optimal solutions. Similarly, in MCOP, tailored algorithms produced higher quality Pareto fronts, with better average hypervolume values and lower standard deviations than generic alternatives. We also discuss recent advancements and suggest future research directions for enhancing metaheuristic applications in optimisation.