In this paper, we propose a population-based implementation of simulated annealing to tackle multi-objective optimisation problems, in particular those of combinatorial nature. The proposed algorithm is called Evolutionary Multi-objective Simulated Annealing Algorithm (EMOSA), which combines local and evolutionary search by incorporating two distinctive features. The first feature is to tune the weight vectors of scalarizing functions (i.e., search directions) for selection during local search using a two-phase strategy. The second feature is the competition between members of the current population with similar weight vectors. We compare the proposed algorithm to three other multi-objective simulated annealing algorithms and also to the Pareto archived evolutionary strategy (PAES). Experiments are carried out on a set of bi-objective travelling salesman problem (TSP) instances with convex or nonconvex Pareto-optimal fronts. Our experimental results demonstrate that the two-phase tuning of weight vectors and the competition between individuals make a significant contribution to the improved performance of EMOSA.