Dominance measures for multi-objective simulated annealing

Simulated annealing (SA) is a provably convergent optimiser for single-objective (SO) problems. Previously proposed MO extensions have mostly taken the form of an SO SA optimising a composite function of the objectives. We propose an MO SA utilising the relative dominance of a solution as the system energy for optimisation, eliminating problems associated with composite objective functions. We also propose a method for choosing perturbation scalings promoting search both towards and across the Pareto front. We illustrate the SA´s performance on standard test problems. The new SA is shown to promote rapid convergence to the true Pareto front with a good coverage of points across it.