Kevin Smith, Jonathan Fieldsend and Richard Everson

Multi-objective optimisation and algorithms to locate the Pareto front, which describes the trade-off between the objectives have been receiving a lot of attention.

Simulated annealing is a provably convergent optimiser for single-objective problems. Previously proposed multi-objective extensions have mostly taken the form of a single-objective simulated annealer optimising a composite function of the objectives. In this project investigate a multi-objective simulated annealer 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.

In the paper Dominance-Based Multi-Objective Simulated Annealing (to appear) we illustrate the simulated annealer's performance on a suite of standard test problems and provide comparisons with another multi-objective simulated annealer and the NSGA-II genetic algorithm. The new simulated annealer is shown to promote rapid convergence to the true Pareto front with a good coverage of solutions across it comparing favourably with the other algorithms. The picture at the top of the page shows an estimated front for the DTLZ3 test problem. The picture at the bottom shows samples from a 3-dimensional attainment surface generated from points marked in red; the attainment surface is used in the estimation of the energy function to drive simulated annealing.

Provided below are the final archives produced in the experiments on the DTLZ test problems in this paper.

• DTLZ 1-7 reference results.

This tarball includes the objective results for each of the test problems DTLZ1-7. The files are named mosa-X-Y.txt, where X is the name of the problem (e.g. dtlz1) and Y is the run number (20 runs for each problem are provided).

The results are whitespace separated, one solution per line, suitable for immediate import into matlab or gnuplot

More details on this and on the relation between greedy multi-objective algorithms and exploratory multi-objective algorithms in Kevin Smith's thesis A Study of Simulated Annealing Techniques for Multi-Ob jective Optimisation.