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A Bayesian Approach to Multiobjective Optimisation

2009; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-90-481-3080-1_16

1876-1119

Paolo Di Barba,

Evolutionary Algorithms and Applications

Evolutionary, genetic and migratory algorithms, often employed in multiobjective problems, are powerful, but affected by some inherent limits, the most evident of which is the absence of theoretical proofs of convergence. In a sense, the only results concern numerical convergence and are stated in terms of a non-zero probability to converge in an infinite runtime. In other words, the convergence condition is the tested incapability of a given algorithm to improve the current population of solutions significantly, during a long enough time interval: this means, in general, that a local front has been reached. On one hand, in fact, no certainty about convergence can be obtained unless an extensive exploration of the search space is achieved, what is unpractical for large discrete spaces and definitely impossible for continuous spaces. On the other hand, however, no information is given about the probability that the local front reached is the global one; the solution is simply to be trusted as the best one reachable by the particular instance of the algorithm implemented. Neglecting this intrinsic limitation is generated by some blind trust in non-deterministic methods, together with (and favoured by) the common lack of knowledge about their heuristics and the unavailability of proper controls on them. The consequences are even of cultural order, because it is commonly accepted that no a priori measure of validity is given about the solution found, which is consequently assumed as the good one. Thus, the search for real convergence is abandoned, swapping the concept of optimisation with the concept of improvement.