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Sponsor: Australian Research Council (Early Career Researcher Award DE160100850); Engineering and Physical Sciences Research Council (EP/M004252/1); Seventh Framework Programme (FP7/2007-2013)Bet-and-run initialisation strategies have been experimentally shown to be beneficial on classical NP-complete problems such as the travelling salesperson problem and minimum vertex cover. We analyse the performance of a bet-and-run restart strategy, where k independent islands run in parallel for t1 iterations, after which the optimisation process continues on only the best-performing island. We define a family of pseudo-Boolean functions, consisting of a plateau and a slope, as an abstraction of real fitness landscapes with promising and deceptive regions. The plateau shows a high fitness, but does not allow for further progression, whereas the slope has a low fitness initially, but does lead to the global optimum. We show that bet-and-run strategies with non-trivial k and t1 are necessary to find the global optimum efficiently. We show that the choice of t1 is linked to properties of the function. Finally, we provide a fixed budget analysis to guide selection of the bet-and-run parameters to maximise expected fitness after t = k * t1 + t2 fitness evaluations

Theoretical results on bet-and-run as an initialisation strategy