Avoiding Redundant Restarts in Multimodal Global Optimization

Naïve restarts of global optimization solvers when operating on multimodalsearch landscapes may resemble the Coupon's Collector Problem, with a potentialto waste significant function evaluations budget on revisiting the same basinsof attractions. In this paper, we assess the degree to which such “duplicaterestarts” occur on standard multimodal benchmark functions, which defines theredundancy potential of each particular landscape. We then propose arepelling mechanism to avoid such wasted restarts with the CMA-ES andinvestigate its efficacy on test cases with high redundancy potential comparedto the standard restart mechanism.