Avoiding Redundant Restarts in Multimodal Global Optimization

Naïve restarts of global optimization solvers when operating on multimodal search landscapes may resemble the Coupon’s Collector Problem, with a potential to waste significant function evaluations budget on revisiting the same basins of attractions. In this paper, we assess the degree to which such ``duplicate restarts’’ occur on standard multimodal benchmark functions, which defines the $\mathit{\text{redundancy}}\mathit{\text{potential}}$ of each particular landscape. We then propose a repelling mechanism to avoid such wasted restarts with the CMA-ES and investigate its efficacy on test cases with high redundancy potential compared to the standard restart mechanism.