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 redundancy 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.