OptiBridge: Multi-Scale Multi-Shift Bridging for Conditioning Optimization Landscapes

This paper introduces OptiBridge, a novel optimization framework designed to tackle the challenges of complex, nonconvex landscapes that contain numerous local optima, as often encountered in NP-hard problems. OptiBridge employs a multi-scale, multi-shift strategy to enlarge the attraction basins of high-quality local minima while simultaneously reducing the influence of their low-quality counterparts. In doing so, it enhances the effectiveness of standard local optimization methods, such as gradient-based first-order algorithms. Through a series of experiments on benchmark nonconvex test functions, we demonstrate that OptiBridge consistently improves the performance of local optimizers.