Multiobjectivization of Local Search: Single-Objective Optimization Benefits From Multi-Objective Gradient Descent
This work addresses optimization challenges for algorithms like evolutionary algorithms, offering a novel approach to improve convergence, though it appears incremental as it builds on existing multi-objective methods.
The paper tackles the problem of local optima hindering optimization algorithms by introducing a multi-objective gradient descent method that escapes local traps, providing visual evidence that multiobjectivization can link single-objective local optima in multimodal landscapes.
Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like evolutionary algorithms in convergence to the global optimum. In this paper we present a new concept of gradient descent, which is able to escape local traps. It relies on multiobjectivization of the original problem and applies the recently proposed and here slightly modified multi-objective local search mechanism MOGSA. We use a sophisticated visualization technique for multi-objective problems to prove the working principle of our idea. As such, this work highlights the transfer of new insights from the multi-objective to the single-objective domain and provides first visual evidence that multiobjectivization can link single-objective local optima in multimodal landscapes.