Multiobjectivization of Local Search: Single-Objective Optimization Benefits From Multi-Objective Gradient Descent

TL;DR

This paper introduces a novel gradient descent method that uses multiobjectivization and multi-objective local search to escape local optima in multimodal optimization problems, bridging insights from multi-objective to single-objective optimization.

Contribution

It presents a new gradient descent approach leveraging multiobjectivization and a modified MOGSA mechanism to improve escape from local optima in multimodal landscapes.

Findings

Visual evidence of linking single-objective local optima via multiobjectivization.

Demonstrates the effectiveness of multi-objectivization in escaping local traps.

Highlights transfer of multi-objective insights to single-objective optimization.

Abstract

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.