Escaping Local Optima in a Class of Multi-Agent Distributed Optimization Problems: A Boosting Function Approach

TL;DR

This paper introduces a systematic boosting function method to help multi-agent systems escape local optima in nonlinear, nonconvex coverage control problems, improving solution quality without guarantees of global optimality.

Contribution

It proposes a novel boosting function approach that exploits the problem structure to escape local optima in distributed multi-agent optimization tasks.

Findings

Boosting functions improve coverage solutions in simulations.

The method ensures non-degradation of the objective function after boosting.

Different families of boosting functions are analyzed for effectiveness.

Abstract

We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic approach for escaping a local optimum, rather than randomly perturbing controllable variables away from it. We show that the objective function for these problems can be decomposed to facilitate the evaluation of the local partial derivative of each node in the system and to provide insights into its structure. This structure is exploited by defining "boosting functions" applied to the aforementioned local partial derivative at an equilibrium point where its value is zero so as to transform it in a way that induces nodes to explore poorly covered areas of the mission space until a new equilibrium point is reached. The proposed boosting process ensures that, at its conclusion, the objective function is no worse than its pre-boosting value. However, the global optima cannot be guaranteed. We define three families of boosting functions with different properties and provide simulation results illustrating how this approach improves the solutions obtained for this class of distributed optimization problems.