Escaping local optima in a class of multi-agent distributed optimization problems: A boosting function approach

Abstract

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.

Multi-Agent Coverage Control with Energy Depletion and Repletion

“…The mission space is a 60 by 50 rectangular area without obstacles. We consider a team of four agents with initial locations (2,2), (4,4), (6,6) and (8,8). The initial state-ofcharge variables are randomly generated, which are 97%, 48%, 71%, and 46%, respectively.…”

“…These approaches typically result in locally optimal solutions, hence possibly poor performance. To escape such local optima, a boosting function approach is proposed in [8] where the performance is ensured to be improved. Recently, the coverage problem was also approached by exploring the submodularity property [9] of the objective function, and a greedy algorithm is used to guarantee a provable bound relative to the optimal performance [10].…”

Optimal composition of heterogeneous multi-agent teams for coverage problems with performance bound guarantees

“…Taking all the aforementioned performance bounds L C , L T , L P and L G defined respectively in (17), (19), (21), and (23), into account, an overall performance bound L satisfying (16) can be established as…”

A submodularity-based approach for multi-agent optimal coverage problems

“…Some widely used on-line methods, such as distributed gradientbased algorithms [2], [6], [7] and Voronoi-partition-based algorithms [5], [8], [9], typically result in locally optimal solutions, hence possibly poor performance. To escape such local optima, a "boosting function" approach is proposed in [10] whose performance can be ensured to be no less than that of these local optima. Alternatively, a "ladybug exploration" strategy is applied to an adaptive controller This work was supported in part by NSF under grants ECCS-1509084 and IIP-1430145, by AFOSR under grant FA9550-12-1-0113, and by the MathWorks.…”

“…Another contribution of the paper is to add a final step to the optimal coverage process, after obtaining the greedy algorithm solution and evaluating the associated lower bound with respect to the global optimum. Specifically, we relax the set of allowable agent positions in the mission space from the imposed discrete set and use the solution of the greedy algorithm as an initial condition for the distributed gradient-based algorithm in [10]. We refer to this as the Greedy-Gradient Algorithm (GGA) which is applicable to the original coverage problem.…”