Evaluating the Efficiency of Robust Team Formation Algorithms

Abstract

Selecting a minimal-cost team from a set of agents, with associated costs, to complete a given set of tasks is a common and important multiagent systems problem. Some degree of fault-tolerance in such teams is often required which enables the team to continue to complete all tasks even if a subset of the agents are incapacitated. A ${k}$-robust team is one that is capable of completing all assigned tasks when any ${k}$ team members are not available. The corresponding decision problem of selecting a ${k}$-robust team that costs no more than a desired cost threshold has been shown to be NP-Complete. We present and experimentally evaluate, for varying problem sizes and characteristics, heuristic and evolutionary approximation approaches to find optimal-cost ${k}$-robust teams which can be used for large problems. We present a Linear Programming approximation algorithm that produces optimal results for small problem sizes and prove that it is a $2\ln (m+k)+O(\ln m)$-factor approximation of the optimal solution, where m is the number of tasks to be completed. We also present three heuristic algorithms and an evolutionary computation approach which scales up to larger problems. Another advantage of the evolutionary scheme is that it can approximate the Pareto-frontier of teams trading off robustness and cost.