*7.2. Task Allocation Problem*

Concerning the tasks-to-robots distribution algorithm, all previous proposals explicitly avoid the combinatorial blow-up of allocation complexity using different heuristics. Nevertheless, heuristic-based approaches make assumptions that cannot be verified at all times. In consequence, when the heuristic fails the robots choose suboptimal distributions.

Taking into account this limitation and since the number of possible distributions depends on both the number of available tasks and the number of robots making a decision, the proposal presented here computes optimal distributions based on more general assumptions such as: (i) Robots can implicitly coordinate their actions; (ii) Asynchronism may keep the number of simultaneous decision making at small values; (iii) Pruning the furthest tasks (out of the scope defined by the human operator –*HO-Threshold*) does not prevent the computation of optimal tasks-to-robots distribution.
