Solving planning and scheduling problems for multiple tasks with highly coupled state and temporal constraints is notoriously challenging. An appealing approach to effectively decouple the problem is to judiciously order the events such that decisions can be made over sequences of tasks. As many problems encountered in practice are over-constrained, we must instead find relaxed solutions in which certain requirements are dropped. This motivates a formulation of optimality with respect to the costs of relaxing constraints and the problem of finding an optimal ordering under which this relaxing cost is minimum. In this paper, we present Generalized Conflict-directed Ordering (GCDO), a branch-and-bound ordering method that generates an optimal total order of events by leveraging the generalized conflicts of both inconsistency and suboptimality from sub-solvers for cost estimation and solution space pruning. Due to its ability to reason over generalized conflicts, GCDO is much more efficient in finding high-quality total orders than the previous conflict-directed approach CDITO. We demonstrate this by benchmarking on temporal network configuration problems, which involves managing networks over time and makes necessary tradeoffs between network flows against CDITO and Mixed Integer-Linear Programing (MILP). Our algorithm is able to solve two orders of magnitude more benchmark problems to optimality and twice the problems compared to CDITO and MILP within a runtime limit, respectively.

We study the multi-agent safe control problem where agents should avoid collisions to static obstacles and collisions with each other while reaching their goals. Our core idea is to learn the multi-agent control policy jointly with learning the control barrier functions as safety certificates. We propose a novel joint-learning framework that can be implemented in a decentralized fashion, with generalization guarantees for certain function classes. Such a decentralized framework can adapt to an arbitrarily large number of agents. Building upon this framework, we further improve the scalability by incorporating neural network architectures that are invariant to the quantity and permutation of neighboring agents. In addition, we propose a new spontaneous policy refinement method to further enforce the certificate condition during testing. We provide extensive experiments to demonstrate that our method significantly outperforms other leading multi-agent control approaches in terms of maintaining safety and completing original tasks. Our approach also shows exceptional generalization capability in that the control policy can be trained with 8 agents in one scenario, while being used on other scenarios with up to 1024 agents in complex multi-agent environments and dynamics.

In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy complex hybrid specifications. The ordering problem is thus fundamental to planning. Promising recent works have explored the ordering problem as search, incorporating a special tree structure for efficiency. However, such approaches only reason over partial order specifications. Having observed that an ordering is inconsistent with respect to underlying constraints, prior works do not exploit the tree structure to efficiently generate orderings that resolve the inconsistency. In this paper, we present Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed search method to incrementally and systematically generate event total orders given ordering relations and conflicts returned by sub-solvers. Due to its ability to reason over conflicts, CDITO is much more efficient than Incremental Total Ordering. We demonstrate this by benchmarking on temporal network configuration problems that involve routing network flows and allocating bandwidth resources over time.