A heuristic distributed and no-wait method for solving multiagent task allocation problems with coupled temporal constraints

Abstract

Temporal constraints, primarily arising from engagement rules and requiring tasks to be performed in a specific order, are critical in task allocation problems (TAPs). However, existing allocation methods often fall short of handling temporal constraints. This paper proposes a heuristic distributed and no-wait algorithm, called the Temporal-Constraints Performance Impact (TC-PI) algorithm, for solving multi-agent TAPs with temporal constraints. By requiring each agent either travels to or immediately executes its assigned task, the TC-PI eliminates unnecessary waiting time and effectively reduces the average task completion time. The proposed algorithm consists of three phases. Firstly, each agent sequentially adds tasks to its task list while ensuring temporal constraints are satisfied. Secondly, conflicts where multiple agents select the same task are resolved through local communication. Finally, any remaining conflicts caused by temporal constraints are further addressed. To maintain task order and minimize completion time, task significance is redefined by incorporating temporal relationships among tasks. A penalty mechanism prevents infinite task reallocation cycles, enhancing system robustness and avoiding deadlocks. Simulation results demonstrate that TC-PI effectively resolves temporal conflicts, achieves no-wait task allocations, and flexibly handles dynamic task arrivals.