In multi-agent collaborative search missions, task allocation is required to determine which agents will perform which tasks. We propose a new approach for decentralized task allocation based on a decentralized genetic algorithm (GA). The approach parallelizes a genetic algorithm across the team of agents, making efficient use of their computational resources. In the proposed approach, the agents continuously search for and share better solutions during task execution. We conducted simulation experiments to compare the decentralized GA approach and several existing approaches. Two objectives were considered: a min-sum objective (minimizing the total distance traveled by all agents) and a min-time objective (minimizing the time to visit all locations of interest). The results showed that the decentralized GA approach yielded task allocations that were better on the min-time objective than those created by existing approaches and solutions that were reasonable on the min-sum objective. The decentralized GA improved min-time performance by an average of 5.6% on the larger instances. The results indicate that decentralized evolutionary approaches have a strong potential for solving the decentralized task allocation problem.