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In many surveillance applications, there are different properties of the environment to check. For example, in the case of robots surveilling an industrial depot, one could be interested in verifying for fire alarms, intrusion alarms or bio-hazards. It is very hard to characterize the solution of this problem in terms of a unique utility function. Indeed, this would require to define a measure of the tradeoff among objectives, which are, by definition, incommensurable quantities. These tradeoffs should be tuned according to contingencies which is, in general, a very difficult task. We present in this paper, an approach to address such issues. We define a multi-robot multi-objective surveillance problem and show how this can be solved by a particular type of heuristic graph search used in the field of multi-objective optimization. The approach has been experimented based on an off-line planner including simulated and real robot plan execution results.