Intelligent Service Robotics https://doi.org/10.1007/s11370-019-00291-w ORIGINAL RESEARCH PAPER FA–QABC–MRTA: a solution for solving the multi-robot task allocation problem Farouq Zitouni 1 · Ramdane Maamri 2 · Saad Harous 3 Received: 21 July 2018 / Accepted: 26 August 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract The problem of task allocation in a multi-robot system is the situation where we have a set of tasks and a number of robots; then each task is assigned to the appropriate robots with the aim of optimizing some criteria subject to constraints, e.g., allocate the maximum number of tasks. We propose an effective solution to address this problem. It implements a two-stage methodology: first, a global allocation based of the well-known firefly algorithm, and then, a local allocation combining advantages of quantum genetic algorithms and artificial bee colony optimization. We compared our proposed solution to one solution from the state of the art. The simulation results show that our scheme significantly performs better than this solution. Our solution allocated 100% of the tasks (in every configuration tried in the experiments) and enhanced the allocation time by 75%. Keywords Multi-robot system · Task allocation · Firefly algorithm · Artificial bee colony optimization · Quantum genetic algorithms 1 Introduction Nowadays, multi-robot systems (MRS) are almost in every aspect of our daily lives, and intensive research is being done to achieve their opportunities. The main motivation behind such attention is because they make it easy to solve many complex problems, such as industrial applications, surveil- lance, and rescue missions in environments hit by natural disasters [11]. Also, it must be mentioned that the design of a MRS must consider interactions between its components—i.e., robots; otherwise, it risks to produce a system with limited and non- B Farouq Zitouni farouq.zitouni@univ-constantine2.dz Ramdane Maamri ramdane.maamri@univ-constantine2.dz Saad Harous harous@uaeu.ac.ae 1 Department of Computer Science, Kasdi Merbah University, Ouargla, Algeria 2 Department of Computer Science, Constantine 2 - Abdelhamid Mehri University, Constantine, Algeria 3 Department of Computer Science, UAE University, Abu Dhabi, United Arab Emirates deterministic performance [10]. Thereby, one of the major coordination problems that researchers must solve in this field is the task allocation—named multi-robot task alloca- tion (MRTA) [9]. In the next section, we define the MRTA problem. 1.1 Definition of the MRTA problem The MRTA problem can be defined as follows: We assume that we have some tasks to be performed and robots that are capable of achieving these tasks. Consider tasks to be allocated, which robots are adequate to execute them. These assignments must optimize the criterion taken into account, e.g., minimize completion time or makespan. So, the goal is to coordinate robots’ behaviors and find an optimal way to allocate all tasks [15]. The basic mathematical formulation of this problem is described in Table 1 [27]. Also, other constraints may be considered, e.g., spatial, energetic, and temporal. In linear programming, this formu- lation is called assignment problem—can be easily solved using a suitable algorithm, e.g., Hungarian method. Gener- ally, exact methods do not capture constraints imposed by real-life problems, and hence, there is a need to rethink them for the treatment of complex cases. 123