## 1 Introduction  
Robotic networks get more and more proliferation in industrial and scientific applications. Robotics network attracts researchers' attention because of its computational, sensing, communications, and movement capabilities. Robotics network is suitable for a wide range of applications where human intervention is limited or denied, such as search and rescue operations, surveillance, logistic, and humanitarian demining. Besides, such networks can lend themselves easily to applications where there are economic benefits such as farming or production line applications. The advantages of using the robotics network including, but are not limited to, the flexibility of modifying the robotics network to match different application scenarios, the robustness of multi-robot systems against failure, and parallelism operation, which leads to time-efficient system [1]. A team of robots can map a specific area and identify unsafe zones. It can allocate tasks either by itself if the robots are equipped with appropriate sensors or with the help of an external system, such as wireless sensor networks (WSN). The task can be carrying goods in a warehouse application, cleaning in a cleaning operation scenario, or finding victims in a surveillance application. In many situations, task locations and requirements are not known beforehand because they emerge as needed in the area. Hence, offline task assignment approaches are not a feasible solution. Therefore, an on-line distributed task allocation approach is required for such dynamic scenarios. Several works have investigated this problem as a multi-objective optimization (MOO) problem and proposed different approaches to solve it including heuristic methods [2; 3; 4; 5; 6; 7; 8]. The existing MRTA approaches can be classified into three major categories: centralized approaches, market-based approaches, and behavior-based approaches. Centralized methods are suitable for a small number of robots in a static environment. They suffer from a single point of failure and high communication overhead, and they respond slowly to local changes [9]. In contrast, fully distributed approaches, such as behavior-based approaches (e.g., [10; 11]), are robust to failures, flexible, and require less computational and communication resources. However, they work on local optimal solutions, which do not necessarily aggregate to produce the globally optimal solution, and thus, they yield suboptimal solutions. Other approaches also include knowledge-based coordination where a set of rules are embedded into the agent that determines its behavior [12]. On the other hand, the market-based/auction-based approach, one of the most popular algorithms of MRTA, is considered to be the mid-point between fully centralized and fully distributed approaches. It works similarly as an auction process in the market, where an auctioneer opens an auction, and then bidders submit their offers, with the auctioneer granting the item to the highest bidder. In the market-based approach, the bid is computed by each robot as a function of its utility in performing a task. There are primarily two common types of auctions: single-task auctions and combinatorial auctions. In a single-task auction, there is one task, and it is granted to the highest bidder. In a combinatorial auction, multiple tasks are offered in one auction, and bidders can bid on any subset of the offered tasks based on the robots' decision. The problem of the single-task approach is that it does not consider the synergy among tasks, which leads to a suboptimal solution. Synergy is a term used to describe the relationship between tasks in terms of their locations [9]. Tasks have positive synergy if the total cost of execution by one robot is less than the total cost if they are executed by more than one robot. In contrast, because the combinatorial auction allows robots to bid on a subset of tasks, robots can bid on tasks that have positive synergy, and thus, it produces a better solution.