## 2 Related Work  
This section presents a review of some of the existing MIP algorithms. It is noted that MIP algorithms can be classified into homogeneous networks with one sink [16; 17; 18; 19; 20; 21], and heterogeneous networks with multiple sinks [22] (based on network topologies). The majority of the existing MIP algorithms are based on the homogeneous network. As such, the works studied in this paper are centered around the homogeneous networks, where the itinerary of each MA is static and predetermined at the sink. The near-optimal itinerary design (NOID) algorithm [21] was proposed to find the optimal number of MAs in MIP. This algorithm iteratively groups the sensor nodes in the network to separate sub-trees that are connected progressively to the processing element (PE) or sink. After NOID finishes constructing sub-trees, the sink dispatched one MA to each sub-tree. An enhanced version of the NOID algorithm termed the second near-optimal itinerary design (SNOID) algorithm was proposed in [23]. SNOID differs from NOID by considering the nodes' communication cost when constructing the MA itinerary. The number of MAs in SNOID is determined by partitioning the area around the sink into concentric zones. The nodes lying within the radius of the first zone around the sink will be the starting points of each itinerary. The first zone radius can be obtained by \(ar_{max}\), where \(a\) is an input parameter in the range [0, 1] and \(r_{max}\) is the maximum transmission range of any sensor node. Each MA itinerary starts from the zones close to the sink and extends to the outer zones. Similarly, a meta-heuristic method called iterated local search (ILS) was further proposed in [24]. This algorithm is like the other tree-based MIP algorithms (NOID and SNOID), but it differs in considering the increase in MA's packet size as well as the energy consumption due to migration over intermediate nodes when it constructs the MA itinerary. Although tree-based MIP algorithms perform better than SIP algorithms, the itinerary of the MA consumes extra energy due to the reverse routes that the MA take--especially when there are a huge amount of branches. The central location-based MIP (CL-MIP) algorithm was proposed by [16], where the determination of the optimal number of MAs in MIP can be divided into four parts; (1) Visiting central location (VCL) selection algorithm, (2) Source grouping algorithm, (3) Determining the source-visiting order using SIP algorithms, (4) Iterative algorithm to ensure that all source nodes have been assigned to their MAs. The main idea of VCL algorithm is to calculate the source nodes density by the distribution of an impact factor among the source nodes. So, if \(n\) represents the number of source nodes, then each source node will receive (\(n-1\)) impact factor from others, and one from itself. Then, the location of the source node with the largest accumulated impact factor will be selected as a VCL (the density of the source nodes). After selecting the VCL, all the source nodes within the radius of VCL are grouped together and assigned to an MA. By using the iterative algorithm, the above process is repeated until all the remaining source nodes are grouped and assigned to the MAs. Finally, each itinerary is determined by using one of the SIP algorithms. Nevertheless, CL-MIP algorithm assumes a cluster-based approach,where the source nodes are arranged geographically and distributed in several clusters. This limits the use of the algorithm when the sensor nodes are sparsely deployed. Moreover, CL-MIP algorithm can result in source nodes isolation (few source nodes are located together) and then assigned a new itinerary. This would lead to an increase in energy consumption, especially when the isolated source nodes are located far from the sink. Motivated by the need to determine the optimal number of MAs in MIP, a directional source grouping-based MIP (DSG-MIP) algorithm was proposed in [20].