A Shared Incumbent Environment for the Minimum Power Broadcasting Problem in Wireless Networks

Abstract. In this study, we consider the minimum power broadcasting problem in wireless actuator networks. We attack the problem with a method - the shared incumbent environment - that executes two algorithms in parallel: a mathematical programming approach and a simulated annealing approach. According to the shared incumbent environment paradigm, when an incumbent solution is found by one method, the other method is notified and profits from the information received. Experimental results show that the shared incumbent environment lead to results which are better than those of the two algorithms combined in it taken singularly. Keywords: Shared incumbent environment, mixed integer linear programming, simulated annealing, matheuristics, minimum power broadcast, wireless networks. 1. Introduction Wireless actuator networks establish communication by using devices called terminals that use omni-directional antennea to send and receive radio signals. The same data can be sent to multiple terminals at the same time, as long as they are within the coverage area of the sender terminal (this is called wireless multicast advantage [1]). Terminals which are outside the coverage area of the sender terminal can still receive the data with the help of intermediate terminals acting as routers [1, 2]. Among the applications of wireless networks, an interesting one is that consisting in commanding from remote the actuators, which are at locations difficult to be reached by people [3]. In such applications, the command is generated in a source terminal and sent to the wireless terminals attached to the actuators. The Minimum Power Broadcast Problem (MPBP) is faced because of the fact that the terminals usually depend on small mobile batteries. This means, there is limited power available for the network. As the coverage area of a terminal increases, the power usage also increases. Therefore, finding a topology where the coverage areas are minimized would decrease the power usage and ensure a longer life span for the network. Thus, MPBP is the problem of finding a topology in which all terminals can receive data from the source terminal, with the total transmission power is minimized [1]. Many different approaches were previously proposed for solving MPBP. Among them are a polynomial-time heuristic called broadcast incremental power algorithm [1] and different approaches based on mixed integer linear programming (MILP) [4, 5]. A